Cheukting/mathqa huggingface dataset:
Question (general): when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 40 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 60 % ( 100 - 40 ) . therefore 0.5 x amount of flower - nectar = 0.60 x amount of honey = 0.60 x 1 kg therefore amount of flower - nectar needed = ( 0.60 / 0.51 ) kg = 1.2 kgs answer : a"
Answer: a
Question (general): sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 7000 ?
Options: a ) 4966 , b ) 2477 , c ) 2877 , d ) 7991 , e ) 8881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 answer : d"
Answer: d
Question (other): the number of sailors on a ship is 50 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 3 : 2 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.50 * officer sailor / officer = 1.50 / 1 = 150 / 100 = 3 / 2 answer will be c"
Answer: c
Question (general): in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 5,4 ) , and ( 5,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8
Rationale: the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b .
Answer: b
Question (general): we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value q of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: q - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .
Answer: a
Question (general): 3 numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d
Answer: d
Question (physics): 20 men do a work in 20 days . how many men are needed to finish the work in 5 days ?
Options: a ) 50 , b ) 20 , c ) 80 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 5 days = 20 * 20 / 5 = 80 answer is c"
Answer: c
Question (gain): a man can row his boat with the stream at 22 km / h and against the stream in 10 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 22 us = 10 s = ? s = ( 22 - 10 ) / 2 = 6 kmph answer : b"
Answer: b
Question (gain): suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 35000 × 8 ) : ( 42000 × 10 ) = 2 : 3 . suganya ' s share = rs . ( 31570 × 2 / 5 ) = rs . 12628 . answer c"
Answer: c
Question (physics): roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 7 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 40 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 7 + 3 ) * 4 = 40 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Question (general): if xy denotes x is raised to the power y , find the last two digits of 19413846 + 19614181
Options: a ) 67 , b ) 74 , c ) 82 , d ) 98 , e ) 34
Rationale: 1941 ^ 3846 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 6 = 24 = 2 means last two digit = 41 and 1972 ^ 4181 unit digit = 1 10 th digit = 7 * 2 = 14 mean last two digit = 41 hence , 41 + 41 = 82
Answer: c
Question (general): all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 156 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1248 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 156 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 156 = 3 k + 156 = > 2 k = 312 = > k = 156 the initial quantity of milk in a = 8 k = 8 * 156 = 1248 liters ."
Answer: a
Question (probability): the chance of rain on any given day in tel - aviv is 50 % . what is the probability a that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days a = 15 / 64 ans a it is ."
Answer: a
Question (physics): a 300 m long train crosses a platform in 27 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 ) 277 m , d ) 278 m , e ) 150 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 27 = 50 / 3 x = 150 m . answer : e"
Answer: e
Question (general): of 67 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 57 , d ) 71 , e ) 92
Rationale: "total = 67 thrower = 37 rest = 67 - 37 = 30 left handed = 30 / 3 = 10 right handed = 20 if all thrower are right handed then total right handed is 30 + 20 = 57 so c . 57 is the right answer"
Answer: c
Question (physics): a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in .
Options: a ) 88 days , b ) 27 days , c ) 78 days , d ) 60 days , e ) 17 days
Rationale: "a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d"
Answer: d
Question (general): when 1 / 10 percent of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 396 , d ) 495 , e ) 500
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 4,000 ? 2 ) what is 1 / 10 of 4,000 ? to calculate 1 / 10 percent of 4,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 4,000 = 1 / 1,000 x 4,000 = 4 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 4,000 . to do this we simply multiply 1 / 10 by 4,000 . 1 / 10 x 4,000 = 400 the answer to part 1 is 4 , and the answer to part 2 is 400 . their difference is 400 – 4 = 396 . answer c ."
