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Question: Asexual, sexual, budding, and parthenogenesis are all forms of what?
Choices:
A. hibernation
B. reproduction
C. photosynthesis
D. absorption
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Asexual, sexual, budding, and parthenogenesis are all forms of reproduction. Reproduction is a process that creates new organisms from existing ones. Some forms, like asexual reproduction, result from damage to the original animal. Other forms, like budding, are useful to animals with little mobility that reproduce sexually. Genetically unique individuals are produced through reproduction. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
The profit earned by selling an article for Rs.753 is equal to the loss incurred when the same article is sold for Rs.455.What should be the sale price for making 50% profit ?
A)706
B)786
C)906
D)896
E)696First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Let C.P =Rs. x
Then as given, (753 - x ) = (x - 455) 2x = 1208 x = 604
There fore S.P= 150% of 604 => Rs. = Rs.906
ANSWER:C | deepmind/aqua_rat |
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
A)1/3
B)2/5
C)2/7
D)3/5
E)4/7First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A | deepmind/aqua_rat |
Question: What do you call the traits that allow a plant, animal, or other organism to survive and reproduce in its environment?
Choices:
A. adaptations
B. additions
C. settings
D. advantages
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Survival may include getting food, building homes, and attracting mates. Traits that allow a plant, animal, or other organism to survive and reproduce in its environment are called adaptations. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 140 m length?
A)82.1 sec.
B)12.5 sec
C)19.1 sec.
D)17.1 sec.
E)42.1 sec.First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 140 = 250 m.
Required time = 250/20 = 12.5 sec.
Answer: B | deepmind/aqua_rat |
Carmelo and LeBron participate in a six-person footrace on the basketball court during All-Star Weekend. If all six contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
A)5040
B)2520
C)360
D)120
E)42First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: 6! = 720
720/2=360 half the time carmelo is in front, vice versa
Answer:
(C) 360 | deepmind/aqua_rat |
Sam purchased 20 dozens of shirts at the rate of $ 375 per dozen. He sold each one of them at the rate of $ 33. What was his percentage profit?
A)5%
B)4.8%
C)5.6%
D)8.2%
E)6%First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: C
5.6%
C.P. of 1 shirt = 375/12 = $ 31.25
S.P of 1 shirt = $ 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6% | deepmind/aqua_rat |
A Flask contains a mixture of AB in the ratio 5:2. When 20 L of Mixture is replaced with liquid B, ratio becomes 4:1. How many liters of liquid A was present in mixture initially.
A)10
B)22
C)15
D)30
E)8First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Let the volume of the initial total mixture was V. When 20L of mixture is removed the volume becomes (V - 20). The concentration stays 5:2.
Next step, when you add 20 litres of B, the amount of A does not change.
So
Amount of A in original mix = Amount of A in final mix
C1 * V1 = C2 * V2
(5/7)*(V - 20) = (4/5)*V
V = 30.8
So volume of A in initial mixture was (5/7) * 30.8 = 22 litres
Answer B | deepmind/aqua_rat |
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m
95 cm is
A)16cm
B)25cm
C)15cm
D)35cm
E)45cmFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Answer: Option D | deepmind/aqua_rat |
Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is
A)2 : 3
B)4 : 3
C)6 : 7
D)9 : 8
E)5 : 4First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √25 : √16
= 5 : 4.
Answer E | deepmind/aqua_rat |
If both 5^2 and 3^3 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
A)49
B)75
C)150
D)225
E)343First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: The number a must include at least 3*5^2 = 75
The answer is B. | deepmind/aqua_rat |
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 9800 envelopes.
A)2
B)3
C)4
D)6
E)7First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 9800 envelopes B will take 9800/1400 hrs = 7 hrs
So the answer is choice E | deepmind/aqua_rat |
The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
A)6
B)9
C)8
D)2
E)3First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81
= 9
Answer:B | deepmind/aqua_rat |
What will be the reminder when (27^27+27) is divided by 28?
A)92
B)43
C)71
D)26
E)31First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: (x^n+1) will be divisible by (x+1) only when n is odd;
(27^27+1) will be divisible by (27+1);
(27^27+1)+26 when divided by 28 will give 26 as remainder.
