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A student places a sheet of black construction paper on her desk. What happens to most of the light that strikes the black construction paper? | [
"The light is bent by the paper.",
"The light reflects off the paper.",
"The light is absorbed by the paper.",
"The light passes through the paper."
] | C | 1 |
|
a machine , working at a constant rate , manufactures 18 dies in 25 minutes . how many dies does it make in 1 hr 15 min ? | [
"53",
"50",
"54",
"55"
] | C | "change 1 hr 15 min to 75 min . for this , we need to set up a simple proportion of dies per time 18 / 25 = s / 75 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 25 in the two denominators . 18 / 1 = s / 3 s = 3 * 18 s = 54 the machine would be 54 dies in 1 hr 15 min . answer : c" | 5 |
in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 9 years older than b , the present age of b is | [
"88 years",
"39 years",
"16 years",
"77 years"
] | B | "let b ' s age = x years . then , as age = ( x + 9 ) years . ( x + 9 + 10 ) = 2 ( x — 10 ) hence x = 39 . present age of b = 39 years answer : c" | 5 |
What process within cells makes sure that every gamete receives a copy of every chromosome? | [
"meiosis",
"fission",
"genomes",
"mutations"
] | A | All of our cells contain DNA. Meiosis ensures that each gamete receives a copy of each chromosome. | 7 |
Let $f(x) = 3x^2 - 7$ and $g(f(4)) = 9$. What is $g(f(-4))$? | [
"f(x) = c, c \\in \\mathbb{R}",
"",
"9",
"\\frac{9}{41}"
] | C | We have $f(-4) = 3(-4)^2 -7 =41$, so we seek $g(f(-4)) = g(41)$. But what's $g(41)$? So, we turn to the other information we are given, $g(f(4)) = 9$. Since $f(4) = 3(4)^2 - 7=41$, this equation gives us $g(41) = \boxed{9}$. | 4 |
how many positive integers , from 2 to 100 , inclusive , are not divisible by even integers greater than 1 ? | [
"10",
"5",
"6",
"50"
] | C | "the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence ans - ( b ) 6" | 5 |
As the population of small fish in a lake decreases, the population of large fish that depend on the small fish for food will | [
"reproduce faster",
"begin to produce their own food",
"decrease in number",
"increase in number"
] | C | 1 |
|
22.085 ã — 0.001 = ? | [
"0.022085",
"0.0022085",
"0.22085",
"2.2085"
] | A | "22.085 ã — 0.001 = ? or , ? = 0.022085 answer c" | 5 |
the average salary of 16 people in the shipping department at a certain firm is $ 20000 . the salary of 5 of the employees is $ 25000 each and the salary of 4 of the employees is $ 16000 each . what is the average salary of the remaining employees ? | [
"$ 12",
"$ 18",
"$ 15",
"$ 18"
] | D | total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a | 5 |
a boy want to make a cuboid of dimension 5 m , 6 m , 7 m from small cubes of . 04 m 3 . later he realized he can make same cuboid by making it hollow . then it takes some cubes less . what is the no . of these cubes ? | [
"2250'",
"2150'",
"2850'",
"2350'"
] | A | volume of cuboid = 5 * 6 * 7 = 210 m 3 volume of inner cuboid = ( 5 - 1 ) * ( 6 - 1 ) * ( 7 - 1 ) = 120 m 3 therefore , volume of hollow cuboid = 210 - 120 = 90 m 3 no of cubes required = 90 / . 04 = 2250 cubes answer : b | 5 |
What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits? | [
"1002",
"1089",
"18",
"900.01345"
] | B | For a number to be divisible by 9, the sum of its digits must be divisible by 9. But since the number has two even digits and two odd digits, the sum of its digits is even. Thus the sum of its digits must be at least 18. This number will be minimized if its thousands digit is 1 and its hundreds digit is 0. This means the remaining two digits must sum to 17, and are hence 8,9. So we see that the smallest possible integer of the desired form is $\boxed{1089}$. | 4 |
Bees and other wild animals perform what function on flowering plants, making them vital for crop reproduction? | [
"pollenation",
"irrigation",
"fertilizer",
"pesticide"
] | A | Animals, like the bee in Figure below , pollinate flowering plants. Many crop plants depend on pollination by wild animals. | 7 |
of the 250 employees at company x , 80 are full - time , and 175 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? | [
"100",
"30",
"80",
"25"
] | D | "250 employees 80 are full - time 175 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 250 - 80 = 170 employees not full time 170 - 20 = 150 employees not full time who worked over a year 175 employees have worked at company x for at least a year - 150 employees not full time who worked over a year = 25 full - time employees of company x have worked at the company for at least a year ans a" | 5 |
What is the only mechanism that consistently causes adaptive evolution? | [
"natural selection",
"genetic drift",
"neutral selection",
"artificial selection"
] | A | 23.4 Natural selection is the only mechanism that consistently causes adaptive evolution. | 7 |
kate and danny each have $ 10 . together , they flip a fair coin 5 times . every time the coin lands on heads , kate gives danny $ 1 . every time the coin lands on tails , danny gives kate $ 1 . after the 5 coin flips , what is the probability that kate has more than $ 10 but less than $ 15 ? | [
"15 / 32",
"12 / 30",
"1 / 2",
"3 / 8"
] | A | the probability of the coin landing tails up either 3 or 4 times = p ( 3 t ) + p ( 4 t ) binomial distribution formula : nck p ^ k ( 1 - p ) ^ ( n - k ) p ( 3 t ) = 5 c 3 ( 1 / 2 ) ^ 3 ( 1 / 2 ) ^ 2 = 10 ( 1 / 2 ) ^ 5 p ( 4 t ) = 5 c 4 ( 1 / 2 ) ^ 4 ( 1 / 2 ) ^ 1 = 5 ( 1 / 2 ) ^ 5 = > p ( 3 t ) + p ( 4 t ) = 15 / 32 answer : d | 5 |
what will be the remainder when 17 ^ 200 is divided by 18 | [
"3",
"1",
"4",
"2"
] | B | "17 ^ 200 % 18 ( 17 - 18 ) ^ 200 % 18 ( - 1 ) ^ 200 % 18 1 % 18 = 1 answer : a" | 5 |
In certain species of plants, purple flowers (P) are dominant to white flowers (p). If two heterozygous plants are crossed, what will be the phenotype of the offspring? | [
"100% purple flowers",
"100% white flowers",
"75% white flowers, 25% purple flowers",
"25% white flowers, 75% purple flowers"
] | D | 0 |
|
A pile of mulch is broken down and when searching for the culprit, a gardener notes | [
"wriggling organisms",
"writing organisms",
"large trees",
"wild fires"
] | A | decomposer is a kind of role in an ecosystem | 6 |
if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y = | [
"3",
"7",
"5",
"4"
] | A | "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d" | 5 |
a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , and 5 , how many palindromes are possible ? | [
"225",
"25",
"75",
"125"
] | D | there are 5 choices for each of the first three digits . the number of possible palindromes is 5 ^ 3 = 125 . the answer is c . | 5 |
if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? | [
"$ 240",
"$ 190",
"$ 180",
"$ 250"
] | D | "120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ." | 5 |
