regisss/math_qa huggingface dataset:
Problem: | x + 3 | – | 4 - x | = | 7 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , s ố x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , s ố í t becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 c
Answer: c
Problem: a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 21 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 3 = 2 ( x + 3 ) â € ¹ = â € º x + 27 = 2 x + 6 x = 21 . answer d"
Answer: d
Problem: an auction house charges a commission of 17 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 205,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.17 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 205,000 ( 17 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Problem: a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?
Options: a ) 200 km , b ) 50 km , c ) 20 km , d ) 60 km , e ) 80 km
Rationale: not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d
Answer: d
Problem: if the a radio is sold for rs 490 and sold for rs 465.50 . find loss % .
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 3 % , e ) 5.5 %
Rationale: "sol . cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b ."
Answer: b
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 6 hours ?
Options: a ) 675 , b ) 750 , c ) 1,800 , d ) 1,350 , e ) 7,500
Rationale: 8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 6 hours ) = 1350 cans . the answer is d .
Answer: d
Problem: a cycle is bought for rs . 900 and sold for rs . 1160 , find the gain percent ?
Options: a ) 11 , b ) 29 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 260 100 - - - - ? = > 29 % answer : b"
Answer: b
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?
Options: a ) 8
b ) 1
c ) 3
d ) 4
e ) 6
Rationale: perimeter of rectangular yard = 2 ( l + b ) = 12 - - > l + b = 6 area = l * b = 9 b = 6 - l l ( 6 - l ) = 9 6 l - l ^ 2 = 9 l ^ 2 - 6 l + 9 = 0 upon simplifying we get l = 3 . answer : b
Answer: b
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 7 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 49
Rationale: explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 7 ^ 2 = 9 / 49 answer : e
Answer: e
Problem: each machine of type a has 3 steel parts and 3 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 60 steel parts and 44 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "look at the below representation of the problem : steel chrome total a 3 3 60 > > no . of type a machines = 60 / 6 = 10 b 6 5 44 > > no . of type b machines = 44 / 11 = 4 so the answer is 14 i . e c . hope its clear ."
Answer: c
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 275 , c ) 360 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 50 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 50 = 225 . total area = 50 + 225 = 275 . answer : b ."
Answer: b
Problem: a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 5 , c ) $ 10 , d ) $ 6 , e ) $ 8
Rationale: sale price ( sp ) = 90 + markup ( mp ) - - > mp = sp - 90 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 90 3 sp / 4 = 90 sp = 120 now a discount of 20 % is given so new sp is . 8 * 120 = 96 profit = 96 - 90 = 6.0 $ answer is d
Answer: d
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 60 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 23,760 , e ) $ 27,360
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.6 * 12000 = 12000 - 7200 x = 4800 earning becomes 9360 + 3 x = 9360 + 3 * 4800 = 23760 ans : d"
Answer: d
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 8915
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 6 ) = rs . 8915 . answer : option e"
Answer: e
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) q = 20 , b ) q = 25 , c ) q = 30 , d ) q = 35 , e ) 40
Rationale: suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d
Answer: d
Problem: a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in .
Options: a ) 24 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : a"
Answer: a
Problem: 5 n + 2 > 12 and 7 n - 5 < 23 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 4 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n > 10 - - > n > 2 7 n < 28 - - > n < 4 2 < n < 4 answer : b"
Answer: b
Problem: how many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 7 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 70 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 and 65 = 7 ans b"
Answer: b
Problem: find the value of 201834 x 99999 = m ?
Options: a ) 20183198166 , b ) 20194181766 , c ) 20175292556 , d ) 20132191166 , e ) 20153198166
Rationale: "201834 x 99999 = 201834 x ( 100000 - 1 ) = 201834 x 100000 - 201834 x 1 = 20183400000 - 201834 = 20183198166 a"
Answer: a
Problem: if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 70 , how much more remains to be paid ?
Options: a ) $ 1120 , b ) $ 1190 , c ) $ 1260 , d ) $ 1330 , e ) $ 1400
Rationale: "95 % remains to be paid so the remaining amount is 19 * 70 = $ 1330 . the answer is d ."
