Cheukting/mathqa huggingface dataset:
Question (general): at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 75 . if the restaurant serves 120 customers today , raising the average to 80 customers per day , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 8 , e ) 20
Rationale: "withoutusing the formula , we can see that today the restaurant served 40 customers above the average . the total amount above the average must equal total amount below the average . this additional 40 customers must offset the “ deficit ” below the average of 80 created on the x days the restaurant served only 75 customers per day . 40 / 5 = 8 days . choice ( a ) . withthe formula , we can set up the following : 80 = ( 75 x + 120 ) / ( x + 1 ) 80 x + 80 = 75 x + 120 5 x = 40 x = 8 answer choice ( d )"
Answer: d
Question (general): dividing by 3 ⁄ 6 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 3
Rationale: "say x / 3 / 6 * 5 / 6 = x * 6 / 3 * 5 / 6 = x * 5 / 3 e"
Answer: e
Question (gain): an inspector rejects 15 % of the meters as defective . how many will he examine to reject 15 ?
Options: a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 15 % of x = 15 ( 15 / 100 ) x = 15 x = ( 15 * 100 * ) / 15 = 100 answer is a"
Answer: a
Question (physics): pipe a fills a tank of capacity 700 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 700 = 50 * n = > n = 14 here n = number of cycles . total time = 14 * 3 = 42 as in one cycle there are 3 minutes . thus 42 minutes answer : a"
Answer: a
Question (geometry): the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 6 , b ) 16 , c ) 8 , d ) 36 , e ) none
Rationale: "2 x * x = 72 = > x = 6 answer : a"
Answer: a
Question (physics): a man can row upstream at 10 kmph and downstream at 20 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 77 , c ) 25 , d ) 88 , e ) 34
Rationale: "us = 20 ds = 30 m = ( 30 + 20 ) / 2 = 25 answer : c"
Answer: c
Question (physics): a and b can finish a work together in 12 days , and b and c together in 16 days . if a alone works for 5 days and then b alone continues for 7 days , then remaining work is done by c in 13 days . in how many days can c alone finish the complete work ?
Options: a ) 22 days , b ) 21 days , c ) 25 days , d ) 24 days , e ) 23 days
Rationale: here lcm of 12 and 16 is taken as total work . ( becomes easy to solve ) assume total work = 48 units then workdone by ( a + b ) in one day = 48 / 12 = 4 units similarly , by ( b + c ) in one day = 48 / 16 = 3 units now according to question , a works 5 days , b for 7 days and c for 13 days to complete total work so , 5 a + 7 b + 13 c = 48 units 5 ( a + b ) + 2 ( b + c ) + 11 c = 48 units 5 * 4 + 2 * 3 + 11 c = 48 units 11 c = 22 units c = 2 units ( c does 2 units of work daily ) therefore , 48 / 2 = 24 days c requires 24 days to complete the work alone . answer d
Answer: d
Question (general): the ages of two person , differ by 20 years . if 5 years ag , the elder one be 5 times as old as the younger one their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 2010 , c ) 3515 , d ) 5117 , e ) 20,17
Rationale: let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a
Answer: a
Question (general): the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?
Options: a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.52 % , e ) 2 %
Rationale: ( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d
Answer: d
Question (geometry): the mass of 1 cubic meter of a substance is 400 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "400 kg - 1 cubic meter ; 400,000 g - 1 cubic meter ; 400,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 400,000 = 10 / 4 = 2.5 cubic centimeters . answer : b ."
Answer: b
Question (general): for what value of â € œ k â €  will the equation ( 2 kx 2 + 5 kx + 1 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 8 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "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 ( 5 k ) ^ 2 - 4 * 2 k * 1 = 0 by solving this equation we get k = 0 , k = 8 / 25 answer : c"
Answer: c
Question (general): in a class of 25 students , 2 students did not borrow any books from the library , 10 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 13 , e ) 15
Rationale: "the average number of books per student was 2 means that total of 2 * 25 = 50 books were borrowed ; 2 + 10 + 8 = 20 students borrowed total of 2 * 0 + 10 * 1 + 8 * 2 = 26 books ; so 50 - 26 = 24 books are left to distribute among 25 - 20 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 4 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 24 - 12 = 12 books . answer : c ."
Answer: c
Question (physics): a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 24 cm . what is the length of the wire ?