The middle school sold 6 more than two times the number of fair tickets as it did tickets to the baseball game. If 25 fair tickets were sold, how many baseball game tickets did the school sell? | [
"110.0",
"56.0",
"50.0",
"12.672"
] | B | Two times the number of fair tickets is 25*2=<<25*2=50>>50 tickets
50+6=<<50+6=56>>56 tickets
#### 56 | 3 |
the sum of two consecutive numbers is 452 . the greatest among these three number is : | [
"226",
"230",
"200",
"229"
] | A | "let the numbers be x , x + 1 then , x + ( x + 1 ) = 452 2 x = 450 x = 225 greatest number , ( x + 1 ) = 226 answer : a" | 5 |
a fruit seller had some oranges . he sells 40 % oranges and still has 300 oranges . how many oranges he had originally ? | [
"500",
"220",
"none of these",
"700"
] | A | "explanation : he sells 40 % of oranges and still there are 300 oranges remaining = > 60 % of oranges = 300 ⇒ ( 60 × total oranges ) / 100 = 300 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d" | 5 |
two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 6 ½ hours if they are walking in the same direction ? | [
"9 km",
"5 km",
"8 1 / 8 km",
"6 km"
] | C | rs = 5 ¾ - 4 ½ = 1 ¼ t = 6 ½ h . d = 5 / 4 * 13 / 2 = 65 / 8 = 8 1 / 8 km answer : c | 5 |
Photoautotrophs and chemoautotrophs are two basic types of what? | [
"plants",
"autotrophs",
"consumers",
"decomposers"
] | B | Producers are organisms that produce food for themselves and other organisms. They use energy and simple inorganic molecules to make organic compounds. The stability of producers is vital to ecosystems because all organisms need organic molecules. Producers are also called autotrophs . There are two basic types of autotrophs: photoautotrophs and chemoautotrophs. | 7 |
if 3 a – 2 b – 4 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ? | [
"10",
"12",
"3",
"9"
] | B | "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d" | 5 |
653 ã — 1001 = ? | [
"653001",
"649011",
"654321",
"540041"
] | A | "653 ã — ( 1000 + 1 ) 653000 + 1 653001 answer d" | 5 |
when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ? | [
"4 / 7",
"11 / 14",
"3 / 7",
"3 / 14"
] | B | "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus w = 11 / 14 of the remaining votes must be against . answer : a ." | 5 |
Photoautotrophs use what energy source to self-manufacture their own food? | [
"water",
"chlorophyll",
"light",
"air"
] | C | every organism uses to power its metabolism. In brief, the energy of sunlight is captured and used to energize electrons, which are then stored in the covalent bonds of sugar molecules. How long lasting and stable are those covalent bonds? The energy extracted today by the burning of coal and petroleum products represents sunlight energy captured and stored by photosynthesis almost 200 million years ago. Plants, algae, and a group of bacteria called cyanobacteria are the only organisms capable of performing photosynthesis (Figure 8.2). Because they use light to manufacture their own food, they are called photoautotrophs (literally, “self-feeders using light”). Other organisms, such as animals, fungi, and most other bacteria, are termed heterotrophs (“other feeders”), because they must rely on the sugars produced by photosynthetic organisms for their energy needs. A third very interesting group of bacteria synthesize sugars, not by using sunlight’s energy, but by extracting energy from inorganic chemical compounds; hence, they are referred to as chemoautotrophs. | 7 |
Find the value of $t$ that satisfies $\frac{1}{t+2} + \frac{2t}{t+2} - \frac{3}{t+2} = 3$. | [
"t",
"2",
" \\frac{t - \\boxed{3}}{(t+2)}\\cdot(3t+6)",
"-8"
] | D | Combining the fractions on the left gives $\dfrac{2t-2}{t+2} = 3$. Multiplying both sides by $t+2$ gives $2t-2 = 3(t+2)$. Expanding the right side gives $2t-2 = 3t+6$. Subtracting $2t$ and 6 from both sides gives $t=\boxed{-8}$. | 4 |
Gregor Mendel studied ratios related to traits passed from parent pea plants to offspring pea plants. Mendel used large numbers of plants to avoid "sampling error." This changed the way scientists studied genetics because it included ideas of | [
"nuclei and DNA.",
"atoms and molecules.",
"ecology and environment.",
"mathematics and probability."
] | D | 1 |
|
The posterior half of the foot is formed by seven tarsal bones. the most superior of these bones is called? | [
"metatarsal",
"calcareous",
"talus",
"patella"
] | C | Tarsal Bones The posterior half of the foot is formed by seven tarsal bones (Figure 8.19). The most superior bone is the talus. This has a relatively square-shaped, upper surface that articulates with the tibia and fibula to form the ankle joint. Three areas of articulation form the ankle joint: The superomedial surface of the talus bone articulates with the medial malleolus of the tibia, the top of the talus articulates with the distal end of the tibia, and the lateral side of the talus articulates with the lateral malleolus of the fibula. Inferiorly, the talus articulates with the calcaneus (heel bone), the largest bone of the foot, which forms the heel. Body weight is transferred from the tibia to the talus to the calcaneus, which rests on the ground. The medial calcaneus has a prominent bony extension called the sustentaculum tali (“support for the talus”) that supports the medial side of the talus bone. | 7 |
mixture contains alcohol and water in the ratio 4 : 3 . if 4 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture . | [
"20",
"27",
"22",
"99"
] | A | "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 16 x = 4 ( 3 x + 5 ) 4 x = 20 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer : a" | 5 |
a train 100 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? | [
"6 sec",
"18 sec",
"9 sec",
"15 sec"
] | A | "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 100 m at 50 / 3 m / sec = 100 * 3 / 50 sec = 6 sec answer : a" | 5 |
Among vertebrates, what broad category of animals is most capable of learning? | [
"reptiles",
"mammals",
"fish",
"birds"
] | B | Mammals are very intelligent. Of all vertebrates, they are the animals that are most capable of learning. Mammalian offspring are fed and taken care of by their parents for a relatively long time. This gives them plenty of time to learn from their parents. By learning, they can benefit from the experiences of their elders. The ability to learn is the main reason that the large mammalian brain evolved. It’s also the primary reason for the success of mammals. | 7 |
The pips of a pumpkin are most commonly | [
"flow to space",
"fueling trucks",
"seasoned and devoured",
"drowned alive"
] | C | a pumpkin contains seeds | 6 |
x is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number . find value of x ? | [
"8",
"7",
"4",
"3"
] | D | let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 a | 5 |
Norris saved $29 in September. He saved $25 in October and $31 in November. Then Hugo spent $75 on an online game. How much money does Norris have left? | [
"179.0",
"39.0",
"10.0",
"53.0"
] | C | The total amount of money saved is $29 + $25 + $31 = $<<29+25+31=85>>85.