Answer: d
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 3 , b ) 1.8 , c ) 6 , d ) 18 , e ) 60
Rationale: concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 4 + 18 ) / 2 ] * 8 = 88 h ( 10 ) = ( 4 + 10 ) / 2 ] * 4 = 28 h ( 18 ) / h ( 10 ) = ( 88 ) / ( 28 ) ~ 3 answer : a
Answer: a
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 60 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 2.5 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 60 = 5 * 1 / 1 = 5 new time in minutes to cross 5 miles stretch = 5 * 60 / 40 = 5 * 3 / 2 = 7.5 time difference = 2.5 ans : b"
Answer: b
Problem: a pyramid has a square base of 6 cm , and the four lateral faces are four congruent equilateral triangles . what is the total surface area of the pyramid in square cm ?
Options: a ) 36 + 18 * sqrt ( 3 )
b ) 36 + 36 * sqrt ( 3 )
c ) 72
d ) 72 + 36 * sqrt ( 3 )
e ) 72 + 72 * sqrt ( 3 )
Rationale: first of all , of course , the base has an area of 36 . for the lateral surfaces , it would be helpful to remember the formula for the area of an equilateral triangle . the area of one equilateral triangle is a = ( s ^ 2 * sqrt { 3 } ) / 4 . we know the side of the equilateral triangle must be the same as the square : s = 6 . thus , one of these equilateral triangles has an area of a = ( 6 ^ 2 * sqrt { 3 } ) / 4 = 9 * sqrt { 3 } . there are four identical triangles , so their combined area is a = 36 * sqrt { 3 } . now , add the square base , for a total surface area of a = 36 + 36 * sqrt { 3 } . answer = b
Answer: b
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1.5 % more . she would get how much ?
Options: a ) 9560 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: ( 8000 * 3 * 1.5 ) / 100 = 360 9200 - - - - - - - - 9560 answer : a
Answer: a
Problem: a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 113 m 2 , c ) 123 m 2 , d ) 115 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 12 ) 2 = 113 m 2 answer b"
Answer: b
Problem: there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 37 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 170 ) = 1057 - 1020 = 37 . answer a"
Answer: a
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 27 seconds . find the length of the faster train ?
Options: a ) 270 m , b ) 189 m , c ) 278 m , d ) 279 m , e ) 917 m
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 27 * 10 = 270 m . the length of the faster train = 270 m . answer : a"
Answer: a
Problem: find the smallest number in gp whose sum is 38 and product is 1728
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x , y , z be the numbers in geometric progression ? y ^ 2 = xz x + y + z = 38 xyz = 1728 xyz = xzy = y ^ 2 y = y ^ 3 = 1728 y = 12 y ^ 2 = xz = 144 z = 144 / x x + y + z = x + 12 + 144 / x = 38 x ^ 2 + 12 x + 144 = 38 x x ^ 2 - 26 x + 144 = 0 ( x - 18 ) ( x - 8 ) = 0 x = 8,18 if x = 8 , z = 38 - 8 - 12 = 18 the numbers are 8,12 , 18 their sum is 38 their product is 1,728 the smallest number is 8 answer : d"
Answer: d
Problem: a fair coin is tossed 4 times . what is the probability of getting at least 2 tails ?
Options: a ) 1 / 16 , b ) 1 / 2 , c ) 3 / 16 , d ) 11 / 16 , e ) 3 / 8
Rationale: "let ' s find the probability of the opposite event and subtract this value from 1 . the opposite event would be getting zero tails ( so all heads ) or 1 tail . p ( hhhh ) = ( 12 ) 4 = 116 p ( hhhh ) = ( 12 ) 4 = 116 . p ( thhh ) = 4 ! 3 ! ∗ ( 12 ) 4 = 416 p ( thhh ) = 4 ! 3 ! ∗ ( 12 ) 4 = 416 , we are multiplying by 4 ! 3 ! 4 ! 3 ! since thhh scenario can occur in number of ways : thhh , hthh , hhth , or hhht ( notice that 4 ! 3 ! 4 ! 3 ! basically gives number of arrangements of 4 letters thhh out of which 3 h ' s are identcal ) . p ( t ≥ 2 ) = 1 − ( 116 + 416 ) = 1116 p ( t ≥ 2 ) = 1 − ( 116 + 416 ) = 1116 . answer : d ."
Answer: d
Problem: find the area of trapezium whose parallel sides are 30 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 360 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 30 + 18 ) * ( 15 ) = 360 cm 2 answer : c"
Answer: c
Problem: the mean of 50 observations is 100 . but later he found that there is decrements of 13 from each observations . what is the the updated mean is ?
Options: a ) 87 , b ) 97 , c ) 67 , d ) 57 , e ) 46
Rationale: "87 answer is a"
Answer: a
Problem: if x and y are integers such that x ^ 2 = y and xy = 27 , then x – y = ?
