regisss/math_qa huggingface dataset:
Problem: a small college reduced its faculty by approximately 15 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 229 , e ) 302
Rationale: "if x is the original number of faculty members , then after 15 % reduction in faculty members number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of faculty members is 229 correct answer - d"
Answer: d
Problem: how many seconds will a train 60 meters long take to cross a bridge 120 meters long if the speed of the train is 30 m / sec ?
Options: a ) 6 sec , b ) 8 sec , c ) 15 sec , d ) 3 sec , e ) 5 sec
Rationale: "d = 60 + 120 = 180 s = 30 mps t = 180 / 30 = 6 sec a ) 6 sec"
Answer: a
Problem: if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?
Options: a ) 38.25 % , b ) 40.25 % , c ) 82.25 % , d ) 50 % , e ) 65 %
Rationale: if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c
Answer: c
Problem: the length of the bridge , which a train 120 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 x = 255 m . answer : option e"
Answer: e
Problem: 4 , 12 , 48 , 240 , 1440 , 10080,80640 ( . . . )
Options: a ) 7620 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 725760
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 , 8,9 answer : option e"
Answer: e
Problem: if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?
Options: a ) 40 km , b ) 76 km , c ) 18 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a"
Answer: a
Problem: there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 140 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d"
Answer: d
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?
Options: a ) 44 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )"
Answer: a
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 32 degrees , c ) 37 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 – 152 = 32 answer : b"
Answer: b
Problem: difference between the length & breadth of a rectangle is 30 m . if its perimeter is 300 m , then its area is ? ? we have : ( l - b ) = 30 and 2 ( l + b ) = 300 or ( l + b ) = 150 ?
Options: a ) 3 : 5 , b ) 2 : 3 , c ) 3 : 6 , d ) 3 : 4 , e ) 3 : 2
Rationale: solving the two equations , we get : l = 90 and b = 60 . the ratio of length and breath is 90 : 60 = 3 : 2 e
Answer: e
Problem: what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c
Answer: c
Problem: if the area of a circle is 16 pi square feet , find its circumference .
Options: a ) 8 pi feet , b ) 28 pi feet , c ) 38 pi feet , d ) 48 pi feet , e ) 58 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 16 pi r * r = 16 ; hence r = 16 feet the circumference is given by 2 * pi * r = 2 * pi * 4 = 8 pi feet correct answer a"
Answer: a
Problem: 892.7 – 573.07 – 95.007 = ?
Options: a ) 224.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 892.7 - ( 573.07 + 95.007 ) = 892.7 - 668.077 = 224.623 . answer a"
Answer: a
Problem: find k if 64 / k = 4 .
Options: a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13
Rationale: since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a
Answer: a
Problem: if 1 + 3 = 10 ; 3 + 5 = 52 ; 5 + 7 = 174 then 7 + 11 = ?
Options: a ) 354 , b ) 225 , c ) 654 , d ) 741 , e ) 464
Rationale: "1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e"
Answer: e
Problem: 10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: 10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d
Answer: d
Problem: 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 14 men make toy in 5 days after 1 day 14 more worker join m 1 / m 2 = d 2 / d 1 14 / 28 = d 2 / 4 = 2 day answer : b
Answer: b
Problem: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19.50 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 11 : 7 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5.50 : 3.50 = 11 : 7"
Answer: c
Problem: a sum of rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months , the total amount of rs 500 is received . find the rate of interest ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: here p = 468.75 which is the principle . amount = rs 500 amount = si + p 500 = [ 468.75 * ( 20 / 12 ) * r ] / 100 + 468.75 31.25 = 156.25 * 5 r / 100 r = 4 % answer : b
Answer: b
Problem: how many positive integers less than 5,000 are evenly divisible by neither 14 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 14 5000 / 14 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 14 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 14 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ."