Norris has $85 - $75 = $<<85-75=10>>10 left.
#### 10 | 3 |
Which property of water can cause a rock to break apart? | [
"Water boiling at 100°C.",
"Water losing energy slowly.",
"Water expanding as it freezes.",
"Water having a high surface tension."
] | C | 1 |
|
Compute
\[\prod_{k = 1}^{12} \prod_{j = 1}^{10} (e^{2 \pi ji/11} - e^{2 \pi ki/13}).\] | [
"0",
"8 \\pi i/13",
"\\frac{1{+}i\\sqrt{13}}{4}",
"1"
] | D | Let
\[P(x) = \prod_{k = 1}^{12} (x - e^{2 \pi ki/13}).\]The roots of this polynomial are $e^{2 \pi ki/13}$ for $1 \le k \le 12.$ They are also roots of $x^{13} - 1 = (x - 1)(x^{12} + x^{11} + x^{10} + \dots + x^2 + x + 1).$ Thus,
\[P(x) = x^{12} + x^{11} + x^{10} + \dots + x^2 + x + 1.\]Now, $e^{2 \pi ji/11},$ for $1 \le j \le 10,$ is a root of $x^{11} - 1 = (x - 1)(x^{10} + x^9 + x^8 + \dots + x^2 + x + 1),$ so $e^{2 \pi ji/11}$ is a root
of
\[x^{10} + x^9 + x^8 + \dots + x^2 + x + 1.\]So, if $x = e^{2 \pi ji/11},$ then
\begin{align*}
P(x) &= x^{12} + x^{11} + x^{10} + \dots + x^2 + x + 1 \\
&= x^2 (x^{10} + x^9 + x^8 + \dots + x^2 + x + 1) + x + 1 \\
&= x + 1.
\end{align*}Hence,
\begin{align*}
\prod_{k = 1}^{12} \prod_{j = 1}^{10} (e^{2 \pi ji/11} - e^{2 \pi ki/13}) &= \prod_{j = 1}^{10} P(e^{2 \pi ji/11}) \\
&= \prod_{j = 1}^{10} (e^{2 \pi ji/11} + 1).
\end{align*}By similar reasoning,
\[Q(x) = \prod_{j = 1}^{10} (x - e^{2 \pi ji/11}) = x^{10} + x^9 + x^8 + \dots + x^2 + x + 1,\]so
\begin{align*}
\prod_{j = 1}^{10} (e^{2 \pi ji/11} + 1) &= \prod_{j = 1}^{10} (-1 - e^{2 \pi ji/11}) \\
&= Q(-1) \\
&= \boxed{1}.
\end{align*} | 4 |
The city’s bus system carries 1,200,000 people each day. How many people does the bus system carry for 13 weeks? | [
"10000.0",
"1800000.0",
"109200000.0",
"1440000.0"
] | C | 13 weeks have 13 * 7 = <<13*7=91>>91 days.
For 91 days the bus system carries 1,200,000 * 91 = <<1200000*91=109200000>>109,200,000 people.
#### 109,200,000 | 3 |
Compute the number of intersection points of the graphs of
\[(x - \lfloor x \rfloor)^2 + y^2 = x - \lfloor x \rfloor\]and $y = \frac{1}{5} x.$ | [
"11",
"16-1",
"6",
"1+\\lfloor 1 \\rfloor"
] | A | We can write $x - \lfloor x \rfloor = \{x\},$ so
\[\{x\}^2 + y^2 = \{x\}.\]Completing the square in $\{x\},$ we get
\[\left( \{x\} - \frac{1}{2} \right)^2 + y^2 = \frac{1}{4}.\]Let $n = \lfloor x \rfloor,$ so $\{x\} = x - n.$ Hence,
\[\left( x - n - \frac{1}{2} \right)^2 + y^2 = \frac{1}{4}.\]Consider the case where $n = 0.$ Then $0 \le x < 1,$ and the equation becomes
\[\left( x - \frac{1}{2} \right)^2 + y^2 = \frac{1}{4}.\]This is the equation of the circle centered at $\left( \frac{1}{2}, 0 \right)$ with radius $\frac{1}{2}.$
Now consider the case where $n = 1.$ Then $1 \le x < 2,$ and the equation becomes
\[\left( x - \frac{3}{2} \right)^2 + y^2 = \frac{1}{4}.\]This is the equation of the circle centered at $\left( \frac{3}{2}, 0 \right)$ with radius $\frac{1}{2}.$
In general, for $n \le x < n + 1,$
\[\left( x - n - \frac{1}{2} \right)^2 + y^2 = \frac{1}{4}\]is the equation of a circle centered at $\left( \frac{2n + 1}{2}, 0 \right)$ with radius $\frac{1}{2}.$
Thus, the graph of $\{x\}^2 + y^2 = \{x\}$ is a chain of circles, each of radius $\frac{1}{2},$ one for each integer $n.$
[asy]
unitsize(3 cm);
draw(Circle((1/2,0),1/2));
draw(Circle((3/2,0),1/2));
draw(Circle((-1/2,0),1/2));
draw(Circle((-3/2,0),1/2));
draw((-2.2,0)--(2.2,0));
draw((0,-1/2)--(0,1/2));
label("$\dots$", (2.2,0.2));
label("$\dots$", (-2.2,0.2));
dot("$(-\frac{3}{2},0)$", (-3/2,0), S);
dot("$(-\frac{1}{2},0)$", (-1/2,0), S);
dot("$(\frac{1}{2},0)$", (1/2,0), S);
dot("$(\frac{3}{2},0)$", (3/2,0), S);
[/asy]
We then add the graph of $y = \frac{1}{5} x.$
[asy]
unitsize(2.5 cm);
int i;
pair P;
for (i = -3; i <= 2; ++i) {
draw(Circle((2*i + 1)/2,1/2));
P = intersectionpoints(Circle((2*i + 1)/2,1/2),(-2.8,-2.8/5)--(2.8,2.8/5))[0];
dot(P);
P = intersectionpoints(Circle((2*i + 1)/2,1/2),(-2.8,-2.8/5)--(2.8,2.8/5))[1];
dot(P);
}
draw((-2.8,-2.8/5)--(2.8,2.8/5));
draw((-3.2,0)--(3.2,0));
draw((0,-1/2)--(0,1/2));
dot("$(-\frac{5}{2},0)$", (-5/2,0), S);
dot("$(-\frac{3}{2},0)$", (-3/2,0), S);
dot("$(-\frac{1}{2},0)$", (-1/2,0), S);
dot("$(\frac{1}{2},0)$", (1/2,0), S);
dot("$(\frac{3}{2},0)$", (3/2,0), S);
dot("$(\frac{5}{2},0)$", (5/2,0), S);
dot("$(\frac{5}{2},\frac{1}{2})$", (5/2,1/2), N);
dot("$(-\frac{5}{2},-\frac{1}{2})$", (-5/2,-1/2), S);
[/asy]
The graph of $y = \frac{1}{5} x$ intersects each of the six circles closest to the origin in two points. For $x > 5,$ $y > \frac{1}{2},$ so the line does not intersect any circles. Similarly, the line does not intersect any circles for $x < -5.$
One point of intersection is repeated twice, namely the origin. Hence, the number of points of intersection of the two graphs is $2 \cdot 6 - 1 = \boxed{11}.$ | 4 |
a has 10000 chocolates . 20 % of the chocolates are eaten . what percentage of the uneaten chocolates must be eaten so that 3 / 2 of all chocolates are eaten ? | [
"37.25",