Options: a ) - 30 , b ) - 20 , c ) - 6 , d ) 5 , e ) 20
Rationale: here x and y are integers . x ^ 2 = y xy = 27 . substitute x ^ 2 = y in xy = > x ^ 3 = 27 . here x 3 is positive , x is also positive . x = 3 then y = 9 . x - y = - 6 so option c is correct
Answer: c
Problem: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 13 , b ) 18 , c ) 40 , d ) 82 , e ) 43
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 answer : c"
Answer: c
Problem: a trader sells 23 meters of cloth for rs . 529 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 88 , c ) 90 , d ) 42 , e ) 18
Rationale: "sp of 1 m of cloth = 529 / 23 = rs . 23 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 23 - rs . 5 = rs . 18 answer : e"
Answer: e
Problem: if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 54 more . what is the cost price ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: 9 % * cost price = $ 54 1 % * cost price = $ 54 / 9 = $ 6 the cost price is $ 600 . the answer is b .
Answer: b
Problem: if 8 cats can kill 8 rats in 8 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 6 minutes , b ) 7 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: it will take 8 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 8 minutes , so 100 cats can kill 100 rats in 8 minutes answer c
Answer: c
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 600 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
Options: a ) 100 % , b ) 12.5 % , c ) 67 % , d ) 25 % , e ) 33 %
Rationale: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 3 years the principal p amounts to $ 400 and after a time of 5 years ( question says after another 5 years so 3 + 2 ) p becomes $ 600 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 400 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 5 r / 100 ) = 600 dividing a 2 by a 1 we get ( 1 + 5 r / 100 ) / ( 1 + 3 r / 100 ) = 6 / 8 after cross multiplication we are left with r = 100 option : a"
Answer: a
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5080 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 762
Rationale: "e 762 ? = 5080 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 762"
Answer: e
Problem: how many integers k greater than 100 and less than 800 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 6 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . 607 | 708 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 6 sets with 10 such number in each set will give 6 x 10 = 60 integers . b"
Answer: b
Problem: √ 4 percent of 4 √ 4 =
Options: a ) 0.16 , b ) 0.17 , c ) 0.18 , d ) 0.2 , e ) 0.19
Rationale: √ 4 = 2 so , √ 4 percent of 4 √ 4 = 2 percent of ( 4 ) ( 2 ) = ( 2 / 100 ) ( 8 ) = 16 / 100 = 0.16 answer : a
Answer: a
Problem: a palindrome is a number that reads the same forward and backward , such as 616 . how many even , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: "first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 2,4 , 6,8 will be odd , which is 4 / 9 ths of the combinations . 4 / 9 * 90 = 40 answer : a"
Answer: a
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 12 hours a day , the number of men required ?
Options: a ) 11 days , b ) 12 days , c ) 9 days , d ) 8 days , e ) 10 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 8 = 8 days e )"
Answer: e
Problem: 8 people decided to split the restaurant bill evenly . if the bill was $ 214.15 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.20
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a"
Answer: a
Problem: in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.35 $ . assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty . how much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75 % bigger ?
Options: a ) $ 78.80 , b ) $ 79.80 , c ) $ 78.90 , d ) $ 79.90 , e ) $ 77.80
Rationale: "lots of calculations . 1.50 * 4 + 3 * . 35 * 32 + 2 * ( 7 / 4 ) * 32 * . 35 answer = $ 78.80 the correct option is a"
Answer: a
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what y percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer"
Answer: d
Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 5113 , b ) 5117 , c ) 5120 , d ) 8119 , e ) 10115
Rationale: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"
Answer: c
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000.00001 more . at the end of the year , their profits amounted to rs . 714 find the share of a .
Options: a ) 240 , b ) 272 , c ) 379 , d ) 277 , e ) 122
Rationale: explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 714 = 272 answer : b
Answer: b
Problem: a train 120 m long running at 60 kmph crosses a platform in 35 sec . what is the length of the platform ?
Options: a ) 338 , b ) 277 , c ) 463 , d ) 456 , e ) 271
Rationale: "d = 60 * 5 / 18 = 35 = 583 – 120 = 463 answer : c"
Answer: c
Problem: jar a has 6 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 2.8 % , b ) 3.0 % , c ) 3.2 % , d ) 3.4 % , e ) 3.6 %
Rationale: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 106 marbles . now , for both jars to have equal marbles we should move 3 marbles from a to b , which is 3 / 106 = ~ 2.8 % of a . answer : a ."
Answer: a
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers t are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes t in this range . answer : a ."
