Cheukting/mathqa huggingface dataset:
Question (physics): the sum of two consecutive integers is 21 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 10 , 11 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 21 2 n + 1 = 21 2 n = 20 n = 10 answer : c"
Answer: c
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 35 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 35 = > 4 / x = 1 / 35 x = 35 ∗ 4 = 140 mins option b"
Answer: b
Question (general): if k is a non - negative integer and 15 ^ k is a divisor of 823,435 then 5 ^ k - k ^ 5 =
Options: a ) 0 , b ) 1 , c ) 35 , d ) 120 , e ) 245
Rationale: "8 + 2 + 3 + 4 + 3 + 5 = 25 , so this number is not divisible by 3 and thus not divisible by 15 . therefore , k = 0 5 ^ k - k ^ 5 = 1 - 0 = 1 the answer is b ."
Answer: b
Question (physics): p alone can complete a job in 5 days . the work done by q alone in one day is equal to one - fourth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 2.5 , b ) 3.0 , c ) 3.5 , d ) 4.0 , e ) 4.5
Rationale: "p ' s rate is 1 / 5 q ' s rate is 1 / 20 the combined rate is 1 / 5 + 1 / 20 = 1 / 4 if they work together , the job will take 4 days . the answer is d ."
Answer: d
Question (general): the number of the members of a club is more than 10 and less than 40 . when 3 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 5 - people groups ( 5 people sit at a table ) . if the members are divided to 7 - people groups , how many people will be left ?
Options: a ) 0 . , b ) 1 . , c ) 2 . , d ) 4 . , e ) 5 .
Rationale: "the number of members is 5 k + 3 = 6 j + 3 the only number in this range which satisfies this is 33 . 33 / 7 = 4 ( 7 ) + 5 the answer is e ."
Answer: e
Question (general): what must be added to each of the numbers 7 , 11 and 19 , so that the resulting numbers may be in continued proportion ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) - 3 , e ) - 2
Rationale: let x be the required number , then ( 7 + x ) : ( 11 + x ) : : ( 11 + x ) : ( 19 + x ) ( 7 + x ) ( 19 + x ) = ( 11 + x ) 2 x 2 + 26 x + 133 = x 2 + 22 x + 121 4 x = - 12 or x = - 3 answer : d
Answer: d
Question (general): find the number , difference between number and its 3 / 5 is 64 .
Options: a ) 160 , b ) 163 , c ) 164 , d ) 165 , e ) 166
Rationale: explanation : let the number = x , then , x - ( 3 / 5 ) x = 64 , = > ( 2 / 5 ) x = 64 = > 2 x = 64 * 5 , = > x = 160 answer : option a
Answer: a
Question (physics): convert the 8 / 36 m / s into kilometers per hour ?
Options: a ) 0.8 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "8 / 36 m / s = 8 / 36 * 18 / 5 = 8 / 10 = 0.8 kmph . answer : a"
Answer: a
Question (general): the mean proportional between 234 and 104 is :
Options: a ) 12 , b ) 39 , c ) 54 , d ) 64 , e ) 156
Rationale: required mean proportion is = ( root of 234 ) ( root of 104 ) = root of ( 13 * 9 * 2 * 13 * 18 ) = ( 13 * 3 * 4 ) = 156 answer : e
Answer: e
Question (general): x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 35 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43 , c ) 40 , d ) 38.6 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 43 * 35 / 43 + 35 = 38.6 answer : d"
Answer: d
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 8 , inclusive ?
Options: a ) 420 , b ) 560 , c ) 840 , d ) 960 , e ) 1080
Rationale: "the integers are 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8 lowest positive integer that is is divisible by each of the integers 1 through 8 = 2 ^ 3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 24 * 35 = 840 answer c"
Answer: c
Question (physics): a man walks west 10 miles , then turns right towards north and walks another 10 miles . how far is he from the place he started walking .
