question stringlengths 1 2.65k | choices listlengths 4 4 | answer stringclasses 4
values | explanation stringlengths 0 4.47k | dataset int64 0 7 |
|---|---|---|---|---|
A glacier sometimes leaves behind large chunks of ice. What is left in the ground when these chunks of ice melt? | [
"a valley",
"a kettle",
"a crater",
"a sinkhole"
] | B | 1 | |
the speed at which a man can row a boat in still water is 14 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 40 metres ? | [
"9 seconds",
"12 seconds",
"34 seconds",
"16 seconds"
] | A | "speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5 / 18 = 40 / 9 m / s hence time taken to cover 40 m = 40 * 9 / 40 = 9 seconds . answer : c" | 5 |
Many animals that give birth to live young have | [
"skin",
"scales",
"exoskeletons",
"gills"
] | A | live birth means developing inside the mother instead of an egg | 6 |
The ovaries produce estradiol and progesterone, which cause secondary sex characteristics and prepare the body for? | [
"breathing",
"adulthood",
"childbirth",
"movement"
] | C | cells. The ovaries produce estradiol and progesterone, which cause secondary sex characteristics and prepare the body for childbirth. | 7 |
a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 54 , what is the total amount ? | [
"116",
"119",
"117",
"234"
] | D | "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 54 39 - - - ? = > 234 answer : a" | 5 |
Let $a,$ $b,$ $c$ be a three-term arithmetic series where all the terms are positive, such that $abc = 64.$ Find the smallest possible value of $b.$ | [
"32",
"4",
"-3",
"9"
] | B | By AM-GM,
\[\frac{a + b + c}{3} \ge \sqrt[3]{abc} = \sqrt[3]{64} = 4.\]Since $a,$ $b,$ $c$ form an arithmetic series, $\frac{a + b + c}{3} = b,$ so $b \ge 4.$
Equality occurs when $a = b = c = 4,$ so the smallest possible value of $b$ is $\boxed{4}.$ | 4 |
at what rate percent on simple interest will rs . 600 amount to rs . 950 in 5 years ? | [
"3.33 %",
"5.93 %",
"11.67 %",
"4.33 %"
] | C | "350 = ( 600 * 5 * r ) / 100 r = 11.67 % answer : e" | 5 |
a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 20 % . the final price is what percent of the original price ? | [
"52 %",
"28 %",
"64 %",
"70 %"
] | C | "just assume original price is 100 . sale price = 80 then it is marked down by 20 % = 80 - 16 = 64 . hence it is 64 % od the original price . hence answer is d ." | 5 |
Steve has 25 socks. He has 4 pairs of socks that match, and all the others don't match. How many mismatching socks does Steve have altogether? | [
"10.0",
"34.0",
"43.0",
"17.0"
] | D | In each pair of socks there are 2/1 = <<2/1=2>>2 socks.
Steve has 2*4 = <<2*4=8>>8 matching socks.
Steve has 25-8 = <<25-8=17>>17 mismatching socks.
#### 17 | 3 |
Which part of a DNA molecule represents encoded information? | [
"phosphate",
"sugar",
"guanine",
"hydrogen bond"
] | C | 1 | |
two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ? | [
"22 / 7 sec",
"20 / 8 sec",
"20 / 4 sec",
"20 / 7 sec"
] | D | "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 100 / 35 = 20 / 7 sec . answer : c" | 5 |
the average salary / head of all the workers ina workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ? | [
"20",
"25",
"22",
"18"
] | C | let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c | 5 |
a number is doubled and 15 is added . if resultant is trebled , it becomes 75 . what is that number | [
"14",
"10",
"5",
"7"
] | C | "explanation : = > 3 ( 2 x + 15 ) = 75 = > 2 x + 15 = 25 = > x = 5 option c" | 5 |
? % of 360 = 144 | [
"none of these",
"64",
"40",
"36"
] | C | "? % of 360 = 144 or , ? = 144 × 100 / 360 = 40 answer d" | 5 |
the product of two numbers is 168 and the sum of their squares is 289 . the sum of the number is ? | [
"a ) 23",
"e ) 35",
"b ) 25",
"c ) 27"
] | C | "let the numbers be x and y . then , xy = 168 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 168 ) = 625 x + y = 25 . option b" | 5 |
Seals have an instinct to give birth in the same area every year. Where do seals give birth normally? | [
"Jupiter",
"space",
"waterfronts",
"houses"
] | C | seals every year return to the same beaches to give birth | 6 |
The polynomial $f(x)$ satisfies $f(x + 1) - f(x) = 6x + 4.$ Find the leading coefficient of $f(x).$ | [
"3",
"-q",
"6",
"\\text{the coefficient of }x^2 \\text{ in }f(x) \\text{ is } 2."