"38.21",
"38.32",
"39.25"
] | A | number of chocolates = 10,000 currently eaten = 10,000 * 20 / 100 = 2000 uneaten chocolates = 10000 - 2000 = 8000 2 / 3 of all chocolates = 5000 the number of chocolates to be eaten to make 2 / 3 of all chocolates eaten = 5000 - 2000 = 3000 so now the question remains - 3000 is how much percentage of uneaten chocolates ( 8000 ) = 3000 * 100 / 8000 = 37.5 answer ( b ) | 5 |
Stella’s antique shop has 3 dolls, 2 clocks and 5 glasses for sale. She sells the dolls for $5 each. The clocks are priced at $15 each. The glasses are priced at $4 each. If she spent $40 to buy everything and she sells all of her merchandise, how much profit will she make? | [
"20.0",
"25.0",
"110.0",
"71.0"
] | B | The dolls will sell for 3 * $5 = $<<3*5=15>>15.
The clocks will bring in 2 * $15 = $<<2*15=30>>30.
The glasses will sell for 5 * $4 = $<<5*4=20>>20.
In total, she will bring in $15 + $30 + $20 = $<<15+30+20=65>>65
Her total profit will be $65 - $40 = $<<65-40=25>>25.
#### 25 | 3 |
A small poultry farm has 300 chickens, 200 turkeys and 80 guinea fowls. A strange, incurable disease hit the farm and every day the farmer lost 20 chickens, 8 turkeys and 5 guinea fowls. After a week, how many birds will be left in the poultry? | [
"349.0",
"890.0",
"13.0",
"650.0"
] | A | There are 300+200+80 = <<300+200+80=580>>580 birds in total
Every day 20+8+5 = <<20+8+5=33>>33 birds are lost
After a week which is 7 days, 33*7 = <<33*7=231>>231 birds would be lost
There would be 580-231 = <<580-231=349>>349 birds left in the poultry
#### 349 | 3 |
suppose f ( x ) is an odd function for which f ( x + 2 ) = f ( x ) for all x , and f ( x ) = x 2 for x 2 ( 0 , 1 ) . compute f ( - 3 / 2 ) + f ( 1 ) . | [
"1 / 4",
"- 1 / 4",
"1 / 2",
"- 1"
] | A | because f is periodic , we know that f ( - 3 / 2 ) = f ( 1 / 2 ) = ( 1 / 2 ) 2 = 1 = 4 . because f is odd , we know that f ( 1 ) = - f ( / 1 ) , but because f is periodic , f ( 1 ) = f ( - 1 ) . therefore , f ( 1 ) = 0 and the answer is 1 = 4 . correct answer d | 5 |
The dispersal of what has a positive impact on plants? | [
"leaves",
"bark",
"branches",
"kernels"
] | D | seed dispersal has a positive impact on a plant | 6 |
two whole numbers whose sum is 24 is the ratio | [
"2 : 8",
"1 : 6",
"2 : 5",
"1 : 3"
] | D | a ) 1 : 3 | 5 |
What bodily substance is formed from cells, and in turn helps make up organs? | [
"tendons",
"tissues",
"ligaments",
"muscles"
] | B | Organisms are organized in the microscopic level from atoms up to cells. The matter is structured in an ordered way. Atoms are arranged into molecules, then into macromolecules, which make up organelles, which work together to form cells. Beyond this, cells are organized in higher levels to form entire multicellular organisms, as shown in Figure below . Cells together form tissues, which make up organs, which are part of organ systems, which work together to form an entire organism. Of course, beyond this, organisms form populations which make up parts of an ecosystem. All of Earth's ecosystems together form the diverse environment that is Earth. | 7 |
Foxes eat | [
"wolves",
"mice",
"man",
"bears"
] | B | predators eat prey | 6 |
r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? | [
"seven",
"four",
"five",
"three"
] | D | "r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , and 36 are even integers ( less than 51 ) that are in both sets . solution : three answer : b" | 5 |
a , b and c invested rs . 600 , rs . 800 and rs . 1200 respectively , in a partnership business . find the share of b in profit of rs . 900 after a year ? | [
"237.8",
"900",
"276.92",
"266.27"
] | C | "explanation : 600 : 800 : 1200 3 : 4 : 6 4 / 13 * 900 = 276.92 answer : a" | 5 |
Electromagnetic waves transfer energy across space as well as through what? | [
"plasma",
"matter",
"filtering",
"osmosis"
] | B | Electromagnetic waves transfer energy across space as well as through matter. They vary in their wavelengths and frequencies, and higher-frequency waves have more energy. The full range of wavelengths of electromagnetic waves, shown in the Figure below , is called the electromagnetic spectrum. | 7 |
the current in a river is 8 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ? | [
"96 miles",
"84 miles",
"69 miles",
"100 miles"
] | B | "upstream speed = 20 - 8 = 12 mph downstream speed = 20 + 8 = 28 mph d / 12 + d / 28 = 10 hours solving for d we get d = 84 answer : b" | 5 |
For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-four representation of $n$ and let $g(n)$ be the sum of the digits in the base-eight representation of $f(n)$. For example, $f(2020) = f(133210_{\text{4}}) = 10 = 12_{\text{8}}$, and $g(2020) = \text{the digit sum of }12_{\text{8}} = 3$. Let $N$ be the least value of $n$ such that the base-sixteen representation of $g(n)$ cannot be expressed using only the digits $0$ through $9$. Find the remainder when $N$ is divided by $1000$.