Answer: c
Question (general): if n = 2.0823 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0023 , c ) 0.0007 , d ) 0.0047 , e ) 0.0153
Rationale: "n * = 2.08 n * - n = 2.08 - 2.0823 - 0.0023 answer : b"
Answer: b
Question (physics): if jack walked 7 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 5.6 , d ) 6.25 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 7 miles speed per hour = distance / time = 7 / ( 5 / 4 ) = 5.6 miles per hour answer c"
Answer: c
Question (general): a grocery shop has a sale of rs . 6635 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4791 , e ) 5291
Rationale: let the sale in the sixth month = x then ( 6635 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6635 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34209 + x = 39000 = > x = 39000 − 34209 = 4791 answer : d
Answer: d
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 150 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.75 gallons , d ) 3.75 gallons , e ) 7.50 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 150 kilometers ? 150 ã · 40 = 3.75 ã — 1 gallon = 3.75 gallons correct answer is d ) 3.75 gallons"
Answer: d
Question (gain): a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 2250 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 3000
Rationale: "p - 2250 = ( p * 5 * 5 ) / 100 p = 3000 answer : e"
Answer: e
Question (general): in a certain country 1 / 3 of 4 = 8 . assuming the same proportion , what would be the value of 1 / 8 of 4 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "e 3"
Answer: e
Question (general): the average age of a group of 12 students is 20 years . if 4 more students join the group , the average age increases by 1 year . the average age of the new students is
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "total age of 12 std = 20 * 12 total age of 16 std = 21 * 16 total age of 4 std = ( 21 * 16 ) - 20 * 12 = 96 avg of 4 std = ( 96 ) / 4 = 24 answer : c"
Answer: c
Question (physics): golu started from his house towards north . after covering a distance of 8 km . he turned towards left and covered a distance of 6 km . what is the shortest distance now from his house ?
Options: a ) 10 km . , b ) 16 km . , c ) 14 km , d ) 2 km . , e ) 4 km .
Rationale: c - - - - - - - - - - - - - b ! ! ! ! ! a ab = 8 km bc = 6 km ac = sqrtof ( 8 ^ 2 + 6 ^ 2 ) ac = 10 km answer : a
Answer: a
Question (physics): a tank can be filled by a tap in 20 minutes and by another tap in 60 minutes . both the taps are kept open for 10 minutes and then the first tap is shut off . after this , the tank will be completely filled in what time ?
Options: a ) 10 mins , b ) 15 mins , c ) 20 mins , d ) 25 mins , e ) 30 mins
Rationale: explanation : how we can solve this question ? first we will calculate the work done for 10 mins , then we will get the remaining work , then we will find answer with one tap work , as part filled by tap a in 1 min = 1 / 20 part filled by tap b in 1 min = 1 / 60 ( a + b ) ' s 10 mins work = 10 ∗ ( 1 / 20 + 1 / 60 ) = 10 ∗ 4 / 60 = 2 / 3 remaining work = 1 − 2 / 3 = 1 / 3 method 1 = > 1 / 60 : 1 / 3 = 1 : x = > x = 20 method 2 1 / 60 part filled by b in = 1 min 1 / 3 part will be filled in = 1 / 3 / 1 / 60 = 60 / 3 = 20 option c
Answer: c
Question (physics): renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 6 = 1 / 6 suma can do it alone in 6 days . answer : a"
Answer: a
Question (physics): an engineer undertakes a project to build a road 15 km long in 300 days and employs 50 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 75 , d ) d . 68 , e ) e . 60
Rationale: "50 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 50 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 125 thus , more men needed to finish the task = 125 - 50 = 75 hence answer is c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 876 m , d ) 200 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 12 ) m = 200 m . answer : d"
Answer: d
Question (physics): a is twice as fast as b . if b alone can do a piece of work in 24 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 12 , c ) 6 , d ) 2 , e ) 8
Rationale: a can do the work in 24 / 2 i . e . , 12 days . a and b ' s one day ' s work = 1 / 12 + 1 / 24 = ( 2 + 1 ) / 24 = 1 / 8 so a and b together can do the work in 8 days . answer : e
Answer: e
Question (gain): the owner of a furniture shop charges his customer 32 % more than the cost price . if a customer paid rs . 5400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 4090 , b ) rs . 4067 , c ) rs . 6290 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5400 ( 100 / 132 ) = rs . 4090 . answer : a"
Answer: a
Question (geometry): in the coordinate plane , a circle centered on point ( - 3 , - 4 ) passes through point ( - 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π
b ) 18 π
c ) 29 π
d ) 37 π
e ) 41 π
Rationale: r ^ 2 = ( - 3 + 1 ) ^ 2 + ( - 4 - 1 ) ^ 2 = 4 + 25 = 29 area of circle = π r ^ 2 = 29 π answer : c
Answer: c
Question (physics): city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 00 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 00 pm + 2 hrs = 7 : 00 pm answer : e . 7 : 00"
Answer: e
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 b 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 b = ( 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 (physics): a cylinder is 6 cms in diameter and 6 cms in height . if spheres of the same size are made from the material obtained , what is the diameter of each sphere ?