] | A | Let $n$ be a positive integer. Setting $x = 0,$ $1,$ $2,$ $\dots,$ $n - 1,$ we get
\begin{align*}
f(1) - f(0) &= 6 \cdot 0 + 4, \\
f(2) - f(1) &= 6 \cdot 1 + 4, \\
f(3) - f(2) &= 6 \cdot 2 + 4, \\
&\dots, \\
f(n) - f(n - 1) &= 6 \cdot (n - 1) + 4.
\end{align*}Adding all the equations, we get
\[f(n) - f(0) = 6 (0 + 1 +... | 4 |
Miles is going to spend 1/6 of a day reading. He will read comic books, graphic novels, and novels. He reads 21 pages an hour when he reads novels, 30 pages an hour when he reads graphic novels, and 45 pages an hour when he reads comic books. If he reads each for 1/3 of his time, how many pages does he read? | [
"128.0",
"308.0",
"342.0",
"516.0"
] | A | Miles will read for 4 hours because 24 x (1/6) = <<24*(1/6)=4>>4
He will read each type for 1 and 1/3 hours because 4 / 3 = 1 and 1/3
He will read 28 pages of novels because 21 x (1 and 1/3) = 28
He will read 40 pages of graphic novels because 30 x (1 and 1/3) = 40
He will read 60 pages of comic books because 45 x (1 a... | 3 |
there is enough provisions for 600 men in an army camp for 25 days . if there were 200 men less , how long will the provision last ? | [
"70 days",
"75 days",
"90 days",
"60 days"
] | B | exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 200 * d 2 d 2 = 600 * 25 / 200 = 75 days . answer : d | 5 |
What chemical reaction is the opposite of oxidation? | [
"mutation",
"condensation",
"evaporation",
"reduction"
] | D | The chemical reaction that is the opposite of oxidation is called reduction. Following from the notion that oxidation was originally thought to mean only the addition of oxygen, reduction was thought to be only the removal of oxygen from a substance. Many naturally occurring metal ores are present as oxides. The pure m... | 7 |
Historically, malaria has rivaled what as the leading cause of human death by infectious disease? | [
"hepatitis",
"cancer",
"tuberculosis",
"heart attack"
] | C | Alloys can be one of two general types. In one type, called a substitutional alloy, the various atoms simply replace each other in the crystal structure. In another type, called an interstitial alloy, the smaller atoms such as carbon fit in between the larger atoms in the crystal packing arrangement. | 7 |
a parking garage rents parking spaces for $ 10 per week or $ 40 per month . how much does a person save in a year by renting by the month rather than by the week ? | [
"$ 240",
"$ 260",
"$ 160",
"$ 40"
] | D | "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 40 = 480 $ 520 - 480 = 40 ans a" | 5 |
how many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph ? | [
"22 sec",
"24 sec",
"11 sec",
"30 sec"
] | D | "explanation : d = 100 + 200 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 10 sec answer : option c" | 5 |
how much time does a train 150 metres long running at 54 km / hr take to pass a pole ? | [
"10 s",
"2.5 s",
"7.5 s",
"7.9 s"
] | A | "explanation : 54 km / hr = 54 * 5 / 18 = 15 m / s speed = distance / time ; v = d / t 15 = 150 / t t = 10 s answer : e" | 5 |
Mrs. Young buys a 300 piece puzzle set for her three sons. She divides the pieces evenly to the three boys. Reyn can place 25 pieces into the puzzle picture. Rhys places twice as much as Reyn. Rory places three times as much as Reyn. Altogether, how many puzzle pieces are still left to be placed? | [
"90.0",
"150.0",
"100.0",
"125.0"
] | B | Each son receives 300 / 3 = <<300/3=100>>100 pieces.
Rhys places 25 x 2 = <<25*2=50>>50 pieces.
Rory places 25 x 3 = <<25*3=75>>75 pieces.
All three boys place 25 + 50 + 75 = <<25+50+75=150>>150 pieces.
The boys have not placed 300 - 150 = <<300-150=150>>150 pieces.
#### 150 | 3 |
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles? | [
"25",
"141",
"21",
"5405"
] | C | Lisa wants to minimize the number of marbles she gives to her friends without giving any two of them the same number of marbles. The minimum number of marbles she can give to a friend is 1. She then gives 2 marbles to another friend, then 3 to another, then 4, and so on, until the last friend receives 10. The total num... | 4 |
The nine horizontal and nine vertical lines on an $8\times8$ checkerboard form $r$ rectangles, of which $s$ are squares. The number $s/r$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
| [
"209",
"125",
"16",
"142"
] | B | To determine the two horizontal sides of a rectangle, we have to pick two of the horizontal lines of the checkerboard, or ${9\choose 2} = 36$. Similarily, there are ${9\choose 2}$ ways to pick the vertical sides, giving us $r = 1296$ rectangles.