Correct Option : D | deepmind/aqua_rat |
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
A)5
B)2
C)3
D)4
E)6First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
ANSWER E | deepmind/aqua_rat |
Question: When is the sun directly over the equator?
Choices:
A. Fall
B. Winter
C. Midsummer
D. equinox
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Solstice refers to the position of the Sun when it is closest to one of the poles. At equinox, the Sun is directly over the Equator. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
0.9999+0.1111=?
A)1
B)1.0001
C)1.0021
D)1.111
E)1.1111First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: 0.9999 + 0.1111
= 0.9999 + 0.111 + 0.0001
= (0.9999 + 0.0001) + 0.111
= 1 + 0.111
= 1.111
D | deepmind/aqua_rat |
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
A)48
B)120
C)72
D)110
E)116First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged among themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words = 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Answer C. | deepmind/aqua_rat |
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
A)42 minutes
B)72 minutes
C)62 minutes
D)32 minutes
E)42 minutesFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 / 150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8 * 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
We can also find the final answer as follows
4.5 x 8 = 32 minutes correct answer D | deepmind/aqua_rat |
1,2,3,2,4,6,4,8,_____
A)10
B)11
C)12
D)13
E)14First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Divide the series:
1,2,3
2,4,6
4,8,?
so it is 12
ANSWER:C | deepmind/aqua_rat |
A train 145 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
A)13 km/hr
B)57.2 km/hr
C)17 km/hr
D)18 km/hr
E)12 km/hrFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Speed of the train relative to man = (145/10) m/sec
= (14.5) m/sec. [(14.5) * (18/5)] km/hr
= 52.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 52.2 ==> x
= 57.2 km/hr.
Answer:B | deepmind/aqua_rat |
If g and h are positive integers, and 3 is not a factor of h, then h may be which of the following?
A)(g−1)·g·(g+1)
B)(g−3)·(g−1)·(g+1)
C)(g−2)·g·(g+2)
D)(g−1)·g·(g+2)
E)(g−3)·(g+1)·(g+2)First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Plugged in values :
let g=5
A. (g−1)·g·(g+1) --> divisible by 3
B. (g−3)·(g−1)·(g+1) --> divisible by 3
C. (g−2)·g·(g+2) --> divisible by 3
D. (g−1)·g·(g+2) --> not divisible. Hence the answer. | deepmind/aqua_rat |
0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance X between any two of the tick marks?
A)1/70
B)1/35
C)2/35
D)1/12
E)1/7First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1
1/5 2/5 3/5 4/5 5/5
expressing the same in terms of the lcm of 5,7 ,i.e 35
0 7/35 14/35 21/35 28/35 35/35
5/35 10/35 15/35 20/35 25/35 30/35
by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.
X=1/35
Answer is B. | deepmind/aqua_rat |
Question: What is the name of a branch of the chemistry that deals with the interconversion of chemical energy and electrical energy?
Choices:
A. Theoretical Chemistry
B. Inorganic chemistry
C. electrochemistry
D. Biochemistry
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Chemical reactions either absorb or release energy, which can be in the form of electricity. Electrochemistry is a branch of chemistry that deals with the interconversion of chemical energy and electrical energy. Redox chemistry, the transfer of electrons, is behind all electrochemical processes. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
A)50
B)45
C)20
D)73
E)27First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A | deepmind/aqua_rat |
If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was
A)Rs 1.56
B)Rs 2.40
C)RS 3.00
D)Rs 3.80
E)Rs 4.20First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: first 1/5 mile costs = 1.00
remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14,
hence 14*0.20=2.80
total fare = 2.80 + 1.00 =3.80
ANSWER:D | deepmind/aqua_rat |
What number has a 5:1 ratio to the number 8?
A)22
B)40
C)88
D)52
E)12First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 5:1 = x: 8
x = 40
Answer: B | deepmind/aqua_rat |
The avg weight of A,B & C is 60 kg. If D joins the group, the avg weight of the group becomes 65 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 64 kg. What is the weight of A?