Answer: e
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 124 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 110 x = 124 answer : d"
Answer: d
Problem: a solid yellow stripe is to be painted in the middle of a certain highway . if 1 gallon of paint covers an area of q square feet of highway , how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
Options: a ) ( 5,280 mt ) / 12 q
b ) ( 5,280 pt ) / 12 m
c ) ( 5,280 pmt ) / 12
d ) ( 5,280 ) ( 12 m ) / pt
e ) ( 5,280 ) ( 12 p ) / mt
Rationale: given that : 1 gallon of paint covers an area ofqsquare feet . question : how many gallonsof paint will be needed . . . in any case you will have : ( total area in square feet ) / ( gallons per feet ) = ( total area in square feet ) / q , so q must be in the denominator : eliminate all but a and d . now , lets see where should be t : ( area in square feet ) = ( width in feet ) * ( length in feet ) - - > width = tinchesas 1 feet = 12 inchesthent inches = t / 12 feet , so ( area in square feet ) = ( t / 12 ) * ( length in feet ) , so t must be in the nominator : only a is left . answer : a .
Answer: a
Problem: a man buys 20 lts of liquid which contains 30 % of the liquid and the rest is water . he then mixes it with 20 lts of another mixture with 20 % of liquid . what is the % of water in the new mixture ?
Options: a ) 59 , b ) 95 , c ) 80 , d ) 75 , e ) 65
Rationale: "30 % in 20 lts is 6 . so water = 20 - 6 = 14 lts . 20 % of 20 lts = 4 . so water in 2 nd mixture = 20 - 4 = 16 lts . now total quantity = 20 + 20 = 40 lts . total water in it will be 14 + 16 = 30 lts . % of water = ( 100 * 30 ) / 40 = 75 . answer : d"
Answer: d
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 7 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 7 x 14 â ‡ ’ r 2 = ( 7 x 14 / 2 ) â ‡ ’ 49 â ‡ ’ r = 7 cm . answer d"
Answer: d
Problem: if 8 men or 12 women can do a piece of work in 30 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 18 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 30 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 30 = 1 / 360 so , 20 women work = 20 / 360 = 1 / 18 ans : 18 days answer : e"
Answer: e
Problem: how many positive integer solutions does the equation 8 x + 2 y = 100 have ?
Options: a ) 50 , b ) 84 , c ) 16 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 8 * 2 ) = 84 answer : b"
Answer: b
Problem: set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d .
Answer: d
Problem: the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .
Options: a ) 1800 , b ) 2000 , c ) 1640 , d ) 2200 , e ) 2400
Rationale: following the above formula , we have the total marks = 50 * 40 = 2000 answer is b
Answer: b
Problem: a man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction , takes 18 seconds to pass him . if the goods train is 420 m long , find its speed .
Options: a ) 32 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "relative speed = ( 420 / 18 ) m / s = ( 420 / 18 ) * ( 18 / 5 ) = 84 kmph speed of goods train = 84 - 64 = 20 kmph answer is d"
Answer: d
Problem: the speed of a car is 95 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 77.5 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 95 + 60 ) / 2 = 77.5 kmph answer : c"
Answer: c
Problem: an article is bought for rs . 675 and sold for rs . 800 , find the gain percent ?
Options: a ) 38 % , b ) 28 % , c ) 18 % , d ) 22 % , e ) 13 %
Rationale: "675 - - - - 125 100 - - - - ? = > = 18 % answer : c"
Answer: c
Problem: a company recently conducted a survey and found that 40,000 of its customers live in rural areas . if the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 90,000 , b ) 91,200 , c ) 92,400 , d ) 93,600 , e ) 94,800
Rationale: the number of customers in urban areas is 40,000 + 1.37 * 40,000 = 94,800 . the answer is e .
Answer: e
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 30 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 7.5 , b ) 15 , c ) 17.5 , d ) 25 , e ) 32.5
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 30 = 2.5 km . the time it takes the hiker to complete this distance is 2.5 / 4 hours = 37.5 minutes the cyclist needs to wait 37.5 - 5 = 32.5 minutes the answer is e ."
Answer: e
Problem: 3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 41.5 % , b ) 42.75 % , c ) 43 % , d ) 45 % , e ) 45.75 %
Rationale: "we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 ã — 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 ã — 57 / 100 12 ã — 100 = 9 ã — 5710012 ã — 100 = 9 ã — 4.75 / 100 = 42.75 % b"
Answer: b
Problem: if x = 3 ^ 9 and x ^ x = 3 ^ k , what is k ?