For $s$, there are $8^2$ unit squares, $7^2$ of the $2\times2$ squares, an... | 4 |
p software has coding line 5 % more than n , n software has coding line 4 / 13 more than m . m software has 78 lines of coding . find p lines . | [
"106",
"107",
"110",
"108"
] | B | "m s / w has 78 line of code n s / w has = 78 + 78 * 4 / 13 = 102 line of code p s / w 5 % more n ' code 102 + 5.1 = 107.1 or 107 line of code answer : b" | 5 |
Which of the following statements best explains why magnets usually stick to a refrigerator door? | [
"The refrigerator door is smooth.",
"The refrigerator door contains iron.",
"The refrigerator door is a good conductor.",
"The refrigerator door has electric wires in it."
] | B | 0 | |
What is the rising and sinking of warm and cooler material called? | [
"depression",
"diffusion",
"convection",
"conveyance"
] | C | Hot lower mantle material rises upward ( Figure below ). As it rises, it cools. At the top of the mantle it moves horizontally. Over time it becomes cool and dense enough that it sinks. Back at the bottom of the mantle, it travels horizontally. Eventually the material gets to the location where warm mantle material is ... | 7 |
a monkey ascends a greased pole 18 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ? | [
"21 st",
"24 th",
"22 nd",
"33 rd"
] | D | "in 2 minutes , he ascends = 1 metre â ˆ ´ 16 metres , he ascends in 32 minutes . â ˆ ´ he reaches the top in 33 rd minute . answer c" | 5 |
Janice needs to go to watch a movie in 2 hours. before she could leave, she needs to finish her homework which takes 30 minutes; clean her room which takes half as long as her homework; walk the dog which takes 5 minutes more than making homework; take out the trash which takes 1/6 of the time it takes her to do the ho... | [
"25.0",
"35.0",
"90.0",
"100.0"
] | B | Janice takes 30/2 = <<30/2=15>>15 minutes to clean her room.
It takes 30 + 5 = <<30+5=35>>35 minutes for her to walk the dog.
It takes her 30 x 1/6 = <<30*1/6=5>>5 minutes to take out the trash.
So, it will take 30 + 15 + 35 + 5 = <<30+15+35+5=85>>85 minutes to do all those chores.
Since there are 60 minutes in 1 hour,... | 3 |
64 + 5 * 12 / ( 180 / 3 ) = ? | [
"29",
"77",
"65",
"22"
] | C | 64 + 5 * 12 / ( 180 / 3 ) = 64 + 5 * 12 / ( 60 ) = 64 + ( 5 * 12 ) / 60 = 64 + 1 = 65 . answer : d | 5 |
Salamanders may be unable to survive in a hot, dry location lacking food and water, but if it has food and water in an ideal location | [
"it is extinguished",
"it may flourish",
"it is financed",
"it may crash"
] | B | when a habitat can support living things , living things can live in that habitat | 6 |
a pharmaceutical company received $ 6 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in ... | [
"15 %",
"72 %",
"45 %",
"52 %"
] | B | "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sa... | 5 |
find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years | [
"306.04",
"306.01",
"306.03",
"244.83"
] | D | "a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a" | 5 |
Transpiration occurs in | [
"the fruit of a pear tree",
"the seeds of a tree",
"the flat appendages on organisms that give off oxygen",
"the lungs of a dog"
] | C | transpiration usually happens in the leaves of a plant | 6 |
if the remainder is 3 when positive integer n is divided by 18 , what is the remainder when n is divided by 6 ? | [
"4",
"3",
"1",
"2"
] | B | assume x is quotient here , n = 18 x + 3 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write first term as n = ( 18 x + 6 ) = 6 ( 3 x + 1 ) + 3 ie 6 ( 3 x + 1 ) + 3 ie the first term is perfectly divisible by 6 . so , the remainder left is 3 . so , answer ( a ) is right choice . | 5 |
The skin is a familiar organ made of what kind of tissue? | [
"epithelial tissue",
"aberrant tissue",
"innate tissue",
"recurrent tissue"
] | A | The skin is a familiar organ made of epithelial tissue. | 7 |
The expression $y^2+10y+33$ can be written as a combination of a square of a binomial and an integer. Find the integer. | [
"8",
"-33",
"4x+13",
"30"
] | A | We will complete the square for $y^2 + 10y + 33.$
The binomial to be squared will be of the form $y+a$ because the coefficient of $y^2$ is 1. By squaring the binomial, we get $y^2+2ay+a^2$. We want $2ay$ to be equal to $10y$, therefore $a=5$. $(y+5)^2=y^2+10y+25$.