A)56
B)65
C)75
D)89
E)87First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: A + B + C = 3 *60 = 180
A + B + C + D = 4 * 65 = 260 ---- (i)
So, D = 80& E = 80 + 3 = 83
B + C + D +E = 64 * 4 = 256 --- (ii)
From Eq. (i) & (ii)
A-E = 260 – 256 = 4
A = E +4 = 83 + 4 = 87
Answer : E | deepmind/aqua_rat |
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
A)1.9
B)1.5
C)1.4
D)1.1
E)1.6First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B | deepmind/aqua_rat |
In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 18 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
A)2/1
B)4/3
C)2/3
D)3/4
E)3/2First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+18) = 36/27 = 4/3.
Answer: B. | deepmind/aqua_rat |
The sum of the numbers is 220. If the first number be twice the second and third number be one-third of the first, then the second number is:
A)48
B)54
C)72
D)60
E)27First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 220
11x/3 = 220
x = 60
ANSWER:D | deepmind/aqua_rat |
What is the least whole number that should be added to 784839 if it is to be divisible by 10?
A)3
B)2
C)1
D)5
E)6First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: A number is divisible by 10 if the last digit is 0.
Here, 784839=9, (last digit is not 0.
1 must be added to 784839 to make it divisible by 10
C | deepmind/aqua_rat |
1+2+2^2=？
A)(2^3-1)(2^3+1)
B)2^6+1
C)2^5-1
D)2^5+1
E)2^3-1First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: From 1+2+2^2=1(2^6-1)/(2-1)=2^3-1, the correct answer is E. | deepmind/aqua_rat |
Two persons start running simultaneously around a circular track of length 250 m from the same point at speeds of 20 kmph and 40 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
A)144
B)15
C)18
D)32
E)38First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Time taken to meet the first time = length of track/relative speed
= 250/ (20 +40) (5/18)
= 250/60 *(18/5) = 15 sec.
Answer : B | deepmind/aqua_rat |
Ajit was driving down the country side when he saw a farmer tending his pigs and ducks in his yard. Ajit asked the farmer how many of each he had.The farmer replied that there were 60 eyes and 86 feet between them.How many ducks and how many pigs were there ?
A)13
B)14
C)15
D)16
E)17First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: let the no of ducks be X and no of pigs be Y.
then,since there are 60 eyes in total and both ducks and pigs have 2 eyes we have : 2X+2Y=60 --(1)
and total no of legs are 86,ducks have 2 legs while a pig has four so.: 2X+4y=86 ---(2)
subtracting (1) from (2) ,we get
2Y=26. ie. Y =13
putting value in (1),
we get X=17
ANSWER:E | deepmind/aqua_rat |
The radius of a semi circle is 6.3 cm then its perimeter is?
A)32.7
B)32.4
C)22.4
D)32.8
E)32.1First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 36/7 r = 6.3 = 32.4
Answer:B | deepmind/aqua_rat |
† and ¥ represent nonzero digits, and (†¥)^2 - (¥†)^2 is a perfect square. What is that perfect square?
A)121
B)361
C)576
D)961
E)1089First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Let the digits be a and b
(ab) can be written as (10a + b)
(ba) can be written as (10b + a)
(ab)^2 - (ba)^2 = (ab + ba)(ab - ba) = (10a + b + 10b + a)(10a + b - 10b - a) = 11(a + b)*9(a - b) = 99(a^2 - b^2)
99(a^2 - b^2) is a perfect square.
So the perfect square must be divisible by 99. Only option E is divisible by 99.
Answer: E | deepmind/aqua_rat |
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
A)33
B)25
C)77
D)28
E)29First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Explanation:
The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b
= 15 + 10 = 25 ways.
Answer: B) 25 | deepmind/aqua_rat |
If a certain sample of data has a mean of 21.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
A)12.0
B)13.5
C)17.0
D)23.5
E)26.5First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 21-7.5=13.5or more than 21+7.5=28.5.
Answer: B. | deepmind/aqua_rat |
The length of a rectangular field is 7/5 its width. If the perimeter of the field is 336 meters, what is the width of the field?
A)50
B)60
C)70
D)80
E)90First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 336, 2(7/5)W + 2W = 336
Solve the above equation to find: W = 70 m and L = 98 m.
correct answer C)70 | deepmind/aqua_rat |
What is the 124th digit to the right of the decimal point in the decimal form of 24/44?
A)8
B)9
C)6
D)4
E)2First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: To solve this question, we first have to use some long division. This long division allows us to get 24/44 in decimal form, which is 0.545454… where “54” is repeating.