Options: a ) 3 ^ 11 , b ) 3 ^ 13 , c ) 3 ^ 25 , d ) 3 ^ 27 , e ) 3 ^ 81
Rationale: solution : we know that x = 3 ^ 9 which implies x ^ x = ( 3 ^ 9 ) ^ ( 3 ^ 9 ) = 3 ^ ( 9 * 3 ^ 9 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 2 * 3 ^ 9 ) = 3 ^ ( 3 ^ ( 2 + 9 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 11 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 11 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 11 answer : a
Answer: a
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 2 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 3 / 8 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 2 ) ( 1 / 4 ) s = ( 1 / 2 ) * ( 1 / 4 ) * s = ( 1 / 8 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 8 ) / s = 3 / 8 answer : d"
Answer: d
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 11.00 ?
Options: a ) 40 , b ) 60 , c ) 90 , d ) 132 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 11 ( 1 / 12 ) * x = 11 x = 132 answer : d"
Answer: d
Problem: for all numbers a and b , the operation is defined by ab = ( a + 2 ) ( b – 3 ) . if 3 x = – 20 , then x =
Options: a ) – 15 , b ) – 6 , c ) 3 , d ) 6 , e ) - 1
Rationale: ( 3 + 2 ) ( x - 3 ) = - 20 . . x - 3 = - 4 . . x = - 1 e
Answer: e
Problem: the length and breadth of a rectangle is increased by 5 % and 15 % respectively . what is the increase in the area ?
Options: a ) 21.25 , b ) 22.75 , c ) 19.25 , d ) 20.75 , e ) 22.25
Rationale: "100 * 100 = 10000 105 * 115 = 12075 - - - - - - - - - - - 2075 10000 - - - - - - 2075 100 - - - - - ? = > 20.75 answer d"
Answer: d
Problem: a train running at the speed of 40 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 150 metres , e ) 100 meters
Rationale: "speed = 40 x 5 / 18 m / sec = 100 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 100 / 9 x 9 m = 100 m . answer : e"
Answer: e
Problem: a chemical supply company has 60 liters of a 35 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 18 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 35 % hno 3 solution means hno 3 = 21 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 21 + x = 50 % of ( 60 + x ) or x = 18 hence , a"
Answer: a
Problem: in how many no . between 10 and 30 exactly two of the digits is 2 ?
Options: a ) 25 , b ) 1 , c ) 35 , d ) 45 , e ) 50
Rationale: "it ' s simple can be solved by elimination of answer choices . option a and c are too large , not possible . even de are large to have correct choice . ans : b"
Answer: b
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 174
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 140 x + ( x - 140 ) = 208 2 x = 348 x = 174 runs answer : e"
Answer: e
Problem: if m ^ 2 - 8 m + 1 = 0 , then m ^ 3 + m ^ ( - 3 ) = ?
Options: a ) 487 , b ) 488 , c ) 489 , d ) 457 , e ) 495
Rationale: here from equation 1 we will get m ^ 2 - 8 m + 1 = 0 m ^ 2 = 8 m - 1 m = ( 8 m - 1 ) / m . . . . . . . . . ( 1 ) m = 8 - 1 / m so m + 1 / m = 8 now in equation 2 m ^ 3 + 1 / m ^ 3 ( m + 1 / m ) ( m ^ 2 - m * 1 / m + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 - 1 + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 + 1 / m ^ 2 - 1 ) ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 m * 1 / m - 1 } { since a ^ 2 + b ^ 2 = ( a + b ) ^ 2 - 2 ab } ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 - 1 } now putting the value of m from equation 1 8 ( 8 ^ 2 - 2 - 1 ) 8 ( 64 - 3 ) = 488 answer : b
Answer: b
Problem: if 3 a – 3 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c
Answer: c
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 3 : 4 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 75 , b ) 150 , c ) 300 , d ) 450 , e ) 600
Rationale: "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . thus 600 - 300 = 300 more acres were planted with tobacco . the answer is c ."