Answer: a
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 400 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 605 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 3000 , b ) 5000 , c ) 2000 , d ) 4000 , e ) 6000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 200 , thus 0.2 x = $ 200 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 . answer : c"
Answer: c
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 4 hours ?
Options: a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 4 hours , the amount of water is 3.6 - 0.5 ( 4 ) = 1.6 gallons the concentration of water is 1.6 / ( 2.4 + 1.6 ) = 40 % the answer is a ."
Answer: a
Problem: what number has a 5 : 1 ratio to the number 10 ?
Options: a ) 74 , b ) 50 , c ) 94 , d ) 59 , e ) 48
Rationale: "answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b"
Answer: b
Problem: a 125 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 126 , e ) 90
Rationale: "s = 125 / 5 * 18 / 5 = 90 kmph answer : e"
Answer: e
Problem: excluding stoppages , the speed of a bus is 80 km / hr and including stoppages , it is 70 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 11 min , b ) 10 min , c ) 8 min , d ) 6 min , e ) 5 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = 10 / 80 * 60 = 8 min . answer : c"
Answer: c
Problem: a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ?
Options: a ) 4 , b ) 9 , c ) 2 , d ) 11 , e ) none
Rationale: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a"
Answer: a
Problem: in the youth summer village there are 200 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 125 , b ) 150 , c ) 100 , d ) 130 , e ) 140
Rationale: total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c
Answer: c
Problem: nitin ranks 18 th in a class of 49 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 49 - 18 ) = 31 nitin is 32 nd from the last answer : c ) 32"
Answer: c
Problem: lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . )
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .
Answer: d
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum q of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . q = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"
Answer: b
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 12 minutes . the length of the bridge is ?
Options: a ) 2000 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 12 * 60 = 2000 m answer is a
Answer: a
Problem: there are 1000 students in a school and among them 30 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 30 , e ) 20
Rationale: 30 % of 1000 gives 300 . so 300 attends chess and 10 % of 300 gives 30 . so 30 enrolled for swimming answer : d
Answer: d
Problem: a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 800 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
Options: a ) 86 , b ) 88 , c ) 90 , d ) 92 , e ) 94
Rationale: "cost price = 800 profit = 10 % = 10 % of 800 = 80 selling price = cp + profit sp = 880 a discount of 10 % to employees means 10 % off on 880 so 10 % of 880 = 88 ans b"
Answer: b
Problem: exactly 15 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 15 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 15 ( # of reporters who cover local politics ) : 0.75 x = 15 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."
Answer: d
Problem: two numbers are respectively 50 % and 20 % more than a third number . the percentage that is first of the second is ?
Options: a ) 125 % , b ) 97 % , c ) 118 % , d ) 52 % , e ) 83 %
Rationale: "i ii iii 150 120 100 120 - - - - - - - - - - 150 100 - - - - - - - - - - - ? = > 125 % answer : a"
Answer: a
Problem: of 70 players on a football team , 43 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 ) 59 , c ) 61 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer"
Answer: c
Problem: in how many seconds will a train 100 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 100 / 10 = 10 seconds the answer is c ."
Answer: c
Problem: a pair of articles was bought for $ 1000 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 555.55 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 1000 / 2 = $ 500 let m . p = $ x 90 % of x = 500 x = 500 * 100 / 90 = $ 555.55 answer is a"
Answer: a
Problem: what is 15 % of 2 / 3 of 0.5 ?
Options: a ) 0.05 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 5 / 10 ) = 150 / 3000 = 0.05 option a"
Answer: a
Problem: the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?
Options: a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these
Rationale: let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a
Answer: a
Problem: a monkey ascends a greased pole 17 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 31 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 15 metres , he ascends in 30 minutes . â ˆ ´ he reaches the top in 31 st minute . answer a"
Answer: a
Problem: a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?
Options: a ) 220 m , b ) 250 m , c ) 280 m , d ) 210 m , e ) 270 m
Rationale: e 270 m
Answer: e
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 26 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 10 % of 140 = rs . 140 - 14 = rs . 126 . gain = rs . 126 â € “ rs . 100 = rs . 26 therefore , gain / profit percent = 26 % . answer : option a"
Answer: a
Problem: what is the tens digit of 36 ^ 5 ?
Options: a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9
Rationale: "36 ^ 5 = 6 ^ 7 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 7 ( dont actually calculate full values ) and answer is d : 3"
Answer: d
Problem: evaluate : | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 72 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72"
Answer: c
Problem: find the simple interest on rs . 500 for 9 months at 6 paisa per month ?