We can see that the 1st, 3rd, 5th digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.
Then the 124 digit to the right of the decimal point and we see that 124 is even, we know that the 124th digit is a 4.
Answer D. | deepmind/aqua_rat |
For four days of work, a clerk had daily earnings of $140, $130, $140, and $140 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
A)Between $10 and $100
B)Between $10 and $50
C)Between $0 and $10
D)Between $10 and $70
E)Between $10 and $90First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(130-(140*3+130)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : C | deepmind/aqua_rat |
A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
A)1/200
B)1/59
C)1/56
D)1/54
E)1/53First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) ×(1/5) × (1/10) = 1/200
Answer: A | deepmind/aqua_rat |
A pair of articles was bought for Rs. 37.40 at a discount of 15%. What must be the marked price of each of the articles ?
A)Rs15
B)Rs 20
C)Rs 22
D)Rs 25
E)None of theseFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Explanation:
As question states that rate was of pair of articles,
So rate of One article = 37.40/2 = Rs. 18.70
Let Marked price = Rs X
then 85% of X = 18.70
=> X = 1870/85 = 22
Option C | deepmind/aqua_rat |
Question: When you heat a pot of water on a stove top, energy moves from the pot to its metal handle by what process?
Choices:
A. convection
B. thermal radiation
C. conduction
D. induction
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: In conduction, energy moves between two objects that are in contact. The higher temperature object transfers heat to the lower temperature object. For example, when you heat a pot of water on a stove top, energy moves from the pot to its metal handle by conduction. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
A and B together can do a piece of work in 8 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
A)0.075 days
B)0.45 days
C)0.55 days
D)0.25 days
E)0.15 daysFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: B = 1/8 – 1/22 =0.075 days
ANSWER:A | deepmind/aqua_rat |
Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 60 days.
A)36 days.
B)17 days.
C)18 days.
D)19 days.
E)20 days.First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 60*6/10 = 36 days.
ANSWER:A | deepmind/aqua_rat |
If n=3*4*p where p is a prime number greater than 3,how many different positive non-prime divisors does n have, excluding 1 and n?
A)Six
B)Seven
C)Eight
D)Nine
E)TenFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: n=3∗2^2∗p
Number of divisors = 2 * 3 * 2 = 12
The 12 divisors includes 1, n, 3, 2 and p
Number of different non prime divisors excluding 1 and n = 12 - 5 = 7
Answer: B | deepmind/aqua_rat |
There are 10 slate rocks, 11 pumice rocks, and 4 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
A)3/20
B)5/26
C)7/34
D)9/37
E)11/49First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: 10/25*9/24 = 3/20
The answer is A. | deepmind/aqua_rat |
If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
A)1/25
B)2/25
C)3/25
D)4/25
E)21/25First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: 0 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3
So, 5x=30 ---> x=6
Red marbles = 2*x = 2*6 = 12
Blue marbles = 3*x = 3*6 = 18
Prob to select a red marble = 12/30 = 2/5
Prob to select 2 red marbles with replacement = 2/5*2*5 = 4/25
Hence, answer will be D. | deepmind/aqua_rat |
In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
A)9X/80
B)13X/20
C)80/9X
D)10X/1
E)80X/9First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: IMT = 0.25T
JI = 0.40 IMT
0.40 IMT = $x b
IMT = $x/(0.40) b
T = 4*IMT = 4x/0.40 = 4x*100/40 = 10x/1
Ans: "D" | deepmind/aqua_rat |
Claire has a total of 92 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
A)39
B)68
C)54
D)57
E)60First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: G+H =92 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =92-H OR 3(92-H) +4H =300 H = 300-276 =24 THEN G= 92-24 = 68
B | deepmind/aqua_rat |
The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
A)1/48
B)1/42
C)1/46
D)1/47
E)1/43First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B | deepmind/aqua_rat |
The radius of a sphere is increased by 10%. The surface area increases by?
A)21%
B)31%
C)41%
D)51%
E)none of theseFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Since 4 x pi x radius x radius = surface area.
Therefore, net % change in area
= ( x + y + xy/100) %
= [10 + 10 + (10 x 10)/100]% or 21%.
ANSWER:A | deepmind/aqua_rat |
Question: What type of habitat do ferns need to grow?