Answer: c
Problem: in a group of 100 cars , 47 cars do not have air conditioning . if at least 55 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53
Rationale: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 55 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 55 . . we have to assign atleast 8 tocars with ac and racing stripes . hence ac = 53 - 8 = 45 . the answer is a"
Answer: a
Problem: at a certain conference , 78 % of the attendees registered at least two weeks in advance and paid their conference fee in full . if 10 % of the attendees who paid their conference fee in full did not register at least two weeks in advance , what percent of conference attendees registered at least two weeks in advance ?
Options: a ) 18.0 % , b ) 62.0 % , c ) 79.2 % , d ) 86.67 % , e ) 82.0 %
Rationale: i do not think that venn will be helpful here . a table will make more sense . but here is my approach . 78 % regestered at least 2 weeks and paid full fee . 10 % paid full fee and did not registered at least 2 weeks in advance . then 90 % paid full fee and registered at least 2 weeks before . 90 % * x = 78 % where x is the number of people who registerd 2 weeks in advance and paid full fee . ( answer d )
Answer: d
Problem: a can do a piece of work in 22 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 11 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 22 ∗ 1 / 2 = 11 days option c"
Answer: c
Problem: if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is :
Options: a ) 2 : 1
b ) 3 : 2
c ) 3 : 5
d ) 3 : 7
e ) none of these
Rationale: explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 8 / 1 = > ( a / b ) 3 = ( 2 / 1 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option a
Answer: a
Problem: what is the dividend . divisor 15 , the quotient is 8 and the remainder is 5
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 125 , e ) e ) 158
Rationale: "d = d * q + r d = 15 * 8 + 5 d = 120 + 5 d = 125 answer : d"
Answer: d
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 20 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 20 days whole work will be done by y in 20 * 5 / 4 = 25 days answer is c"
Answer: c
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 5 years ?
Options: a ) 14300 , b ) 24883 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 5 = 24883 b )"
Answer: b
Problem: by selling an article at rs . 500 , a profit of 25 % is made . find its cost price ?
Options: a ) 400 , b ) 267 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 500 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / ( 100 + 25 ) ] = 500 * [ 100 / 125 ] = rs . 400 answer : a"
Answer: a
Problem: in a class of 32 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 40 = english + 22 - 12 + 0 - - > english = 22 - - > only english = english - both = 22 - 12 = 10 . answer : b ."
Answer: b
Problem: the ratio of radius of a circle and the side of a square is 2 : 5 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 25 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 5 â ‡ ’ area of circle / area of square = 4 / 25 answer : b"
Answer: b
Problem: a lion chases a pony 7 hours after the pony runs . lion takes 8 hours to reach the pony . if the average speed of the lion is 49 kmph , what s the average speed of the pony ?
Options: a ) 28.3 kmph , b ) 29.8 kmph , c ) 28.4 kmph , d ) 29.5 kmph , e ) 29.4 kmph
Rationale: pony take 15 hours and lion take 8 hours . . . then distance chased by them is 49 * 8 . so speed of pony is ( 49 * 8 ) / 15 = 29.4 kmph . answer is e
Answer: e
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 360 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 360 ) = 2 + 2 ( extra ) = > 2 x - 720 = x = > x = 720 . answer : e"
Answer: e
Problem: the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b"
Answer: b
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 45 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 900 * ( 25 / 100 ) = 225 - - - - 5 ? - - - - 1 = > rs . 45"
Answer: a
Problem: rectangular tile each of size 80 cm by 55 cm must be laid horizontally on a rectangular floor of size 210 cm by 330 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 26 , b ) 16 , c ) 18 , d ) 19 , e ) 20
Rationale: "area of tile = 80 * 55 = 4400 area of floor = 210 * 330 = 72600 no of tiles = 72600 / 4400 = 16.5 so , the no of tile = 16 answer : b"
Answer: b
Problem: sowdharya had 90 currency notes in all , some of which are of rs 95 denomination and the remaining of rs 45 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 45 ?
Options: a ) 75 , b ) 72 , c ) 71 , d ) 76 , e ) 73
Rationale: let the number of 45 - rupee notes = x then , the number of 95 - rupee notes = ( 90 – x ) 45 x + 95 ( 90 – x ) = 5000 : x = 71 answer : c
Answer: c
Problem: if an investor puts $ 700 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 769.75 , b ) $ 771.75 , c ) $ 773.75 , d ) $ 775.75 , e ) $ 777.75
Rationale: "1.05 * 1.05 * 700 = $ 771.75 the answer is b ."