$y^2+10y+33=(y^2+10y+25)+8=(y+5)^2+8$. Therefore, the b... | 4 |
a coin is tossed 6 times . what is the probability of getting exactly 5 heads ? | [
"3 / 8",
"3 / 32",
"7 / 64",
"3 / 16"
] | B | "the number of possible outcomes is 2 ^ 6 = 64 there are 6 ways to get exactly 5 heads . p ( exactly 5 heads ) = 6 / 64 = 3 / 32 the answer is d ." | 5 |
How do decomposers obtain their food? | [
"hunting and killing prey for food",
"changing carbon dioxide and water into food",
"absorbing food from dead organisms",
"producing food from oxygen and sunlight"
] | C | 1 | |
in a box of 8 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ? | [
"4 / 13",
"6 / 17",
"3 / 11",
"5 / 14"
] | D | "p ( neither pen is defective ) = 5 / 8 * 4 / 7 = 5 / 14 the answer is d ." | 5 |
How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5? | [
"1295",
"5607",
"4999",
"620"
] | A | We have 6 digits to choose from: 0, 1, 6, 7, 8, and 9. We therefore have 6 choices for each of the digits in a 4-digit number, where we think of numbers with fewer than four digits as having leading 0s. (For example, 0097 is 97.) Since we have 6 choices for each of the four digits in the number, there are $6^4 = 129... | 4 |
An antigen is a macromolecule that reacts with components of what? | [
"immune system",
"circulatory system",
"digestion system",
"pulmonary system"
] | A | Figure 42.10 An antigen is a macromolecule that reacts with components of the immune system. A given antigen may contain several motifs that are recognized by immune cells. Each motif is an epitope. In this figure, the entire structure is an antigen, and the orange, salmon and green components projecting from it repres... | 7 |
The important equation pv = nrt holds true for substances in what state of matter? | [
"products",
"liquids",
"solids",
"gas"
] | D | PV = nRT This equation is known as the ideal gas law. An ideal gas is defined as a hypothetical gaseous substance whose behavior is independent of attractive and repulsive forces and can be completely described by the ideal gas law. In reality, there is no such thing as an ideal gas, but an ideal gas is a useful concep... | 7 |
Which best describes a parallel circuit? | [
"Electricity flows along one pathway.",
"The flow of electricity comes from one source.",
"Electricity flows along more than one pathway.",
"The flow of electricity comes from more than one source."
] | C | 0 | |
Amoebas have zero options and must preform | [
"zero duties",
"most duties",
"all responsibilities",
"some duties"
] | C | if a cell can not specialize then that cell must perform all life functions | 6 |
a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between th... | [
"85",
"59",
"210",
"215"
] | B | the average of existing 2 package is 150 + 280 / 2 = 430 / 2 = 215 remaining allowed weight = 1100 - 200 - 430 = 470 . allowed per package = 470 / 3 = 156 so difference in average of existing and allowable = 215 - 156 = 59 hence a | 5 |
A class planted trees and shrubs in an empty dirt lot beside the school. The roots of the plants can help protect the soil. The soil is most likely being protected from what? | [
"a drought",
"wind erosion",
"an earthquake",
"water pollution"
] | B | 1 | |
Happy Island has 60 turtles. This means there are 10 more than 2 times as many turtles on Happy Island as on Lonely Island. How many turtles are there on Lonely Island? | [
"130.0",
"25.0",
"56.0",
"120.0"
] | B | After subtracting 10 from the number of turtles on Happy Island, we get 60 - 10 = <<60-10=50>>50 turtles
Dividing this number by two, we find that the number of turtles on Lonely Island is 50/2=<<50/2=25>>25 turtles.
#### 25 | 3 |
according to the directions on a can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 4 cans of water to make orange juice . how many 12 ounce cans of concentrate are required to prepare 120 6 - ounce servings of orange juice ? | [
"10",
"18",
"16",
"12"
] | D | 1 x 12 ounce can of concentrate + 4 x 12 ounce cans of water = 60 ounces of the mixture . 60 ounces of mixture gives ( 60 / 6 ) = 10 servings . thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture . to make 120 servings of the mixture , we need 120 / 10 = 12 cans of the concentrate . the a... | 5 |
the ratio of 2 numbers is 3 : 7 and their h . c . f . is 10 . their l . c . m . is ? | [
"210",
"220",
"252",
"236"
] | A | "let the numbers be 3 x and 7 x their h . c . f . = 10 so the numbers are 3 * 10 , 7 * 10 = 30,70 l . c . m . = 210 answer is b" | 5 |
a man took a loan from a bank at the rate of 8 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | [
"rs . 2000",
"none",
"rs . 10",
"rs . 22"
] | D | solution principal = rs . ( 100 x 5400 / 8 x 3 ) = rs . 22,500 . answer d | 5 |
When a dog smells food and begins drooling, it is responding to an external stimulus. Which of these describes a response to an internal stimulus? | [
"A cat sees a mouse and crouches.",
"A parrot hears a name and repeats it.",
"A person eats spoiled food and vomits.",
"A worm senses water and moves to the surface."