Choices:
A. cold
B. moist
C. dry
D. elevated
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Ferns need a moist habitat. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ?
A)230
B)225
C)232
D)220
E)240First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12
= 256.3 + 40.3 – 66.12 ≈ 232
Answer C | deepmind/aqua_rat |
Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?
A)1,300
B)1,000
C)900
D)700
E)650First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(250) + 3*(50) = 1000
I = 350
Total number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650
Answer: E | deepmind/aqua_rat |
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
A)1/37
B)1/36
C)1/28
D)1/29
E)1/23First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B | deepmind/aqua_rat |
The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability D that Tommy CANNOT form a triangle from the 3 sticks?
A)11/32
B)13/32
C)15/32
D)17/32
E)19/32First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability D that a triangle is not formed = 30/64 = 15/32
C is the correct option here. | deepmind/aqua_rat |
Average monthly income of a family of 4 earning members was Rs. 782. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
A)Rs. 1178
B)Rs. 820
C)Rs. 990
D)Rs. 1385
E)NoneFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 782 x 4 - 650 x 3 Rs.
= 1178 Rs.
Correct Option: A | deepmind/aqua_rat |
What is the unit digit in 15^100?
A)0
B)1
C)2
D)3
E)5First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Unit digit in 15^100 = unit digit in [(15^4)^25 ]
But unit digit in 15^4=5
unit digit 15^100= 5
Answer is E | deepmind/aqua_rat |
If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails, on the second toss the coin lands on heads, and then lands on tails on the last toss?
A)1/8
B)1/3
C)1/4
D)1/2
E)1First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: P(THT) = 1/2*1/2*1/2=1/8
The answer is A. | deepmind/aqua_rat |
P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
A)8
B)5
C)4
D)6
E)3First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation :
Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
Answer : Option D | deepmind/aqua_rat |
Arrange the following in descending order :
A) 111(4),
B) 110 x 109 x 108 x 107,
C)109 x 110 x 112 x 113
A)all are equal
B)B,A.C
C)A,B,C
D)A,C,B
E)NoneFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation :
if you see option B...you can easily say it is the lowest value. Now about A and C you can see the sum of the values on both side is equal on this type of cases the side which as more number of values closer than other side and to the maximum value among given numbers will be the biggest value..If you couldn't understand the explanation take two sample and compare
Answer : D | deepmind/aqua_rat |
In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
A)200
B)210
C)220
D)250
E)360First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E | deepmind/aqua_rat |
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
A)5
B)2
C)10
D)12
E)15First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: 4/12+X/15=1
x=10
ANSWER C | deepmind/aqua_rat |
If n is an integer, then which of the following statements is/are FALSE?
I)n^3 – n is always even.
II)8n^3 +12n^2 +6n +1 is always even.
III)√ (4n^2 – 4n +1) is always odd.
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II and IIIFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: 1) n^3 – n
n^2(n-1)
two cases
if n=odd then n-1 is even thus n^2(n-1) is even
if n=even then n^2 is even thus n^2(n-1) is even------>true for all cases
2) 8n^3 +12n^2 +6n +1
8n^3 +12n^2 +6n=Even
but Even +1 =odd------------>Always False
3) for this i tried picking number upto 15 and find all cases True------>True
However will be looking for any algebraic solution
Ans B | deepmind/aqua_rat |
The ratio between the sale price and the cost price of an article is 9:7. What is the ratio between the profit and the cost price of that article?
A)2:9
B)2:7
C)3:6
D)2:0
E)2:1First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Let C.P. = Rs. 7x and S.P. = Rs. 9x.
Then, Gain = Rs. 2x
Required ratio = 2x : 7x = 2:7
Answer:B | deepmind/aqua_rat |
A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
A)7 days
B)6 days
C)9 days
D)5 days
E)4 daysFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer:D | deepmind/aqua_rat |
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than seven times?
A)37/256
B)56/256
C)65/256
D)70/256
E)1/256First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: More than 7 times tails = 8times = 8C8 = 1
2 2 2 2 2 2 2 2
2^8 times total events and 1 events where tails side up .
So probability = 1/2^8 = 1/256 (Answer E) | deepmind/aqua_rat |
Soymilk are sold in packages of two or three only. If Hannah bought 17 Soymilk exactly, what could be the number of large packs Hannah bought?