Options: a ) 6 cm , b ) 4 cm , c ) 8 cm , d ) 3 cm , e ) 9 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 24 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 4 cm answer : b"
Answer: b
Question (general): boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d .
Answer: d
Question (physics): a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in meters ) is :
Options: a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these
Rationale: "speed = ( 5 * 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 * 15 * 60 ) m = 1250 m . correct option : d"
Answer: d
Question (physics): a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 14 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 14 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2 m / s a"
Answer: a
Question (gain): mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8010 / - . find out the amount that he borrowed .
Options: a ) s . 5266 , b ) s . 5269 , c ) s . 5228 , d ) s . 5201 , e ) s . 52192
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8010 = p + ( 54 p / 100 ) 8010 = ( 100 p + 54 p ) / 100 8010 = 154 p / 100 p = ( 8010 * 100 ) / 154 = rs . 5201.298 answer : d"
Answer: d
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2340 , e ) 2300
Rationale: "d number of valid votes = 80 % of 6500 = 5200 . valid votes polled by other candidate = 45 % of 5200 = ( 45 / 100 x 5200 ) = 2340 ."
Answer: d
Question (general): if 9 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 4 is allowed . imo b .
Answer: b
Question (general): if 21 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) d , e ) 7
Rationale: "21 - 7 * 3 18 - 3 * 3 * 2 15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 9 is allowed . imo d ."
Answer: d
Question (general): the average of 13 result is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 46 , d ) 48 , e ) 50
Rationale: sum of all the 13 results = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . c
Answer: c
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , ( . . . )
Options: a ) 53 , b ) 67 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 67 answer : b"
Answer: b
Question (general): if x / ( 9 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c"
Answer: c
Question (gain): after decreasing 25 % in the price of an article costs rs . 1500 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1300 , c ) 1200 , d ) 2000 , e ) 1500
Rationale: "cp * ( 75 / 100 ) = 1500 cp = 20 * 100 = > cp = 2000 answer : d"
Answer: d
Question (geometry): if the sides of a triangle are 52 cm , 48 cm and 20 cm , what is its area ?
Options: a ) 480 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"
Answer: a
Question (general): 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ?
Options: a ) 4264 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 881
Rationale: "x * ( 95 / 100 ) * ( 85 / 100 ) = 3443 x = 4264 answer : a"
Answer: a
Question (gain): adam borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years , and at the rate of 14 % p . a . for the period beyond 4 years . if he pays a total interest of 11900 at the end of 9 years , how much money did he borrow ?
Options: a ) 10,526 , b ) 12,526 , c ) 14,000 , d ) 16,000 , e ) 16,536
Rationale: let the sum borrowed be x . then , ( x × 6 × 21 / 00 ) + ( x × 9 × 3 / 100 ) + ( x × 14 × 4 / 100 ) = 11900 ⇒ ( 3 ⁄ 25 x + 27 ⁄ 100 x + 14 ⁄ 25 x ) = 11400 ⇒ 95 ⁄ 100 x = 11900 ⇒ x = ( 11900 × 100 / 95 ) = 12526 hence , sum borrowed = 12,526 answer b
Answer: b
Question (physics): 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 6 men , 4 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 8 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 6 men ’ s 1 day ’ s work = 1 × 6 / 96 = 1 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 6 men + 4 women + 10 children ) ’ s 1 day ’ s work = 1 / 16 + 1 / 48 + 1 / 24 = 1 / 8 the required no . of days = 8 days answer : option d"
Answer: d
Question (general): if henry were to add 6 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 48 , c ) 64 , d ) 80 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 6 galls 1 / 8 * x = 6 gallons x = 48 gallons answer b"
Answer: b
Question (physics): in what time will a railway train 120 m long moving at the rate of 70 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 120 / 70 * 18 / 5 = 6 sec answer : d"
Answer: d
Question (gain): there are 400 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "there are 396 managers and 4 others . the 4 others would compose 2 % of the total number of people if there were 200 people in the room . thus 200 managers must leave . the answer is d ."
Answer: d
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 97 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 33 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 97 % water and 3 % of non - water , so now 1 pound of non - water composes 3 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.03 = 34 pounds . answer : b ."
Answer: b
Question (physics): the two trains of lengths 400 m , 600 m respectively , running at same directions . the faster train can cross the slower train in 180 sec , the speed of the slower train is 48 km . then find the speed of the faster train ?