| [
"151",
"3",
"8",
"1002"
] | A | Let's work backwards. The minimum base-sixteen representation of $g(n)$ that cannot be expressed using only the digits $0$ through $9$ is $A_{16}$, which is equal to $10$ in base 10. Thus, the sum of the digits of the base-eight representation of the sum of the digits of $f(n)$ is $10$. The minimum value for which this is achieved is $37_8$. We have that $37_8 = 31$. Thus, the sum of the digits of the base-four representation of $n$ is $31$. The minimum value for which this is achieved is $13,333,333,333_4$. We just need this value in base 10 modulo 1000. We get $13,333,333,333_4 = 3(1 + 4 + 4^2 + \dots + 4^8 + 4^9) + 4^{10} = 3\left(\dfrac{4^{10} - 1}{3}\right) + 4^{10} = 2*4^{10} - 1$. Taking this value modulo $1000$, we get the final answer of $\boxed{151}$. | 4 |
What is the least positive integer with exactly $10$ positive factors? | [
"12",
"22",
"48",
"7020"
] | C | We need to find the smallest integer, $k,$ that has exactly $10$ factors. $10=5\cdot2=10\cdot1,$ so $k$ must be in one of two forms:
$\bullet$ (1) $k=p_1^4\cdot p_2^1$ for distinct primes $p_1$ and $p_2.$ The smallest such $k$ is attained when $p_1=2$ and $p_2=3,$ which gives $k=2^4\cdot3=48.$
$\bullet$ (2) $k=p^9$ for some prime $p.$ The smallest such $k$ is attained when $p=2,$ which gives $k=2^9>48.$
Thus, the least positive integer with exactly $10$ factors is $\boxed{48}.$ | 4 |
If the Earth revolved around another planet instead of a star, what might it lack? | [
"continents",
"satellites",
"starry skies",
"seasons"
] | D | the Earth revolving around the Sun causes the seasons to change on its axis | 6 |
Write the following expression as a polynomial: $$(2x^2+3x+7)(x+1)-(x+1)(x^2+4x-63)+(3x-14)(x+1)(x+5).$$ | [
"4x^3+4x^2",
"2x^3+5x^2-4x+9x+21-x^3-5x^2-3x+63-3x^2-15x-28+3x^2+15x+35",
"-3x^3 + 5x^2 - 12x - 210",
"2x^3 + x^2 + 26x - 48"
] | A | Factoring out $(x+1)$, we have:
\begin{align*}
&(x+1)((2x^2+3x+7)-(x^2+4x-63)+(3x-14)(x+5))\\
=\text{ }&(x+1)(2x^2+3x+7-x^2-4x+63+3x^2+x-70) \\
=\text{ }&(x+1)(2x^2-x^2+3x^2+3x-4x+x+7+63-70) \\
=\text{ }&(x+1)(4x^2+0x+0) \\
=\text{ }&4x^2(x+1) \\
=\text{ }&\boxed{4x^3+4x^2}.
\end{align*} | 4 |
for what value of â € œ k â € will the equation ( 2 kx 2 + 3 kx + 2 ) = 0 have equal roots ? | [
"9 / 4",
"16 / 9",
"2 / 7",
"16 / 25"
] | B | for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 3 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 9 answer : e | 5 |
What is stacked in layers in "layer cake geology"? | [
"horizontal stata",
"sediment",
"soil",
"rock stata"
] | D | Geologists say that the Grand Canyon ( Figure above ) has "layer cake geology. " This is because the rock strata are in layers. They are extremely easy to see. Sedimentary rocks are like a book that tells the story of the environment in which they formed. Rock units can be traced across large expanses. Looking down into the Grand Canyon, you get a sense of the vastness of space and of time. | 7 |
given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 16 = f ( x – 6 ) ? | [
"13",
"1",
"7",
"4"
] | B | "2 ( 3 x - 5 ) - 16 = 3 ( x - 6 ) - 5 3 x = 3 x = 1 the answer is a ." | 5 |
The square with vertices $(-a, -a), (a, -a), (-a, a), (a, a)$ is cut by the line $y = x/2$ into congruent quadrilaterals. The perimeter of one of these congruent quadrilaterals divided by $a$ equals what? Express your answer in simplified radical form. | [
"\\frac{3}{2}",
"ly.\n\n\n$ Example A:{}\n\n",
"4+\\sqrt{5}",
"2"
] | C | The line $y=\frac x2$ will intersect the two vertical sides of the square, as shown below:
[asy]
real f(real x)
{
return x/2;
}
import graph;
size(6cm);
real a = 8;
pair A=(-a,a), B=(a,a), C=(a,-a), D=(-a,-a);
draw(A--B--C--D--cycle);
draw(graph(f,-11,11),Arrows);
axes(Arrows(4));
dot("$(-a,a)$",A,N);
dot("$(a,a)$",B,N);
dot("$(a,-a)$",C,S);
dot("$(-a,-a)$",D,S);
real eps=0.2;
dot((8,4)^^(-8,-4));
draw(shift((10,0))*"$2a$",(-a+eps,-a/2-.5)--(a-eps,-a/2-.5),Arrows);
draw(shift((0,10))*"$a$",(a+2*eps,-a/2)--(a+2*eps,a/2),Arrows);[/asy]
The equation of the right side of the square is $x=a,$ so we have $y= \frac x2 = \frac a2,$ which means that the intersection point with the right side of the square is $\left(a, \frac a2 \right).$ Similarly, the equation of the left side of the square is $x=-a,$ so we have $y= \frac x2 = -\frac a2,$ which means that the intersection point with the left side of the square is $\left(-a, -\frac a2 \right).$ It follows that the sides of each quadrilateral have lengths $\frac a2,$ $2a,$ $\frac{3a}2,$ and $\sqrt{a^2 + (2a)^2} = a\sqrt{5},$ by the Pythagorean theorem. Hence, the perimeter of the quadrilateral is \[\frac a2 + 2a + \frac{3a}2 + a\sqrt{5} = \left(4+\sqrt5\right)a,\]and when this is divided by $a,$ we get $\boxed{4+\sqrt{5}}.$ | 4 |
18 men shake hands with each other . maximum no of handshakes without cyclic handshakes . | [
"220",
"190",
"210",
"153"