A)1
B)4
C)3
D)5
E)8First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Let number of packs of three = t
let number of packs of two = w
3t + 2w = 17
Now , we need to test for values of w .
Since sum 17 is odd and 2w will always be even, therefore w can't be even .
Now , we can test for values w = 1 , 3 and 5
2*4 + 3*3 = 8 + 9 = 17
Answer C | deepmind/aqua_rat |
Question: How many millions of years ago did pangaea begin breaking apart?
Choices:
A. 500
B. 600
C. 250
D. 400
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Pangaea has been breaking apart since about 250 million years ago. Divergent plate boundaries formed within the continents to cause them to rift apart. The continents are still moving apart. The Pacific is shrinking as the Atlantic is growing. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
G is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of G, and y is the minimum value of the sum of k distinct members of G, what is x + y?
A) kn
B) kn + k^2
C) kn + 2k^2
D) 2kn – k^2
E) 2knFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so G, the set of the first n positive odd numbers would be: G={1, 3, 5};
Say k=1, so X, the maximum value of the sum of K distinct members of G would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of G would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E. | deepmind/aqua_rat |
The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is:
A)2200
B)5500
C)3054.9
D)1100
E)4400First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Cylinder volume = πr(power2)h
= 22/7 × 9 × 9 × 12
= 3054.9 m(power3)
Answer is C. | deepmind/aqua_rat |
Question: What are the primary producers in terrestrial biomes?
Choices:
A. gases
B. animals
C. plants
D. soil
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Plants are the primary producers in terrestrial biomes. They make food for themselves and other organisms by photosynthesis. The major plants in a given biome help determine the types of animals and other organisms that can live there. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
A)15.4.
B)20.5.
C)25.5.
D)31.25.
E)32.5.First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: 135/6=22.5
164/6=27.33
Only C fits in between these two limits.
Answer: C | deepmind/aqua_rat |
A vessel of capacity 2 litre has 35% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
A)31%.
B)71%.
C)49%.
D)29%.
E)37%.First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: 35% of 2 litres = 0.7 litres
50% of 6 litres = 3 litres
Therefore, total quantity of alcohol is 3.7 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%
E | deepmind/aqua_rat |
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 181 cms. What was the ratio of men to women?
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 10:1First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 181cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 181M)/(W+M) = 180
170W + 181M = 180W + 180M
1M = 10W
M/W = 10/1
The ratio of men to women is 10 to 1.
E | deepmind/aqua_rat |
A package contains 8 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A)3/5
B)3/7
C)6/8
D)7/9
E)1/3First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: B
Explanation: Let number of balls = (8+6) = 14.
Number of white balls = 6.
P (drawing a white ball) = 6/14=3/7
B | deepmind/aqua_rat |
A man can row his boat with the stream at 12 km/h and against the stream in 8 km/h. The man's rate is?
A)2 kmph
B)6 kmph
C)7 kmph
D)4 kmph
E)9 kmphFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Explanation:
DS = 12
US = 8
S = ?
S = (12- 8)/2 =2 kmph
Answer: A | deepmind/aqua_rat |
The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
A)76
B)35
C)25
D)28
E)62First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Answer: A | deepmind/aqua_rat |
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
A)1×13/17 hours
B)2×8/11 hours
C)3×9/17 hours
D)4×1/2 hours
E)5×1/2 hoursFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: (a+b+c) can fill in (1/5+1/6-1/12) =3x9/17
ANSWER:C | deepmind/aqua_rat |
Find the cost of fencing around a circular field of diameter 12 m at the rate of Rs.3.50 a meter?
A)131.95
B)132.9
C)140.33
D)123.4
E)190.4First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: 2 * 22/7 * 6 = 37.7
37.7 * 3 1/2 = Rs.131.95
Answer: A | deepmind/aqua_rat |
Question: The primary function of insulin is to facilitate the uptake of what into body cells?