Answer: b
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12002 , b ) 12000 , c ) 12028 , d ) 12020 , e ) 12013
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer : b"
Answer: b
Problem: to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . find how many parts the company made and how many days this took .
Options: a ) 600 , b ) 500 , c ) 575 , d ) 655 , e ) 675
Rationale: let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . so answer is e .
Answer: e
Problem: how many positive integers less than 100 have a reminder 5 when divided by 7 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "take the multiples of 7 and add 5 0 x 7 + 5 = 5 . . . . 13 x 7 + 5 = 96 there are 14 numbers answer d"
Answer: d
Problem: what is the 10 th digit of ( 5 ! * 4 ! * 4 ! - 5 ! * 4 ! * 3 ! ) / 2880 ?
Options: a ) 4 , b ) 1 , c ) 6 , d ) 7 , e ) 8
Rationale: "( 5 ! * 4 ! * 4 ! - 5 ! * 4 ! * 3 ! ) / 2880 ? = 5 ! * 4 ! ( 4 ! - 3 ! ) / 4 ! * 5 ! = 4 ! - 3 ! = 18 sum of digits = 1 answer b"
Answer: b
Problem: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weights 8 g / cm cube , then find the weight of the pipe .
Options: a ) 3.696 kg
b ) 3.686 kg
c ) 2.696 kg
d ) 2.686 kg
e ) none of these
Rationale: explanation : in this type of question , we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow . oh ! line become a bit complicated , sorry for that , lets solve it . external radius = 4 cm internal radius = 3 cm [ because thickness of pipe is 1 cm ] volume of iron = π r 2 h = 22 / 7 ∗ [ 42 − 32 ] ∗ 21 cm 3 = 22 / 7 ∗ 1 ∗ 21 cm 3 = 462 cm 3 weight of iron = 462 * 8 = 3696 gm = 3.696 kg option a
Answer: a
Problem: village x has a population of 72000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 72000 - 1200 p = 42000 + 800 p 2000 p = 30000 p = 15 answer is a ."
Answer: a
Problem: what is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 21 / 216 , e ) 32 / 216
Rationale: "the other way would be to list out each option . the options for a sum of 8 : ( 6 , 1,1 ) has 3 options ie ( 6 , 1,1 ) , ( 1 , 6,1 ) , ( 1 , 1,6 ) ; ( 5 , 2,1 ) has 6 options , ( 4 , 3,1 ) has 6 options , ( 4 , 2,2 ) has 3 options , ( 3 , 3,2 ) has 3 options . we have 21 options to get 8 . the options for a sum of 14 : ( 6 , 4,4 ) has 3 options , ( 6 , 5,3 ) has 6 options , ( 6 , 6,2 ) has 3 options , ( 5 , 5,4 ) has 3 options . we have 15 options to get 14 . total : 21 + 15 = 36 / 216 = 1 / 6 . answer a ."
Answer: a
Problem: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is :
Options: a ) 50 , b ) 90 , c ) 80 , d ) 28 , e ) 93
Rationale: let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : option c
Answer: c
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 60 / 10 sq . metre , whose base & perpendicular distance from the other side being 34 m & 34 m respectively ?
Options: a ) s . 1156 , b ) s . 1300 , c ) s . 1400 , d ) s . 2480 , e ) s . 3600
Rationale: "area of the parallelogram = length of the base * perpendicular height = 34 * 34 = 1156 total cost of levelling = rs . 1156 a"
Answer: a
Problem: find the remainder of the division ( 3 ^ 33 ) / 7 .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 33 ) / 7 gives us a remainder of 6 final answer : e ) 6
Answer: e
Problem: an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 4 ?