] | D | "1 st person will shake hand with 17 people 2 nd person will shake hand with 16 people 3 rd person will shake hand with 15 people . . . . . . total no . of handshakes = 17 + . . . + 3 + 2 + 1 = 17 * ( 17 + 1 ) / 2 = 153 or , if there are n persons then no . of shakehands = nc 2 = 18 c 2 = 153 answer : b" | 5 |
A shady restaurant is charging customers gratuities after taxes without them being aware. If my total bill was $140, the sales tax in my city is 10%, I ordered a NY Striploin for $80, and I ordered a glass of wine for $10, how much did they charge me for gratuities? | [
"60.0",
"50.0",
"41.0",
"114.0"
] | C | The total bill before taxes or gratuities was $80 for the steak + $10 for the wine = $80+$10 = $<<80+10=90>>90
If the tax is 10%, then the taxes paid were $90 * 10% = $<<90*10*.01=9>>9
That means that the total bill before gratuities was $90 + $9 = $<<90+9=99>>99
If the final bill was $140, then you were charged $140-$99 = $<<140-99=41>>41 for gratuities
#### 41 | 3 |
if 6 cats can kill 6 rats in 6 minutes , how long will it take 100 cats to kill 100 rats ? | [
"4 minutes",
"2 minutes",
"1 minutes",
"6 minutes"
] | D | "it will take 6 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 6 minutes , so 100 cats can kill 100 rats in 6 minutes answer e" | 5 |
After the Meyer tree's flowers pedals drop you are left with | [
"a bee sign",
"something sweet",
"a bird bath",
"a party"
] | B | some flowers become fruits | 6 |
Jorge bought 24 tickets for $7 each. For purchasing so many, he is given a discount of 50%. How much, in dollars, did he spend on tickets? | [
"96.0",
"10.0",
"14.08",
"84.0"
] | D | Jorge spent 24 tickets * $7 per ticket = $<<24*7=168>>168 total.
After applying the discount, Jorge spent $168 * 0.50 = $<<168*0.50=84>>84.
#### 84 | 3 |
find the number , difference between number and its 3 / 5 is 50 . | [
"123",
"124",
"359",
"125"
] | D | "explanation : let the number = x , then , x - ( 3 / 5 ) x = 50 , = > ( 2 / 5 ) x = 50 = > 2 x = 50 * 5 , = > x = 125 option d" | 5 |
What helps the cell continually renew itself? | [
"centrosome",
"lysosomes",
"lymphocytes",
"vacuole"
] | B | 7 |
|
What is it called when one or more ending digits are dropped to get the correct number of significant figures? | [
"rounding",
"basing",
"scientific notation",
"turning"
] | A | Rounding is done when one or more ending digits are dropped to get the correct number of significant figures. Simple rules state when to round up and when to round down. | 7 |
Which element has atomic number 87? | [
"francium",
"iron",
"argon",
"barium"
] | A | Francium has an atomic number of 87. Write the chemical equation for the alpha particle emission of 212Fr. What is the daughter isotope?. | 7 |
a jogger running at 9 km / hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? | [
"89 sec",
"40 sec",
"87 sec",
"67 sec"
] | B | "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 280 + 120 = 400 m . time taken = 400 / 10 = 40 sec . answer : e" | 5 |
if p / q = 3 / 5 , then 2 p + q = ? | [
"15",
"12",
"16",
"11"
] | D | "let p = 3 , q = 5 then 2 * 3 + 5 = 11 so 2 p + q = 11 . answer : b" | 5 |
9 log 9 ( 4 ) = ? | [
"3",
"2",
"1",
"4"
] | D | "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d" | 5 |
What is the upper-most atmosphere known as? | [
"thermosphere",
"ionosphere",
"xerosphere",
"exosphere"
] | A | The atmosphere is a big part of the water cycle. What do you think would happen to Earth’s water without it?. | 7 |
At the Hardey Fitness Center, the management did a survey of their membership. The average age of the female members was 40 years old. The average age of the male members was 25 years old. The average age of the entire membership was 30 years old. What is the ratio of the female to male members? Express your answer as a common fraction. | [
"\\frac{8}{3}",
"\\frac{1}{5}",
"\\frac{1}{2}",
"\\frac{1}{1}"
] | C | Let $m$ denote the number of male members and $f$ the number of female members. The sum of the ages of the female members is $40f$ and the sum of the ages of the male members is $25m$. The sum of the ages of all the members is $40f+25m$, and the total number of members is $f+m$. Since the average age for all the members is $30$, we have \[
\frac{40f+25m}{f+m}=30.
\] Multiply both sides by $f+m$ to get \[
40f+25m=30f+30m.
\] Collecting like terms we find $10f=5m$ so $f/m=\boxed{\frac{1}{2}}$. | 4 |
Mrs. Watson is grading 120 final exams from her American History class. On Monday, she grades 60% of the exams. On Tuesday, she grades 75% of the remaining exams. On Wednesday, how many more exams does she need to grade? | [
"4.0",
"12.0",
"120.0",
"54.0"
] | B | On Monday, Mrs. Watson grades 120 x 60% = <<120*60*.01=72>>72 final exams.
At the end of Monday, she has 120 - 72 = <<120-72=48>>48 exams left to grade.
On Tuesday, she grades 48 x 75% = <<48*75*.01=36>>36 final exams.
On Wednesday, she has 48 - 36 = <<48-36=12>>12 exams left to grade.