Options: a ) 5 cms
b ) 2 cms
c ) 3 cms
d ) 4 cms
e ) 6 cms
Rationale: since the sphere is made out of the cylinder material their volume will be same volume of cylinder = pi * 3 ^ 2 * 6 volume of one sphere = 4 / 3 * pi * r ^ 3 ( where r is radius of sphere ) so if there are n such sphere ' s equating the volumes , pi * r ^ 2 * h = n * ( 4 / 3 ) * pi * r ^ 3 n is the number of spheres , substituting the , r and h 9 * 6 = n * ( 4 / 3 ) * ( d / 2 ) ^ 3 d is the diameter of a sphere , n = ( 9 * 6 * 3 * 8 ) / ( 4 * d ^ 3 ) n = 324 / d ^ 3 now substitute the given answers for d and find the values for n , since a n has to be an integer only value fit for d is 3 , answer : c
Answer: c
Question (general): a number x is 8 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 8 . then y = 1 is less than x = 8 by ( 8 - 1 ) / 8 * 100 = 7 / 8 * 100 = 87.5 % . answer : b ."
Answer: b
Question (physics): if 20 typists can type 44 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 198 , d ) 216 , e ) 400
Rationale: "20 typists can type 44 letters , so 30 typists can type = 44 * 30 / 20 44 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 44 * 30 * 60 / 20 * 20 = 198 c is the answer"
Answer: c
Question (general): if ( 1 / 5 ) ^ m * ( 1 / 2 ) ^ 5 = 1 / ( ( 10 ) ^ 5 ) , then m =
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 / 5 ) ^ m ( 1 / 2 ) ^ 5 = 1 / { ( 10 ) ^ 5 } ( 10 ) ^ 5 / 2 ^ 5 = 5 ^ m [ ( 2 ^ 5 ) ( 5 ^ 5 ) ] / [ 2 ^ 5 ] = 5 ^ m 5 ^ 5 = 5 ^ m m = 5 e"
Answer: e
Question (general): amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is :
Options: a ) rs . 4250 , b ) rs . 4288 , c ) rs . 4227 , d ) rs . 4218 , e ) rs . 4219
Rationale: "explanation : amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } { 6 } = 4250 answer : a"
Answer: a
Question (gain): a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 105 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.28 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 105 ( multiplying factor is 7 : ( 105 / 15 ) ) then typical dosage would be 2 * 7 = 14 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 14 ) * 100 = 14.28 % e is the answer ."
Answer: e
Question (gain): a discount electronics store normally sells all merchandise at a discount of 5 percent to 45 percent off the suggested retail price . if , during a special sale , an additional 2 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 215.00 , b ) $ 200.00 , c ) $ 215.80 , d ) $ 182.00 , e ) $ 215.60
Rationale: "original price : 400 $ max first discount = - 45 % thus : 400 â ˆ — ( 1 â ˆ ’ 45 / 100 ) = 220 second discount on the discounted price = - 2 % thus : 220 â ˆ — ( 1 â ˆ ’ 2 / 100 ) = 215.60 answer e"
Answer: e
Question (gain): a man sold 20 articles for $ 40 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 67.5
Rationale: "production cost per article : $ 40 * ( 100 % - 20 % ) / 20 = $ 1.6 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 1.6 = 67.5 thus , solution e is correct ."
Answer: e
Question (physics): two trains are moving in the same direction at 162 kmph and 18 kmph . the faster train crosses a man in the slower train in 33 seconds . find the length of the faster train ?
Options: a ) 1300 , b ) 1310 , c ) 1320 , d ) 1330 , e ) 1340
Rationale: "relative speed = ( 162 - 18 ) * 5 / 18 = 8 * 5 = 40 mps . distance covered in 33 sec = 33 * 40 = 1320 m . the length of the faster train = 1320 m . answer : c"
Answer: c
Question (general): a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served only for 9 months and receiveduniform and rs . 650 , find the price of the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 130 , d ) rs . 170 , e ) rs . 190
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Question (general): 500 x 223 + 500 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 150000 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 500 x 300 = 150000 answer is c"
Answer: c
Question (other): how many factors of 220 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 220 has 4 prime factors . of these prime factors 2 are odd and 2 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 1 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Question (gain): in xyz business school , 88 % are taking their specialization as finance at the same time 76 % taking their specialization as marketing . if 90 % are taking their specialization as finance then , what is % of marketing specialization students ?
Options: a ) 55 , b ) 75 , c ) 43 , d ) 52 , e ) 45
Rationale: percentage of finance specialization = 88 ; percentage of marketing specialization = 75 % ; total = 90 * 100 ; percentage of finance specialization = 90 - 88 = 2 ; percentage of marketing specialization = 100 - 75 = 25 ; then percentage of marketing specialization = 0.75 * 24 = 18 . then total percentage of marketing specialization = 25 + 18 = 43 . answer : c
Answer: c