Choices:
A. chloride
B. water
C. glucose
D. sucralose
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Insulin The primary function of insulin is to facilitate the uptake of glucose into body cells. Red blood cells, as well as cells of the brain, liver, kidneys, and the lining of the small intestine, do not have insulin receptors on their cell membranes and do not require insulin for glucose uptake. Although all other body cells do require insulin if they are to take glucose from the bloodstream, skeletal muscle cells and adipose cells are the primary targets of insulin. The presence of food in the intestine triggers the release of gastrointestinal tract hormones. This is in turn the initial trigger for insulin production and secretion by the beta cells of the pancreas. Once nutrient absorption occurs, the resulting surge in blood glucose levels further stimulates insulin secretion. Precisely how insulin facilitates glucose uptake is not entirely clear. However, insulin appears to activate a tyrosine kinase receptor, triggering the phosphorylation of many substrates within the cell. These multiple biochemical reactions converge to support the movement of intracellular vesicles containing facilitative glucose transporters to the cell membrane. In the absence of insulin, these transport proteins are normally recycled slowly between the cell membrane and cell interior. Insulin triggers the rapid movement of a pool of glucose transporter vesicles to the cell membrane, where they fuse and expose the glucose transporters to the extracellular fluid. The transporters then move glucose by facilitated diffusion into the cell interior. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
Three unbiased coins are tossed. What is the probability of getting at most two heads?
A)3/4
B)1/4
C)3/8
D)7/8
E)None of theseFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) = n(E) / n(S) =7/8.
ANSWER IS D | deepmind/aqua_rat |
The average age of a husband and his wife was 32 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
A)11
B)53/3
C)19
D)25
E)27First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation:
Sum of the present ages of husband, wife and child = (32 * 2 + 5 * 2) + 1 = 75 years.
Required average = 75/3= 25 years.
Answer: D | deepmind/aqua_rat |
The average age of a board of 8 functional directors in a company is the same as it was 3 years ago, a younger man having been substituted for one of the directors. How much younger was the new man than the director whose place he took.
A)24 years
B)26 years
C)28 years
D)27 years
E)None of the aboveFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Let the new man was younger than the director = x years and 3 years ago, the sum of ages of board of directors
= S – 8 × 3 = S – 24
Then, 3 years ago, average age of board of directors
= S−24/8
Now, S−24/8=S−x/8
⇒ x = 24 years
Shortcut Method : If the new young director would have been not substituted, then total age would have increased at present by 8 × 3 = 24 years.
Therefore, the new man is 24 years younger keeping the average at present same as 3 years ago.
Answer A | deepmind/aqua_rat |
Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?
A)10 minutes
B)15 minutes
C)12 minutes
D)9 minutes
E)8 minutesFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Explanation:
Let B be turned off after X minutes.
Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1
=> x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1
=> x(2/75 + 1/45) + (30-x)2/75 = 1
=> 11x + 180 – 6x = 225
Therefore, x = 9 minutes
ANSWER: D | deepmind/aqua_rat |
A raffle is being held at a party with 25 guests. Each guest has a numbered ticket (1 through 25). Three numbers will be randomly chosen and prizes given out. Paul and Jane have numbers 22 and 23. What is the probability both will win a prize?
A)1/2
B)1/3
C)1/100
D)1/10
E)3/25First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 25C3 - 5!/(3!(5 - 3)!) = 2,300
Number 22 possible = 1C1 = 1
Number 23 possible = 1C1 = 1
Number other possible = 23C1 = 23
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(22, 23) = (1C1)(1C1)(23C1)/25C3 = 23/2,300 = 1/100
Answer: C | deepmind/aqua_rat |
Susan, John, Daisy, Tim, Matt, Jane and Kim need to be seated in 7 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
A)36
B)120
C)800
D)2400
E)2520First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: E
Explanation: Total # of arrangement of 7 people is 7!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 7!/2=2520.
Answer: E. | deepmind/aqua_rat |
There are three persons A, B and C when the age of A is added to half of the age of B, the result is equal to C's age. One-third of the age of 'B' is equal to one-fourth of the age of 'C'. If one-fifth of A's age is added to half of B's age, the result is equal to half of C's age. Then what is the age of 'B' ?