Options: a ) 11.11 , b ) 10 , c ) 14.14 , d ) 16.15 , e ) 1
Rationale: as we can see the man moves in configuration of a right angle triangle . the man has walked on the sides and now we need to calculate the length of the hypotenuse which is the distance of the man from the starting point to his current location . since we know the length of two sides , we can find the length of hypotenuse . as per pythagoras : a ^ 2 + b ^ 2 = c ^ 2 a = 10 b = 10 10 ^ 2 + 10 ^ 2 = c ^ 2 100 + 100 = c ^ 2 200 = c ^ 2 c = squareroot 200 c = 14.14 miles ans : c
Answer: c
Question (general): the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 60 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 1 / 21 , d ) 2 / 35 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 60 / 1260 = 1 / 21 correct option : c"
Answer: c
Question (physics): a certain car uses 12 gallons of gasoline in traveling 300 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 10
Rationale: "300 / 10 = 30 . the difference is 30 - 25 = 5 . answer c"
Answer: c
Question (physics): a 300 m long train crosses a platform in 30 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 286 m , b ) 350 m , c ) 200 m , d ) 278 m , e ) 267 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 30 = 50 / 3 x = 200 m . answer : c"
Answer: c
Question (physics): a train 110 m long is running with a speed of 65 km / hr . in what time will it pass a man who is running at 7 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 8.2 , e ) 5.5
Rationale: "speed of train relative to man = 65 + 7 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the men = 110 * 1 / 20 = 5.5 sec . answer : option e"
Answer: e
Question (geometry): the radius of a cylinder is 8 m , height 13 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 2614.9 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 8 ã — 8 ã — 13 = 2614.9 m ( power 3 ) answer is b ."
Answer: b
Question (general): marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 58 % , c ) 60 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 125 . actual / projected * 100 = 75 / 125 * 100 = 60 % . answer : c ."
Answer: c
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 900 then loss of pyarelal ?
Options: a ) 610 , b ) 710 , c ) 810 , d ) 900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 900 , loss of pyarelal = 900 * 9 x / 10 x = 810 answer : c"
Answer: c
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 975 in 5 years ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "225 = ( 750 * 5 * r ) / 100 r = 6 % . answer : e"
Answer: e
Question (general): a container holds 4 quarts of diesel and 4 quarts of petrol . how many quarts of water must be added to the container to create a mixture that is 3 parts dieselto 5 parts water by petrol ?
Options: a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3
Rationale: an alternate to the alligation method is the more direct / algebraic method : let x be the amount of petrol to be added . new total amount of water = 4 + x total amount of diesel = 4 new total = 4 + 4 + x = 8 + x final ratio required ( for petrol ) = 5 / ( 5 + 3 ) = 5 / 8 thus , ( 4 + x ) / ( 8 + x ) = 5 / 8 - - > solving for x you get x = 8 / 3 . d is thus the correct answer .
Answer: d
Question (physics): at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 1.5 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 1.5 < 9 = ~ 8 . answer : b ."
Answer: b
Question (geometry): tough and tricky questions : number properties . what is the smallest positive integer x such that 1512 x is the cube of a positive integer ?
Options: a ) 7 , b ) 14 , c ) 28 , d ) 35 , e ) 49
Rationale: we want to know the smallest x that will make 1512 x a cube of some number . let ' s call that number y . let ' s first figure out what we ' re working with . the prime factorization of 450 can be visualized : . . . . . . . . . 1512 . . . . . . . . / . . . . . . . \ . . . . . . 216 . . . . . . 7 . . . . . / . . \ . . . . . . . 36 . . . . 6 . . . . . . / . \ . . . . / . \ . . . . 6 … . 6 … 2 … 3 . / . \ . . / \ 2 . . 3 2 … 3 so , we have 2 * 2 * 2 * 3 * 3 * 3 * 7 that can be multiplied together to get 1512 . now we need to figure out what we need to make 1512 * x into a cube of y ( y ^ 3 = 1512 * x ) . we have two 5 s , two 3 s , and one 2 . to arrange these numbers in identical triples ( 2 , 3,7 ) , we need at least one more 5 , one 3 , and two 2 ' s . each of these triples will give us the value of y ( 2 * 3 * 7 = 42 ) , which , multiplied by itself three times , gives us 1512 * x . looking at the factors we need to complete the triples , we get 7 * 7 = 49 . we know this is the smallest number possible because prime factors by definition can not be broken down any further . therefore , we can go with answer choice d . if time permits , we can do a sanity check . we calculated that y should be 2 * 3 * 7 , or 42 . 42 * 42 * 42 = 74088 . also , 1512 * 49 = 74088 . answer : e
Answer: e
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat - weavers in 8 days ?
Options: a ) 4 , b ) 16 , c ) 8 , d ) 1 , e ) 2
Rationale: explanation : let the required number of mats be x more mat - weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) hence we can write as ( mat - weavers ) 4 : 8 ( days ) 4 : 8 } : : 4 : x ⇒ 4 × 4 × x = 8 × 8 × 4 ⇒ x = 2 × 2 × 4 = 16 answer : option b
Answer: b
Question (general): if x + y = - 4 , and x = 6 / y , what is the value of x ^ 2 + y ^ 2 ?