] | C | 1 | |
the sector of a circle has radius of 21 cm and central angle 130 o . find its perimeter ? | [
"89.7",
"91.7",
"91.1",
"91.4"
] | A | "perimeter of the sector = length of the arc + 2 ( radius ) = ( 130 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 47.7 + 42 = 89.7 cm answer : a" | 5 |
What can renewable resources can be replaced by? | [
"human processes",
"change processes",
"natural processes",
"fossil fuels"
] | C | Renewable resources can be replaced by natural processes as quickly as they are used. | 7 |
an alloy of copper and zinc contains copper and zinc in the ratio 5 : 3 . another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ? | [
"4 : 3",
"7 : 3",
"1 : 5",
"3 : 1"
] | D | "alloy - 1 : copper : zinc = 5 : 3 , let quantity = x i . e . copper in alloy - 1 = [ 5 / ( 5 + 3 ) ] * x = ( 5 / 8 ) x and zinc in alloy - 1 = [ 3 / ( 5 + 3 ) ] * x = ( 3 / 8 ) x alloy - 2 : copper : zinc = 1 : 7 , let quantity = y i . e . copper in alloy - 2 = [ 1 / ( 1 + 7 ) ] * y = ( 1 / 8 ) y and zinc in alloy - 1... | 5 |
The first four terms in an arithmetic sequence are $x + y, x - y, xy,$ and $x/y,$ in that order. What is the fifth term? | [
"\\frac{1}{1 - a}",
"\\frac{123}{40}",
"\\frac{1}{5}",
"-2x"
] | B | Note that $(x - y) - (x + y) = xy - (x - y),$ which simplifies to $xy - x + 3y = 0.$ Solving for $x,$ we find
\[x = \frac{3y}{1 - y}.\]Also, $(x - y) - (x + y) = \frac{x}{y} - xy,$ which simplifies to
\[\frac{x}{y} - xy + 2y = 0.\]Substituting $x = \frac{3y}{1 - y},$ we get
\[\frac{3}{1 - y} - \frac{3y^2}{1 - y} + 2y ... | 4 |
what is the rate percent when the simple interest on rs . 910 amount to rs . 260 in 4 years ? | [
"7.14",
"3.14",
"5.14",
"2.14"
] | A | "260 = ( 910 * 4 * r ) / 100 r = 7.14 % answer : a" | 5 |
What conveys signals received by the eye to the brain? | [
"sciatic nerve",
"optic nerve",
"motor nerve",
"sensory nerve"
] | B | 26.1 Physics of the Eye The eye is perhaps the most interesting of all optical instruments. The eye is remarkable in how it forms images and in the richness of detail and color it can detect. However, our eyes commonly need some correction, to reach what is called “normal” vision, but should be called ideal rather than... | 7 |
if d = 1 / ( 2 ^ 3 * 5 ^ 8 ) is expressed as a terminating decimal , how many nonzero digits will d have ? | [
"one",
"seven",
"three",
"two"
] | D | "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 8 ) = multiply and divide by 2 ^ 5 = 2 ^ 5 / ( 2 ^ 3 * 2 ^ 5 * 5 ^ 8 ) = 2 ^ 5 / 10 ^ 8 = > non zero digits are 32 = > ans b" | 5 |
on a scale of map , 0.6 cm represent 6.6 km . if the distance between the points on the map is 80.5 cm , the actual distance between these points is : | [
"885.5 km",
"none of these",
"72.5 km",
"9 km"
] | A | solution let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) ∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6 x = 80.5 × 6.6 ⇔ x = ⇔ x = 80.5 x 6.6 / 0.6 = x = 885.5 . answer d | 5 |
there is a 20 % chance sandy will visit china this year , while there is a 70 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? | [
"48 %",
"70 %",
"54 %",
"62 %"
] | D | "p ( china and not malaysia ) = 0.2 * 0.3 = 0.06 p ( malaysia and not china ) = 0.7 * 0.8 = 0.56 total probability = 0.06 + 0.56 = 0.62 = 62 % the answer is d ." | 5 |
Milo is making a giant loaf of bread, and the recipe calls for pounds of eggs instead of telling him the number. He needs 6 pounds in total. He looks up online that an egg weighs 1/16 of a pound. If he needs 6 pounds of eggs, how many dozen should he buy? | [
"8.0",
"660.0",
"1.0",
"100.0"
] | A | If one egg weighs 1/16 of a pound then 1 pound will be made up of 1/(1/16) = 16 eggs
One pound of eggs is 16 eggs so 6 pounds is 6*16 = <<6*16=96>>96 eggs
One dozen is 12 eggs so 96 eggs will make 96/12 = <<96/12=8>>8 dozens
#### 8 | 3 |
Dots are spaced one unit part, horizontally and vertically. What is the number of square units enclosed by the polygon?