#### 12 | 3 |
if x ^ 2 + ( 1 / x ^ 2 ) = 9 , x ^ 4 + ( 1 / x ^ 4 ) = ? | [
"12",
"79",
"14",
"11"
] | B | "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 9 ^ 2 - 2 = 79 . thus , the answer is e ." | 5 |
Let $\overline{AB}$ be a diameter of circle $\omega$. Extend $\overline{AB}$ through $A$ to $C$. Point $T$ lies on $\omega$ so that line $CT$ is tangent to $\omega$. Point $P$ is the foot of the perpendicular from $A$ to line $CT$. Suppose $\overline{AB} = 18$, and let $m$ denote the maximum possible length of segment $BP$. Find $m^{2}$.
| [
"9876",
"over",
"$$.\\",
"432"
] | D | [asy] size(250); defaultpen(0.70 + fontsize(10)); import olympiad; pair O = (0,0), B = O - (9,0), A= O + (9,0), C=A+(18,0), T = 9 * expi(-1.2309594), P = foot(A,C,T); draw(Circle(O,9)); draw(B--C--T--O); draw(A--P); dot(A); dot(B); dot(C); dot(O); dot(T); dot(P); draw(rightanglemark(O,T,C,30)); draw(rightanglemark(A,P,C,30)); draw(anglemark(B,A,P,35)); draw(B--P, blue); label("\(A\)",A,NW); label("\(B\)",B,NW); label("\(C\)",C,NW); label("\(O\)",O,NW); label("\(P\)",P,SE); label("\(T\)",T,SE); label("\(9\)",(O+A)/2,N); label("\(9\)",(O+B)/2,N); label("\(x-9\)",(C+A)/2,N); [/asy]
Let $x = OC$. Since $OT, AP \perp TC$, it follows easily that $\triangle APC \sim \triangle OTC$. Thus $\frac{AP}{OT} = \frac{CA}{CO} \Longrightarrow AP = \frac{9(x-9)}{x}$. By the Law of Cosines on $\triangle BAP$,\begin{align*}BP^2 = AB^2 + AP^2 - 2 \cdot AB \cdot AP \cdot \cos \angle BAP \end{align*}where $\cos \angle BAP = \cos (180 - \angle TOA) = - \frac{OT}{OC} = - \frac{9}{x}$, so:\begin{align*}BP^2 &= 18^2 + \frac{9^2(x-9)^2}{x^2} + 2(18) \cdot \frac{9(x-9)}{x} \cdot \frac 9x = 405 + 729\left(\frac{2x - 27}{x^2}\right)\end{align*}Let $k = \frac{2x-27}{x^2} \Longrightarrow kx^2 - 2x + 27 = 0$; this is a quadratic, and its discriminant must be nonnegative: $(-2)^2 - 4(k)(27) \ge 0 \Longleftrightarrow k \le \frac{1}{27}$. Thus,\[BP^2 \le 405 + 729 \cdot \frac{1}{27} = \boxed{432}\]Equality holds when $x = 27$. | 4 |
What is the sum of the prime numbers less than 10? | [
"36",
"2",
"17",
"25"
] | C | The prime numbers less than $10$ are $2,3,5,7$, so the sum is $2+3+5+7=\boxed{17}$. | 4 |
Capillaries in the chorionic villi filter fetal wastes out of the blood and return clean, oxygenated blood to the fetus through what? | [
"skin vein",
"umbilical vein",
"Back Vein",
"separates vein"
] | B | The placenta develops throughout the embryonic period and during the first several weeks of the fetal period; placentation is complete by weeks 14–16. As a fully developed organ, the placenta provides nutrition and excretion, respiration, and endocrine function (Table 28.1 and Figure 28.12). It receives blood from the fetus through the umbilical arteries. Capillaries in the chorionic villi filter fetal wastes out of the blood and return clean, oxygenated blood to the fetus through the umbilical vein. Nutrients and oxygen are transferred from maternal blood surrounding the villi through the capillaries and into the fetal bloodstream. Some substances move across the placenta by simple diffusion. Oxygen, carbon dioxide, and any other lipid-soluble substances take this route. Other substances move across by facilitated diffusion. This includes water-soluble glucose. The fetus has a high demand for amino acids and iron, and those substances are moved across the placenta by active transport. Maternal and fetal blood does not commingle because blood cells cannot move across the placenta. This separation prevents the mother’s cytotoxic T cells from reaching and subsequently destroying the fetus, which bears “non-self” antigens. Further, it ensures the fetal red blood cells do not enter the mother’s circulation and trigger antibody development (if they carry “non-self” antigens)—at least until the final stages of pregnancy or birth. This is the reason that, even in the absence of preventive treatment, an Rh− mother doesn’t develop antibodies that could cause hemolytic disease in her first Rh+ fetus. Although blood cells are not exchanged, the chorionic villi provide ample surface area for the two-way exchange of substances between maternal and fetal blood. The rate of exchange increases throughout gestation as the villi become thinner and increasingly branched. The placenta is permeable to lipid-soluble fetotoxic substances: alcohol, nicotine, barbiturates, antibiotics, certain pathogens, and many other substances that can be dangerous or fatal to the developing embryo or fetus. For these reasons, pregnant women should avoid fetotoxic substances. Alcohol consumption by pregnant women, for example, can result in a range of abnormalities referred to as fetal alcohol spectrum disorders (FASD). These include organ and facial malformations, as well as cognitive and behavioral disorders. | 7 |
Roberta takes $158 with her on a shopping trip to the mall. She spends $45 on new shoes, $17 less on a new bag, and a quarter of the price of the bag for lunch. How much money does she have left after these purchases? | [
"0.0",
"105.0",
"110.0",
"78.0"
] | D | Roberta's bag costs $45 - $17 = $<<45-17=28>>28.
Roberta spend $28 / 4 = $<<28/4=7>>7 on lunch.
Roberta spend 45 + 28 + 7 = <<45+28+7=80>>80 in total.
Roberta has $158 - 80 = $<<158-80=78>>78 left.