A)16 yrs
B)20 yrs
C)24 yrs
D)30 yrs
E)35 yrsFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Explanation :
A + B/2 = C .......(i)
B/3 = C/4 ........(ii)
A/5 + B/2 = C/2 ........(iii)
Solving these three eqns, A = 20, B = 24 and C = 32
Answer : Option C | deepmind/aqua_rat |
The distance between a book store and a coffee shop is approximately 5.3 x 10^4 inches. Which of the following is closest to the distance between the book store and a coffee shop, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
A)1.4
B)2.2
C)1.9
D)2.5
E)2.9First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the book store and a coffee shop is approximately 5.3 x 10^4 inches. To convert inches to kilometers, we need to multiply 5.3 x 10^4 inches by the ratio we just found out.
kilometers = 5.3 x 10^4 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 5.3x10^5/3.9x10^4 km
km = 1.36 = 1.4 km
Therefore, we can see that the closest answer is A. | deepmind/aqua_rat |
Question: What force causes waves to topple over and break on the shore?
Choices:
A. vibration
B. tension
C. momentum
D. friction
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: Waves topple over and break on the shore because of friction with the bottom in shallow water. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
A merchant has selected two items to be placed on sale, one of which currently sells for 30 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
A)22 %
B)30%
C)42 6/7%
D)70%
E)130%First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: C
Explanation: Expensive item = $100;
Cheap item = $70;
We must increase $70 to $100, so by $30, which is approximately 40% increase: (100-70)/70 = 3/7 = ~0.42.
Answer: C. | deepmind/aqua_rat |
A set of books costs the merchant $500. At what price would the merchant be sold the set of books if he got loss of 5% ?
A)$475
B)$480
C)$485
D)$495
E)None of theseFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Cost Price = $500
Loss % = 5
Selling Price = ?
Selling Price = (100 - loss %) * Cost Price /100
= (100 - 5) * 500 / 100
= 475
Answer is A | deepmind/aqua_rat |
Question: Virtually all of the effects of pregnancy can be attributed in some way to the influence of what?
Choices:
A. hormones
B. acids
C. proteins
D. enzymes
First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Virtually all of the effects of pregnancy can be attributed in some way to the influence of hormones—particularly estrogens, progesterone, and hCG. During the early weeks of pregnancy, the corpus luteum generates these hormones. The placenta gradually takes over as the endocrine organ of pregnancy. Estrogen levels climb throughout the pregnancy, increasing significantly by childbirth. Estrogens prevent ovulation, induce the growth of fetal tissues, promote fetal viability, and stimulate maternal tissue growth. Relaxin helps prepare the mother’s body for childbirth by increasing the elasticity of joints and ligaments and dilating the cervix during labor. | https://huggingface.co/datasets/allenai/sciq + unsloth/gemma-3-12b-it-unsloth-bnb-4bit |
Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
A)$146.6
B)$120
C)$180
D)$220
E)$260First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.15E ==> 11A =220 +11.5E -------(2)
Substituting (1) in (2):
13E = 220+11.5E ==>1.5E= 220 or E =440/3 =146.6
A | deepmind/aqua_rat |
From the set of numbers x, y, t, z and w, how many different combinations can we have without the t and z in them? Ex:. (x,y), (x), (w,y,x), etc and (x,y)=(y,x)
A)6
B)14
C)15
D)16
E)30First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Another way: Any letter (x, y, w) can be included or not. So, we have 2^3 combinations - 2 empty combination = 6 combinations
A | deepmind/aqua_rat |
At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $75 billion of credit, or 1/2 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
A)412.16
B)150
C)400
D)416.67
E)420.34First, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: D
Explanation: System of Equations
a = (36/100) c
(1/2) a = 75 --> a = 150
Substitution
150 = (36/100) c
c = (100/36) 150
Calculate 150/36 * 100
The Correct Answer is D
- The correct answer will be slightly smaller than 513. Therefore, the correct answer is 475. | deepmind/aqua_rat |
A man sells an article at 5% profit. If he had bought it at 5% less and sold it for 1 less, he would have gained 10%. The cost price of the article is :
A)200
B)150
C)240
D)280
E)None of theseFirst, state only the correct answer in the format: <Your answer>. Then, provide a detailed explanation starting on a new line with Explanation:.
| Answer: A
Explanation: Let the CP of the article be x.
Then, SP = 105x⁄100
Now, new CP = 95x⁄100 and new SP = 105x⁄100 - 1
According to the question
105x/100−1−95/100=10×95x/100×100
∴ x = 200
Answer A | deepmind/aqua_rat |
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