[asy]
/* AMC8 1998 #6P */
size(1inch,1inch);
pair a=(0,0), b=(10,0), c=(20,0), d=(30, 0);
pair e=(0,10), f=(10,10), g=(20,10), h=(30,10);
pair i=(0,20), j=(10,20), k=(20,20), l=(30,20);
pair m=(0,30),... | [
"6",
"\\frac{4963}{230}",
"9",
"8"
] | A | Slide triangle $A$ down to fill in triangle $B$. The resulting $2\times 3$ rectangle has area $\boxed{6}$. [asy]
/* AMC8 1998 #6S */
size(1inch,1inch);
pair a=(0,0), b=(10,0), c=(20,0), d=(30, 0);
pair e=(0,10), f=(10,10), g=(20,10), h=(30,10);
pair i=(0,20), j=(10,20), k=(20,20), l=(30,20);
pair m=(0,30), n=(10,30), o... | 4 |
there are two names given johnson and jones . if one letter is picked from both simultaneously at random , then find the probability that the letter is same ? | [
"17 / 35",
"24 / 35",
"6 / 35",
"1 / 25"
] | C | this question can also be solved by using ' brute force ' - you just have to ' map out ' the possibilities . the namejohnsonhas 7 letters and the namejoneshas 5 letters , so there are ( 7 ) ( 5 ) = 35 possible pairings of letters that can occur . of those 35 , the pairings that include the same letter both times are : ... | 5 |
What is the layer above the mesophere called? | [
"thermosphere",
"troposphere",
"stratosphere",
"exosphere"
] | C | The mesosphere is the layer above the stratosphere. It rises to about 85 kilometers (53 miles) above the surface. Temperature decreases with altitude in this layer. | 7 |
after decreasing 50 % in the price of an article costs rs . 620 . find the actual cost of an article ? | [
"1100",
"1200",
"1240",
"1500"
] | C | "cp * ( 50 / 100 ) = 620 cp = 12.4 * 100 = > cp = 1240 answer : b" | 5 |
what is the total number of d integers between 100 and 200 that are divisible by 3 ? | [
"33",
"31",
"32",
"30"
] | A | yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as ... | 5 |
Given that $x$ is real and $x^3+\frac{1}{x^3}=52$, find $x+\frac{1}{x}$. | [
"0.58",
"\\pm2\\sqrt{3}\\pm\\sqrt{12}",
"\\frac{52}{x^4}",
"4"
] | D | We know that $$\left(x+\frac{1}{x}\right)^3=x^3+3(x^2)\left(\frac{1}{x}\right)+3(x)\left(\frac{1}{x}\right)^2+\left(\frac{1}{x}\right)^3=x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right).$$Let $x+\frac{1}{x}=a$. Then our equation is $a^3=x^3+\frac{1}{x^3}+3a$. We know $x^3+\frac{1}{x^3}=52$, so we have $a^3=52+3a$ or $a^3-... | 4 |
a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length | [
"30 seconds",
"50 seconds",
"40 seconds",
"none of these"
] | C | "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds option c" | 5 |
what is 15 % of 2 / 3 of 0.7 ? | [
"none of the above",
"0.9",
"90",
"0.07"
] | D | "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 7 / 10 ) = 210 / 3000 = 0.07 option a" | 5 |
Which phylum is made up of segmented worms such as earthworms? | [
"annelida",
"nematoda",
"arthropod",
"chordata"
] | A | The phylum Annelida is made up of segmented worms such as earthworms. Segmented worms are divided into many repeating segments. There are roughly 15,000 species of annelids. Most belong to one of three classes. A species in each class is pictured in Figure below . | 7 |
in one hour , a boat goes 13 km / hr along the stream and 9 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is : | [
"11 kmph",
"15 kmph",
"14 kmph",
"13 kmph"
] | A | "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 13 + 9 ) kmph = 11 kmph . answer : option a" | 5 |
the area of a circle is increased by 300 % . by what percent has the radius of the circle increased ? | [
"800 %",
"100 %",
"400 %",
"600 %"
] | B | "the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : c" | 5 |
Rachel makes $12.00 as a waitress in a coffee shop. In one hour, she serves 20 different people and they all leave her a $1.25 tip. How much money did she make in that hour? | [
"37.0",
"31.0",
"25.0",
"242.5"
] | A | She served 20 people and they all tipped her $1.25 so she made 20*1.25 = $<<20*1.25=25.00>>25.00 in tips
She makes $12.00 an hour and she made $25.00 in tips so she made 12+25 = $<<12+25=37.00>>37.00 in one hour
#### 37 | 3 |
renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ? | [
"1.2",
"4.6",
"4.8",
"4.7"
] | C | "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 8 = 5 / 24 suma can do it alone in 4.8 days . answer : a" | 5 |
if 6 spiders make 6 webs in 6 days , then 1 spider will make 1 web in how many days ? | [
"7",
"4",
"6",
"3"
] | C | "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 6 webs 6 : 1 1 x 6 x x = 6 x 1 x 6 = > x = 6 answer is b" | 5 |
what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 4 ? | [
"2",
"4",
"none of the above",
"3"
] | C | "notice that in the brackets we have the sum of 9 even multiples of 4 , hence the sum in the brackets will be even multiple of 4 ( the sum of 9 even numbers is even ) . which yields remainder of 0 upon division by 4 . answer : e" | 5 |
For her gift present, Lisa has saved $1200. She asks her mother, as well as her brother, to help her raise the total amount of money she needs to buy the gift.,If her mother gave her 3/5 times of what she had saved and her brother gave her twice the amount her mother gave her, calculate the price of the gift she wanted... | [
"400.0",
"760.0",
"3760.0",
"100.0"
] | C | Lisa's mother gave her 3/5*$1200 = $<<3/5*1200=720>>720 for her birthday gift.