Options: a ) 76 kmph , b ) 68 kmph , c ) 87 kmph , d ) 56 kmph , e ) 10 kmph
Rationale: length of the two trains = 600 m + 400 m speed of the first train = x speed of the second train = 48 kmph 1000 / x - 48 = 180 1000 / x - 48 * 5 / 18 = 180 50 = 9 x - 120 x = 68 kmph answer : b
Answer: b
Question (physics): a light flashes every 5 seconds , how many times will it flash in ? of an hour ?
Options: a ) 720 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 5 sec for 1 min = 12 flashes so for 1 hour = 12 * 60 = 720 flashes . answer : a"
Answer: a
Question (general): what is the units digit of 3333 ^ ( 333 ) * 3333 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 6 . final answer : d"
Answer: d
Question (gain): a 6 litre sol is 40 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1.2 , c ) c . 2.1 , d ) d . 3 , e ) e . 5.4
Rationale: "40 % of 6 = 2.4 50 % of 6 = 3 shortage is 0.6 so we need to have 0.6 / 50 % to get 50 % alcohol content . = 1.2 b"
Answer: b
Question (general): in how many ways can the integer 54 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "54 = ( 3 ^ 3 ) * 2 since 54 is not a perfect square , no of ways = 4 answer d"
Answer: d
Question (other): find the number of different prime factors of 2400
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "explanation : l . c . m of 2400 = 3 x 2 x 2 x 2 x 2 x 2 x 5 x 5 3 , 2 , 5 number of different prime factors is 3 . answer : option c"
Answer: c
Question (general): in arun ' s opinion , his weight is greater than 63 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 66 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 64.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 63 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 66 . the values satisfying all the above conditions are 64 and 65 . required average = ( 64 + 65 ) / 2 = 64.5 kg answer : b"
Answer: b
Question (other): a cat leaps 5 leaps for every 4 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 5 : 6 , b ) 3 : 2 , c ) 4 : 8 , d ) 1 : 2 , e ) 7 : 8
Rationale: given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 5 / 3 * 4 = 5 : 6 . ' ' answer : 5 : 6 ;
Answer: a
Question (gain): the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ?
Options: a ) 2000 , b ) 2778 , c ) 1840 , d ) 2778 , e ) 2771
Rationale: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 115 % of rs . 1600 = 115 / 100 * 1600 = rs . 1840 . answer : c"
Answer: c
Question (general): a is an integer greater than 19 but less than 32 , b is an integer greater than 29 but less than 42 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 20 and b = 40 so , a / b = 1 / 2 max value of a / b will be when b is lowest and a is highest - - - > a = 30 and b = 30 so , a / b = 1 range is 1 - ( 1 / 2 ) = 1 / 2 . answer should be b"
Answer: b
Question (gain): rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 125 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 2688 , d ) 1000 , e ) 2500
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 125 x = 2500 answer : e"
Answer: e
Question (physics): jerry travels 8 miles at an average speed of 40 miles per hour , stops for 13 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 48 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 13 minutes + ( 20 / 60 ) * 60 minutes = 35 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 35 / 60 ) hours = 28 * 60 / 35 = 48 miles per hour answer : option a"
Answer: a
Question (general): the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 18 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 2,109
Rationale: first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 18 and c = 1 / 2 into the equation and simplify to get the answer 2109 . option e .
Answer: e
Question (geometry): surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ?
Options: a ) 1 : 9
b ) 1 : 8
c ) 1 : 3
d ) 1 : 4
e ) 1 : 5
Rationale: 1 : 8 answer : b
Answer: b
Question (geometry): if the area of a circle decreases by 30 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 16 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 30 ) % = ( 100 − 10 √ 70 ) % = 100 - 84 = 16 % answer b"
Answer: b
Question (probability): two unbiased coins are tossed . what is the probability of getting at most one head ?
Options: a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 1 / 2
Rationale: "s = { hh , tt , ht , th } e = event of getting at most one head . e = { tt , ht , th } . p ( e ) = n ( e ) / n ( s ) = 3 / 4 answer is option c"
Answer: c
Question (general): the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 25 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347 , b ) 987 , c ) 1070 , d ) 1371 , e ) 1667
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 25 = 2 r a = 12 / 5 r and r = 75 a = 180 required total cost = 4 * 180 + 3 * 75 + 5 * 25 = 720 + 225 + 125 = $ 1070 c"
Answer: c