Options: a ) 287 , b ) 270 , c ) 276 , d ) 129 , e ) 211
Rationale: "i = ( 500 * 9 * 6 ) / 100 = 270 answer : b"
Answer: b
Problem: evaluate : 60 - 12 ÷ 4 × 2 =
Options: a ) a ) 45 , b ) b ) 54 , c ) c ) 63 , d ) d ) 72 , e ) e ) 81
Rationale: "according to order of operations , 12 ÷ 4 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 4 × 2 = 3 × 2 = 6 hence 60 - 12 ÷ 4 × 2 = 60 - 6 = 54 correct answer is b ) 54"
Answer: b
Problem: on a trip , a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles . if the cyclist returned immediately via the same route and took a total of 9 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 7.6 , b ) 7.8 , c ) 8 , d ) 8.2 , e ) 8.4
Rationale: the time to go 42 miles was 22 / 11 + 20 / 10 = 2 + 2 = 4 hours . the average speed for the return trip was 42 miles / 5 hours = 8.4 mph . the answer is e .
Answer: e
Problem: on increasing the number of lines in a page by 100 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 71.4 % , e ) 60 %
Rationale: "explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d"
Answer: d
Problem: find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?
Options: a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none
Rationale: answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b
Answer: b
Problem: 3 distinct single digit no a , b , c are in g . p . if abs ( x ) for real x is the absolute value of x ( x if x is positive or zero , and x if x is negative ) , then the no . of different possible values of abs ( a + b - c ) is
Options: a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2
Rationale: if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d
Answer: d
Problem: sum of 19 odd numbers is ?
Options: a ) 341 , b ) 351 , c ) 361 , d ) 371 , e ) 381
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c"
Answer: c
Problem: an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 25 coaches are attached .
Options: a ) 90 , b ) 85 , c ) 80 , d ) 60 , e ) 70
Rationale: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 90 - 20 = 70 e"
Answer: e
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 188 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 264 + l ) / 20 = l / 8 2112 + 8 l = 20 l l = 2112 / 12 = 176 m answer b"
Answer: b
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 12 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 11.5 , b ) 9.5 , c ) 13.5 , d ) 10.6 , e ) 14.5
Rationale: "step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d"
Answer: d
Problem: a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee . find his net profit or loss percent ?
Options: a ) 73 1 / 3 % , b ) 13 1 / 3 % , c ) 33 1 / 3 % , d ) 23 1 / 3 % , e ) 93 1 / 3 %
Rationale: "explanation : the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 4 profit = sp - cp = 4 - 3 = 1 profit percent = 1 / 3 * 100 = 33 1 / 3 % answer : c"
Answer: c
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 × 15 = 180 m . then , speed of train = 180 ⁄ 18 = 10 m / s now , length of train = 10 × 15 = 150 m ∴ required time = 150 ⁄ 10 = 15 sec . answer c"
Answer: c
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 16 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a"
Answer: a
Problem: prints a page 40 pg per min . if the printed for 2 hours except 20 min . where there was an paper jam , how many page did it print
Options: a ) 4,000 , b ) 12,880 , c ) 14,880 , d ) 8,880 , e ) 18,880
Rationale: 40 pages - - - - - - - > 1 min 2 hrs except 20 mints means = 2 * 60 = 120 - 20 = 100 mints i . e . , 100 * 40 = 4,000 pages printed . answer : a
Answer: a
Problem: a train 450 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 39 sec , c ) 27 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 450 m at 50 / 3 m / sec = 450 * 3 / 50 sec = 27 sec answer : c ."
Answer: c
Problem: during a thanksgiving weekend , a car rental company rented 6 - tenths of their vehicles , including two - fifths of the 4 wds that it had . if 40 % of the vehicles are 4 wds , then what percent of the vehicles that were not rented were not 4 wds ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: 4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .
Answer: c
Problem: if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 11 , d ) 8 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c"
Answer: c
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100000 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100000 n = 1000 satisfies this . e"
Answer: e
Problem: jim drove 1096 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 104 miles , b ) 432 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 1096 = 104 miles correct answer a"
Answer: a
Problem: ram , who is half as efficient as krish , will take 18 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 18 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 18 days is 18 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 18 w / 3 w = 6 days answer d"
Answer: d
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 weighs 8 g / cm ^ 3 , then the weight of the pipe is :
Options: a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg
Rationale: "external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"
Answer: b
Problem: the average weight of 7 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 75.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 7 × 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c"
Answer: c