She also received 2*$720 = $<<2*720=1440>>1440 from her brother for the gift.
If she still had to find $400 to fully reach her birthday gift cost, it means her gift's total cost was $1200+$1440+$720+$400 = $<<1200+1440+720+400=3760>>3760
###... | 3 |
Many ionic compounds with relatively large cations and a 1:1 cation:anion ratio have this structure, which is called the what? | [
"cesium chloride structure",
"boron chloride structure",
"analogous structure",
"hydrocarbon structure"
] | A | Common Structures of Binary Compounds As shown in part (a) in Figure 12.8 "Holes in Cubic Lattices", a simple cubic lattice of anions contains only one kind of hole, located in the center of the unit cell. Because this hole is equidistant from all eight atoms at the corners of the unit cell, it is called acubic hole. A... | 7 |
three numbers are in the ratio 4 : 5 : 6 and their average is 42 . the largest number is : | [
"28",
"36",
"45",
"50.4"
] | D | "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 42 15 x = 126 x = 8.4 largest number = 6 x = 50.4 . answer d" | 5 |
Find the range of the function
\[f(x) = \frac{\sin^3 x + 6 \sin^2 x + \sin x + 2 \cos^2 x - 8}{\sin x - 1},\]as $x$ ranges over all real numbers such that $\sin x \neq 1.$ Enter your answer using interval notation. | [
"[1,1]",
"[0,2 \\pi)",
"[2,12)",
"\\left\\lbrack -\\sqrt{3} , \\sqrt{3} \\right\\rbrack"
] | C | Since $\cos^2 x = 1 - \sin^2 x,$ we can write
\begin{align*}
f(x) &= \frac{\sin^3 x + 6 \sin^2 x + \sin x + 2(1 - \sin^2 x) - 8}{\sin x - 1} \\
&= \frac{\sin^3 x + 4 \sin^2 x + \sin x - 6}{\sin x - 1} \\
&= \frac{(\sin x - 1)(\sin x + 2)(\sin x + 3)}{\sin x - 1} \\
&= (\sin x + 2)(\sin x + 3) \\
&= \sin^2 x + 5 \sin x ... | 4 |
Animals need to get ready for the changing seasons in various ways. One way bears get ready for the Winter is by having their | [
"ears fall off",
"fur get thinner",
"fur get thicker",
"nose get blue"
] | C | An example of a seasonal change is an animal growing thick fur for keeping warm in the winter | 6 |
Mutation creates new genetic variation in what? | [
"form pool",
"disease pool",
"gene pool",
"mutation pool"
] | C | Mutation creates new genetic variation in a gene pool. | 7 |
there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl & 2 boys are selected ? | [
"720",
"480",
"120",
"780"
] | D | n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 and 1 girl from 10 = 13 c 2 * 10 c 1 = 780 ans - c | 5 |
When rain falls for two solid weeks, flooding will be evident | [
"at the middle of a mountain",
"inside of the mountain",
"at the base of a mountain",
"at the top of a mountain"
] | C | as elevation of a place decreases , how much a flood will affect that place will increases | 6 |
a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train . | [
"50 kmph",
"45 kmph",
"55 kmph",
"73 kmph"
] | D | "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e" | 5 |
Find $1+2\cdot3-4+5.$ | [
"",
"8",
"19",
"10"
] | B | Recall that multiplication should be done before addition and subtraction. So, \begin{align*}1+2\cdot3-4+5 &=1+(2\cdot3)-4+5\\ &=1+6-4+5=\boxed{8}.\end{align*} | 4 |
Kettles are lakes which are formed when chunks of glaciers | [
"freeze",
"drown",
"float",
"dissipate"
] | D | a kettle is formed when chunks of ice left by glaciers melt | 6 |
The substances that comprise heterogeneous mixtures can also be separated by what means? | [
"atmospheric",
"physical",
"thermal",
"chemical"
] | B | The substances that comprise heterogeneous mixtures can also be separated by physical means. We will discuss separation techniques in the following lesson. | 7 |
Keanu was surfing towards the shore at a speed of 20 miles per hour. A shark was swimming alongside him, riding the same wave, when it doubled its speed and moved away from Keanu. There was a pilot fish swimming alongside Keanu and the shark, and when the shark increased its speed, the pilot fish also increased its s... | [
"30.0",
"66.66",
"20.0",
"2.0"
] | A | The shark went from 20 miles per hour to a speed of 2*20=40 miles per hour.