Options: a ) 4000 , b ) 8000 , c ) 5000 , d ) 4500 , e ) 6000
Rationale: "let the number of meters to be examined be x then , 0.05 % of x = 4 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 4 x = 8000 answer is b"
Answer: b
Problem: a train passes a platform in 34 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 210 meter , d ) 200 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 34 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 34 = > 300 + l = 15 × 34 = 510 = > l = 510 - 300 = 210 meter answer : option c"
Answer: c
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 3 students is 14 years and that of the other 11 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 7 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 3 + 16 x 11 ) ] = ( 225 - 218 ) = 7 years . answer d"
Answer: d
Problem: a number x is 6 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 83.3 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: say y = 1 and x = 6 . then y = 1 is less than x = 6 by ( 6 - 1 ) / 6 * 100 = 5 / 6 * 100 = 83.3 % . answer : b .
Answer: b
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 10 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 30 mph , e ) 60 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 30 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 30 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 30 mph therefore answer is d"
Answer: d
Problem: what is the compound interest paid on a sum of rs . 3000 for the period of 2 years at 10 % per annum .
Options: a ) 630 , b ) 620 , c ) 610 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3000 = 3000 * ( 21 / 100 ) = 630 answer a"
Answer: a
Problem: what is the least integer greater than – 2 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: irst , let ' s take care of the arithmetic : ( - 2 ) + ( 0.5 ) = - 1.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 2 to - 1.5 ) . next , the question asks for the least integer that is greater than - 1.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 1.5 is - 1 . final answer : b
Answer: b
Problem: if 5 x + y = 15 , 5 y + z = 25 and 2 z + x = 2 , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 1
Rationale: "explanation : 5 x + y = 15 – - - - - - - - i * 5 5 y + z = 25 – - - - - - - ii 2 z + x = 2 - - - - - - - - iii subtract ( i ) and ( ii ) 25 x + 5 y + 0 = 75 - 0 + 5 y + z = 25 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 25 x + 0 – z = 50 … . . . . . . . . . . iv multiply ( iv ) * 2 , we get 50 x – 2 z = 100 adding ( iii ) and ( iv ) we get , 50 x – 2 z = 100 + x + 2 z = 2 - - - - - - - - - - - - - - - - - - - - - - - - 51 x = 102 x = 2 the value of x = 2 answer : a"
Answer: a
Problem: a boy perform 5 times a reaction and his reading are 2 , 2.1 , 2 , 2.2 but unfortunately 5 th reading clearly not visible because a drop of chemical fall onto it . but luckily he have mean of all reading which is 2 . please help him in finding 5 th reading .
Options: a ) 2 , b ) 1.7 , c ) 1.9 , d ) 1.8 , e ) 2.1
Rationale: solution let 5 th reading be x ( 2 + 2.1 + 2 + 2.2 + x ) / 5 = 2 8.3 + x = 10 x = 1.7 answer b
Answer: b
Problem: thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 12 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: 30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 12 = 42 members have not passed the test , thus 0.7 * total = 42 - - > total = 60 . answer : a .
Answer: a
Problem: a certain rectangular window is ( 1 / 3 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2
b ) 11 by 3
c ) 10.5 by 3.5
d ) 10 by 4
e ) 9 by 3
Rationale: 2 x + 2 y = 28 x + y = 14 x + ( 1 / 3 ) x = 14 4 x = 14 * 3 x = 10.5 answer c
Answer: c
Problem: there are 8 teams in a certain league and each team plays each of the other teams exactly once . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 64
Rationale: "number of ways 2 teams can be selected out of 8 teams : c 8 / 2 = 8 ∗ 7 / 2 = 28 ans : ' ' c ' '"
Answer: c
Problem: 3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"
Answer: c
Problem: if p is the product of the integers from 1 to 36 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "36 ! has 3 , 6 , 9 , . . . . 30 , 33 , 36 as factors , which are 12 multiples of 3 . we need to add 5 more to these 12 because of 9 , 18 , 27 , and 36 . the greatest integer of k is 17 . the answer is c ."
Answer: c
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 3 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 4.76 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 3 xr ) / 100 r = 4.76 % answer : option c"
Answer: c
Problem: what is the total surface area in square meters of a rectangular solid whose length is 8 meters , width is 7 meters , and depth is 4 meters ?