Options: a ) 10 , b ) 15 , c ) 6 , d ) 4 , e ) 5
Rationale: x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 4 and x * y = 6 ( x + y ) ( x + y ) = ( - 4 ) ( - 4 ) = x ^ 2 + y ^ 2 + 2 * ( 6 ) x ^ 2 + y ^ 2 = 16 - 12 = 4 answer : d
Answer: d
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together for 4 days then the fraction of the work that is left is ?
Options: a ) 1 / 4 , b ) 1 / 10 , c ) 7 / 15 , d ) 8 / 15 , e ) 9 / 13
Rationale: "explanation : a ’ s one day work = 1 / 15 b ’ s one day work = 1 / 20 ( a + b ) ’ s one day work is = 1 / 15 + 1 / 20 = 7 / 60 their 4 days work = 4 x 7 / 60 = 7 / 15 remaining work = 8 / 15 answer : option d"
Answer: d
Question (gain): the profit obtained by selling an article for rs . 66 is the same as the loss obtained by selling it for rs . 22 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 44
Rationale: s . p 1 - c . p = c . p – s . p 2 66 - c . p = c . p - 22 2 c . p = 66 + 22 ; c . p = 88 / 2 = 44 answer : e
Answer: e
Question (general): an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2400 , what will be the difference between q and r ' s share ?
Options: a ) 1266 , b ) 3000 , c ) 2866 , d ) 2999 , e ) 2678
Rationale: "4 - - - 2000 5 - - - ? = > 3000 answer : b :"
Answer: b
Question (general): a car ferry can hold up to 60 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 4 tons ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "the weight of one car and one truck is 4.75 tons . 60 / 4.75 = 12 plus a remainder the ferry could carry 12 cars and 12 trucks for a total of 24 vehicles . the answer is d ."
Answer: d
Question (gain): if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 65 then sum is
Options: a ) s . 5000 , b ) s . 6500 , c ) s . 5800 , d ) s . 6000 , e ) s . 6200
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 65 6500 answer : b"
Answer: b
Question (probability): in a throw of dice what is the probability of ge æ « ng number greater than 1
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 6 , e ) none of these
Rationale: "explanation : number greater than 1 is 2 , 3 , 4 , 5 & 6 , so only 5 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 5 / 6 answer : e"
Answer: e
Question (gain): the price of an item is discounted 7 percent on day 1 of a sale . on day 2 , the item is discounted another 7 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 83.7 % , b ) 85.2 % , c ) 86.8 % , d ) 78.8 % , e ) 69.4 %
Rationale: "let initial price be 100 price in day 1 after 7 % discount = 93 price in day 2 after 7 % discount = 86.49 price in day 3 after 10 % discount = 77.84 so , price in day 3 as percentage of the sale price on day 1 will be = 77.84 / 93 * 100 = > 83.7 % answer will definitely be ( a )"
Answer: a
Question (general): a volunteer organization is recruiting new members . in the fall they manage to increase their number by 4 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.76 % , c ) 14.14 % , d ) 13.13 % , e ) 12.12 %
Rationale: "( 100 % + 4 % ) * ( 100 % - 19 % ) = 1.04 * . 81 = 0.8424 . 1 - 0.8424 = 15.76 % lost = - 15.76 % the answer is b the organization has lost 15.76 % of its total volunteers from fall to spring ."
Answer: b
Question (general): find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 0.81 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 2.5 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.81 ) + ( √ 0.81 ) / ( √ 0.49 ) 11 / 9 + 9 / 7 = > 2.50 answer is b"
Answer: b
Question (physics): a cubical tank is filled with water to a level of 3 feet . if the water in the tank occupies 48 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "the volume of water in the tank is h * l * b = 48 cubic feet . since h = 3 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 48 / 64 = 3 / 4 the answer is c ."
Answer: c
Question (gain): a and b began business with rs . 6000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 273 , d ) 877 , e ) 361
Rationale: "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 13 / 30 * 630 = 273 answer : c"
Answer: c
Question (probability): there are 18 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Rationale: there are 18 balls in a jar . you take out 3 blue balls without putting 3 blue balls + 15 / 5 = 6 answer : e
Answer: e
Question (gain): sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 45 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: 45 % is 15 % - points above 30 % and 15 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 1 . 1 / 2 * 70 % = 35 % the answer is c .