The shark increased its speed by 40-20=<<40-20=20>>20 miles per hour.
Half of the shark's increase in speed is 20/2=<<20/2=10>>10 miles per hour.
Thus the pilot fish had increased its speed to 20+10=<<20+10=30>>30 miles per hour.
#### 30 | 3 |
What kind of variation does a rate measure? | [
"construction to time",
"value to time",
"environment to time",
"property to time"
] | D | A rate is a measure of how some property varies with time. Speed is a familiar rate that expresses the distance traveled by an object in a given amount of time. Wage is a rate that represents the amount of money earned by a person working for a given amount of time. Likewise, the rate of a chemical reaction is a measur... | 7 |
What are the subatomic particles of the nucleus called? | [
"cores",
"nucleons",
"protons",
"eukaryotes"
] | B | Summary Subatomic particles of the nucleus (protons and neutrons) are called nucleons. Anuclide is an atom with a particular number of protons and neutrons. An unstable nucleus that decays spontaneously is radioactive, and its emissions are collectively called radioactivity. Isotopes that emit radiation are Saylor URL:... | 7 |
if you write down all the numbers from 1 to 50 , then how many times do you write 3 ? | [
"e ) 22",
"c ) 20",
"a ) 11",
"b ) 15"
] | D | "explanation : explanation : clearly , from 1 to 50 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 , 33 , 43 , and ten numbers with 3 as the ten ' s digit - 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 . so , required number = 5 + 10 = 15 . answer : b" | 5 |
Let $z$ be a complex number such that $|z| = 2.$ Find the largest possible distance between $(3 + 4i)z^3$ and $z^5$ when plotted in the complex plane. | [
"\\frac{1}{4}",
"63 - 80 = \\boxed{-17}",
"7",
"72"
] | D | We want to maximize
\[|(3 + 4i)z^3 - z^5| = |z^3| |3 + 4i - z^2| = |z|^3 |3 + 4i - z^2| = 8 |3 + 4i - z^2|.\]In other words, we want to maximize the distance between $3 + 4i$ and $z^2.$
Since $|z| = 2,$ the set of complex numbers of the form $z^2$ lie on a circle with radius $|z|^2 = 4.$ The distance between $3 + 4i$ ... | 4 |
Quadrilateral $ABCD$ is a square, and segment $AE$ is perpendicular to segment $ED$. If $AE = 8$ units and $DE = 6$ units, what is the area of pentagon $AEDCB$, in square units? [asy]
size(150);
pair A, B, C, D, E;
A=(0,10);
B=(0,0);
C=(10,0);
D=(10,10);
E=(6.4,5.2);
draw(A--B--C--D--A);
draw(A--E--D);
label("A", A, NW... | [
"24+.20=26",
"\\frac{4}{3}",
"18",
"76"
] | D | Noticing that $ADE$ is a 3-4-5 right triangle scaled by a factor of 2, we have $AD=2 \cdot 5=10$. Thus, the area of square $ABCD$ is $10 \cdot 10=100$. The area of triangle $ADE$ is $\frac{1}{2}\cdot 6 \cdot 8=3 \cdot 8=24$. Finally, we calculate the area of pentagon $ABCDE$ to be the difference of the two: $100-24=\bo... | 4 |
Any organism that causes disease is called what? | [
"a microbe",
"a pathogen",
"a parasite",
"a virus"
] | B | You have ten times as many bacterial cells as human cells in your body. Luckily for you, most of these bacteria are harmless. However, some of them can cause disease. Any organism that causes disease is called a pathogen . Diseases caused by bacterial pathogens include food poisoning, strep throat, and Lyme disease. | 7 |
how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 30 km / hr ? | [
"60",
"45",
"25",
"30"
] | A | "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 400 / 6.66 ) sec = 60 sec . answer : e" | 5 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.