Options: a ) 132 m 2 , b ) 145 m 2 , c ) 165 m 2 , d ) 152 m 2 , e ) 120 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 8 * 7 + 7 * 4 + 8 * 4 ) = 2 ( 56 + 28 + 32 ) = 2 * 116 = 132 m 2 answer : a"
Answer: a
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22.78 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.93
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 19 + 14 ) = 66 cm perimeter of the square = 66 cm i . e . 4 a = 66 a = 16.5 diameter of the semicircle = 16.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16.5 ) = 1 / 2 ( 22 / 7 ) ( 16.5 ) = 25.93 cm to two decimal places answer : e"
Answer: e
Problem: john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 15 + 2 - - - > 0.5 t = 17 - - - > t = 34 seconds . d is the correct answer ."
Answer: d
Problem: a ratio between two numbers is 3 : 4 and their l . c . m . is 84 . the first number is
Options: a ) 60 , b ) 45 , c ) 21 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 84 ⇔ x = 7 . hence , the first number is 21 . answer c"
Answer: c
Problem: the principal that amounts to rs . 4813 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4036 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4813 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4036 . answer : b"
Answer: b
Problem: the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 8 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 18 × b ∴ l = 18 m and l – b = 10 ∴ b = 18 – 10 = 8 m answer b"
Answer: b
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 38500 = 2 * 2 * 5 * 5 * 5 * 7 * 11 john participated 7 times . the answer is b .
Answer: b
Problem: the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 40 % ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 2 , e ) 8
Rationale: we need on - time departure rate to be higher than 4 / 10 , so it should be at least 5 / 11 , which means that 5 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 5 - 3 = 2 subsequent flights need to depart on - time . answer : d
Answer: d
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 160 billion gallons to 200 billion gallons . if the storm increased the amount of water in the reservoirs to 40 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 260 , b ) 280 , c ) 325 , d ) 340 , e ) 355
Rationale: "let total capacity be x we know 200 = 0.40 x x = 200 / 0.40 = 500 prior to storm , we had 160 bn gallons 500 - 160 = 340 answer : d"
Answer: d
Problem: a number when divided by a divisor leaves a remainder of 23 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 36 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 23 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 36 as d is also integer and 36 is a prime number , the d should be 36 to satisfy the above equation . hence answer is ' d '"
Answer: d
Problem: two years ago , ram put $ 500 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 600 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 500 ?
Options: a ) 19 % , b ) 28 % , c ) 30 % , d ) 32 % , e ) 25 %
Rationale: investment 500 dollars 1 st year total gained = 100 total amount end of first year = 600 second year account increased by 10 % = 600 * 0.1 = 60 therefore total amount by second year end = 660 so total percentage increase in money = ( 660 - 500 ) * 100 / 500 = 32 % correct answer d = 32 %
Answer: d
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 10 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 980241 , d ) 1036750 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 10 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1036750 d"
Answer: d
Problem: if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 3 and 100 respectively , then the sum of the reciprocal of the numbers is equal to :
Options: a ) 103 / 300 , b ) 103 / 200 , c ) 112 / 300 , d ) 154 / 140 , e ) 100 / 300
Rationale: let the numbers be a and b . then , a + b = 45 and ab = 3 * 100 = 300 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 103 / 300 answer : a
Answer: a
Problem: what is the value of ( 2 ) ^ - 3 ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 8 , d ) 1 / 9 , e ) 1 / 7
Rationale: "2 ^ - 3 = 1 / ( 2 ) ^ 3 = 1 / 8 answer : c"
Answer: c
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 45 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 9 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "let me try a simpler one . lets assume that candidate got 45 % votes and total votes is 100 . candidate won = 45 remaining = 55 to get 50 % , candidate requires 5 votes from 100 which is 5 % and 5 votes from 55 . 5 / 55 = 1 / 11 = . 09 = 9 % which is approx 9 % . hence the answer is a ."
Answer: a
Problem: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 12 = > 1 / x = 1 / 6 - 1 / 12 = ( 2 - 1 ) / 12 = 1 / 12 = > x = 12 . answer : e"
Answer: e
Problem: w and x start a business with rs . 5000 and rs . 20000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 4 : 1 , b ) 1 : 3 , c ) 1 : 4 , d ) 1 : 5 , e ) 2 : 1
Rationale: they should share the profits in the ratio of their investments . the ratio of the investments made by w and x = 5000 : 20000 = > 1 : 4 . answer : c
Answer: c