Answer: c
Question (general): in august , a cricket team that played 120 matches won 20 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 24 + x by solving we get x = 80 answer : d"
Answer: d
Question (general): dacid obtained 72 , 45 , 72 , 77 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 68 , c ) 87 , d ) 26 , e ) 75
Rationale: "average = ( 72 + 45 + 72 + 77 + 75 ) / 5 = 341 / 5 = 68 . answer : b"
Answer: b
Question (geometry): find the area of a parallelogram with base 24 cm and height 16 cm .
Options: a ) 379 , b ) 384 , c ) 345 , d ) 342 , e ) 376
Rationale: "area of a parallelogram = base * height = 24 * 16 = 384 cm 2 area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : option b"
Answer: b
Question (physics): two pipes a and b can fill a tank in 30 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 18 hours , b ) 15 hours , c ) 10 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 30 part filled by b in 1 hour = 1 / 45 part filled by ( a + b ) in 1 hour = 1 / 30 + 1 / 45 = 5 / 90 = 1 / 18 both the pipes together fill the tank in 18 hours answer is a"
Answer: a
Question (general): a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price d per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average d = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Question (general): a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 120,000 and variables costs averaging $ 8 per item . if the manufacturer ’ s selling price per item is $ 12 , how many items the manufacturer produce and sell to earn an annual profit of $ 140,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 21,429 , d ) 35,000 , e ) 65,000
Rationale: "let the items manufactured or sold bex 120000 + 8 x = 12 x - 140000 4 x = 260000 x = 65000 ans : e"
Answer: e
Question (physics): there are 20 poles with a constant distance between each pole . a car takes 24 seconds to reach the 12 th pole . how much time will it take to reach the last pole ?
Options: a ) 25.25 s , b ) 17.45 s , c ) 35.75 s , d ) 41.45 s , e ) none of these
Rationale: let the distance between each pole be x m . then , the distance up to 12 th pole = 11 xm speed = 11 x ⁄ 24 m / s time taken to covers the total distance of 19 x = 19 x × 24 / 11 x = 41.45 s answer d
Answer: d
Question (other): in a group of 90 students , 36 are taking history , and 32 are taking statistics . if 57 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 25 , d ) 27 , e ) 31
Rationale: number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 57 number of students taking neither history nor statistics = n = 90 - 57 = 33 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 32 + 33 - x or x = 11 now , number of students taking only history will be h - x or 36 - 11 = 25 answer : - c
Answer: c
Question (general): if a - b = 4 and a 2 + b 2 = 18 , find the value of ab .
Options: a ) 9 , b ) 1 , c ) 2 , d ) 18 , e ) 19
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 18 - 16 = 2 ab = 1 . answer : b"
Answer: b
Question (physics): one computer can upload 100 megabytes worth of data in 5 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 40 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 5 seconds then in 5 * 8 = 40 seconds it can upload 8 * 100 = 800 megabytes worth of data , hence the second computer in 40 seconds uploads 1300 - 800 = 500 megabytes worth of data . the second computer can upload 100 megabytes of data in 8 seconds . answer : b ."
Answer: b
Question (general): a batsman makes a score of 88 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 40 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 88 = 17 x therefore x = 40 answer : c"
Answer: c
Question (physics): two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 2 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 2 days = 2 ( 1 / 18 ) = 1 / 9 . answer d"
Answer: d
Question (general): find the area between two concentric circles defined by x 2 + y 2 - 2 x + 4 y + 1 = 0 x 2 + y 2 - 2 x + 4 y - 11 = 0
Options: a ) 11 pi , b ) 12 pi , c ) 13 pi , d ) 14 pi , e ) 15 pi
Rationale: rewrite equations of circles in standard form . hence equation x 2 + y 2 - 2 x + 4 y + 1 = 0 may be written as ( x - 1 ) 2 + ( y + 2 ) 2 = 4 = 22 and equation x 2 + y 2 - 2 x + 4 y - 11 = 0 as ( x - 1 ) 2 + ( y + 2 ) 2 = 16 = 42 knowing the radii , the area of the ring is pi ( 4 ) 2 - pi ( 2 ) 2 = 12 pi correct answer is b ) 12 pi
Answer: b
Question (physics): stacy has a 63 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 8.5 , e ) 21
Rationale: "63 / 3 = 21 answer : e"
Answer: e