#### 78 | 3 |
maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 94 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ? | [
"5",
"4",
"10",
"3"
] | C | "total distance = 94 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 90 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 90 / 10 = 9 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 9 = 36 + 4 = 40 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 40 / 4 = 10 hrs . . . answer e" | 5 |
if 10 % of 30 % of 50 % of a number is 90 , then what is the number ? | [
"4000",
"4400",
"none of these",
"6000"
] | D | "let the number be a given , 10 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 1 / 10 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 6000 . answer : b" | 5 |
pollination is when wind carry pollen from one flower to another | [
"genetically similar thing",
"rock",
"cloud",
"water"
] | A | pollination is when wind carry pollen from one flower to another flower | 6 |
What equals the mass of the object (in kilograms) times the acceleration due to gravity (9.8 m/s 2 )? | [
"velocity",
"weight",
"density",
"speed of light"
] | B | Weight is a measure of the force of gravity pulling on an object of a given mass. It equals the mass of the object (in kilograms) times the acceleration due to gravity (9.8 m/s 2 ). | 7 |
evaluate : 20 - 12 ÷ 12 × 2 = | [
"e ) 20",
"c ) 12",
"b ) 8",
"d ) 16"
] | C | "according to order of operations , 12 ÷ 12 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 12 × 2 = 1 × 2 = 2 hence 20 - 12 ÷ 12 × 2 = 20 - 12 = 8 correct answer is b ) 8" | 5 |
Which is true? | [
"balloons and stars are composed of exactly the same materials",
"balloons and stars are the same size",
"stars and balloons share some of the same gases",
"balloons and stars contain sodium"
] | C | a star is made of gases | 6 |
Josie's mom gave her a $20 bill and asked her to go to the store for a few items. The list included a carton of milk for $4.00, a loaf of bread for $3.50, a box of laundry detergent for $10.25 and 2 pounds of bananas that were $0.75 per pound. Her mom also gave her a coupon for $1.25 off of the laundry detergent. At checkout, the clerk told her the milk was 1/2 off today. How much money did Josie have left over after she bought all of the groceries? | [
"330.0",
"2.0",
"2.28",
"4.0"
] | D | The milk cost $4.00 but was on sale for 1/2 off so 4*.50 = $<<4*.50=2.00>>2.00
She bought 2 pounds of bananas at $0.75 per pound so 2 *.75 = $<<2*0.75=1.50>>1.50
She had a $1.25 coupon off of laundry detergent so 10.25 - 1.25 = $<<10.25-1.25=9.00>>9.00
When you add all of her purchases together then 2 + 1.50 +3.50 + 9.00 = $<<2+1.50+3.50+9=16.00>>16.00
She paid with a $20 bill so 20-16 = $<<20-16=4>>4 left over
#### 4 | 3 |
Archie received his medical receipt from his doctor, and he needs to take antibiotics three times a day. If antibiotic costs $3 each and he needs to take it for a week, how much money does he need to buy the antibiotics? | [
"8.0",
"4.0",
"63.0",
"49.0"
] | C | Archie needs $3 x 3 = $<<3*3=9>>9 per day to buy 3 antibiotics.
Therefore Archie needs $9 x 7 = $<<9*7=63>>63 to buy antibiotics that will last for a week.
#### 63 | 3 |
raja spends 60 % of his monthly income on household items , 10 % of his monthly income on buying cloths , 10 % of his monthly income on medicines and saves the remaining amount which is rs . 5000 . find his monthly income . | [
"rs . 25000",
"rs . 50000",
"rs . 36000",
"none of these"
] | A | "savings 20 % - 5000 expenditure 80 % - 20000 total - 25000 answer : d" | 5 |
how many natural numbers between 23 and 137 are divisible by 7 ? | [
"15",
"13",
"16",
"17"
] | C | "solution : these numbers are 28 , 35 , 42 , … . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c" | 5 |
What is the most prevalent gas in the atmosphere, but not the most vital for life? | [
"carbon dioxide",
"argon",
"oxygen",
"nitrogen"
] | D | Most of the atmosphere is nitrogen, but it doesn't do much. Carbon dioxide and oxygen are the gases in the atmosphere that are needed for life. | 7 |
What type of muscle is found in the walls of other internal organs such as the stomach? | [
"inorganic muscle",
"smooth muscle",
"Fiber Muscle",
"Tube Muscle"
] | B | Smooth muscle is found in the walls of other internal organs such as the stomach. It isn’t striated because its muscle fibers are arranged in sheets rather than bundles. Contractions of smooth muscle are involuntary. When smooth muscles in the stomach contract, they squeeze food inside the stomach. This helps break the food into smaller pieces. | 7 |
What occurs when a cold air mass runs into a warm air mass? | [
"a snow day",
"a stationary front",
"a cold front",
"an occluded front"
] | C | A cold front occurs when a cold air mass runs into a warm air mass. This is shown in Figure below . The cold air mass moves faster than the warm air mass and lifts the warm air mass out of its way. As the warm air rises, its water vapor condenses. Clouds form, and precipitation falls. If the warm air is very humid, precipitation can be heavy. Temperature and pressure differences between the two air masses cause winds. Winds may be very strong along a cold front. | 7 |
Timber companies can best manage the number of trees in forests by | [
"converting deforested areas into malls.",
"planting trees to replace what they cut down.",
"adding pesticides to the soil around the trees.",
"removing the tree stumps when trees are cut down."
] | B | 1 |
|
Organisms are highly organized, coordinated structures that consist of one or more what? | [
"nucleus",
"lipids",
"proteins",
"cells"
] | D | Organisms are highly organized, coordinated structures that consist of one or more cells. Even very simple, single-celled organisms are remarkably complex: inside each cell, atoms make up molecules; these in turn make up cell organelles and other cellular inclusions. In multicellular organisms (Figure 1.10), similar cells form tissues. Tissues, in turn, collaborate to create organs (body structures with a distinct function). Organs work together to form organ systems. Sensitivity or Response to Stimuli. | 7 |
Glutathione is a low-molecular-weight compound found in living cells that is produced naturally by what? | [
"blood",
"brain",
"amino acids",
"liver"
] | D | Glutathione is a low-molecular-weight compound found in living cells that is produced naturally by the liver. Healthcare providers give glutathione intravenously to prevent side effects of chemotherapy and to prevent kidney problems. | 7 |
Billy's family likes to keep their bicycles stored in the garage when they're not being used. They own a total of 4 bicycles. Each bicycle wheel has 10 spokes. How many spokes are inside the garage? | [
"160.0",
"7.0",
"80.0",
"4.0"
] | C | Each bicycle has 2 wheels, so there are a total of 4*2=<<4*2=8>>8 wheels in the garage as there are 4 bicycles.
Since each wheel has 10 spokes, this means there are 8*10=<<8*10=80>>80 spokes in total.
#### 80 | 3 |
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