regisss/math_qa huggingface dataset:
Problem: if ( a - b - c + d = 12 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 9 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 12 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 12 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 6 ( 2 ) simplify - b + d = 3 b - d = - 3 ( b - d ) ^ 2 = ( - 3 ) ^ 2 = 9 my answer : b"
Answer: b
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1000 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1000 , loss of pyarelal = 1000 * 9 x / 10 x = 900 answer : d"
Answer: d
Problem: what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298
Rationale: "let the side of the square plot be a ft . a 2 = 81 = > a = 9 length of the fence = perimeter of the plot = 4 a = 36 ft . cost of building the fence = 36 * 58 = rs . 2088 . answer : d"
Answer: d
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 105 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 145 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 174
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 174 min * leg a - b - - - > d = 105.174 / 60 = 18270 / 60 * leg b - a - - - - > d = 145 * 126 / 60 = 18270 / 60 so the correct ans . ise"
Answer: e
Problem: in a competitive examination in a state a , 10 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 12 % candidates got selected with 100 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 4000 , b ) 5000 , c ) 5500 , d ) 6500 , e ) 4200
Rationale: "let the number of candidates appeared be x then , 12 % of x - 10 % of x = 100 2 % of x = 100 x = 100 * 100 / 2 = 5000 answer is b"
Answer: b
Problem: if it is assumed that 80 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 375 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 80 % = 300 / 0.8 = 375 option a"
Answer: a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 13 what is the no . ?
Options: a ) 6.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 13 = > 2 x = 13 = > x = 6.5 a"
Answer: a
Problem: in arun ' s opinion , his weight is greater than 66 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 69 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 67.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 66 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 69 . the values satisfying all the above conditions are 67 and 68 . required average = ( 67 + 68 ) / 2 = 67.5 kg answer : b"
Answer: b
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 20 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1634 , d ) 1678 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 20 5 x = 1345 x = 269 large number = 269 + 1365 = 1634 c"
Answer: c
Problem: by selling 9 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 4 , e ) 6
Rationale: "80 % - - - 9 120 % - - - ? 80 / 120 * 9 = 6 answer : e"
Answer: e
Problem: in a public show 62 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 228
Rationale: "75 % of 600 = 62 / 100 × 600 = 372 therefore , the number of vacant seats = 600 - 372 = 228 . answer : e"
Answer: e
Problem: there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 4576 , then what was the price of the article initially ?
Options: a ) rs . 5000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 2000 , e ) rs . 6000
Rationale: "let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 4576 for 114.4 - - - > 100 ; 4576 - - - > ? required price = ( 4576 * 100 ) / 114.4 = 40 * 100 = rs . 4000 . answer : c"
Answer: c
Problem: 50 boys and 100 girls are examined in a test ; 50 % of the boys and 40 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 42.5 % , b ) 62.1 % , c ) 56.7 % , d ) 39.9 % , e ) 51.4 %
Rationale: "total number of students = 50 + 100 = 150 number of students passed = ( 50 % of 50 + 40 % of 100 ) = 25 + 40 = 65 number of failures = 85 * 100 / 150 = 56.7 % answer is c"
Answer: c
Problem: if ( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 5 ) ( 9 ^ 3 ) = 3 ( 15 ^ x ) = > 5 ^ 5 * 3 ^ 6 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 5 * 3 ^ 6 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 5 answer a"
Answer: a
Problem: 5356 x 51 = ?
Options: a ) 273156 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5356 x 51 = 5356 x ( 50 + 1 ) = 5356 x 50 + 5356 x 1 = 267800 + 5356 = 273156 . a"
Answer: a
Problem: marts income is 60 percent more than tims income and tims income is 60 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 64 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 40 / 100 ) j = > m = ( 64 / 100 ) j answer b ."
Answer: b
Problem: a man swims downstream 16 km and upstream 10 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 7.0 , b ) 8.2 , c ) 6.5 , d ) 7 , e ) 6
Rationale: "16 - - - 2 ds = 8 ? - - - - 1 10 - - - - 2 us = 5 ? - - - - 1 m = ? m = ( 8 + 5 ) / 2 = 6.5 answer : c"
Answer: c
Problem: the manufacturing cost of a shoe is rs . 190 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 234 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 190 + ( 500 / 100 ) = 195 . gain = 20 % = > sp = 1.2 cp = 1.2 x 195 = 234 answer : a"
Answer: a
Problem: what is the area of a circle having the same perimeter as that of a square whose area is 121 .
Options: a ) 306
b ) 307
c ) 308
d ) 309
e ) 310
Rationale: side of the square = sqrt ( 12 ) = 11 perimeter of the square = 44 2 * pie * r = 44 r = 44 / 2 * pie area of the circle = pie * r ^ 2 = 308 answer : c
Answer: c
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 20 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.09
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 20 % are damaged - - > available tomatoes to sell = 80 80 * x - 80 = 0.08 * 80 80 x - 80 = 6.4 80 x = 86.64 x = 86.64 / 80 = 87 / 80 ( approx ) = 1.0875 x is slightly under 1.0875 = 1.09 answer : e"
Answer: e
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 3 % p . a . in 5 years . what is the sum ?
Options: a ) 26775 , b ) 28772 , c ) 28821 , d ) 89255 , e ) 28871
Rationale: "principal = ( 100 * 4016.25 ) / ( 3 * 5 ) = rs . 26775 . answer : a"
Answer: a
Problem: what is the units digit of ( 498 ) ( 915 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 2 . imo c ."
Answer: c
Problem: a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 10 books for a total of $ 42.00 , and on tuesday the store sold 20 maps and 15 books for a total of $ 70.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 3.5 , d ) $ 2.5 , e ) $ l . 25
Rationale: "12 x + 10 y = 42 20 x + 15 y = 70 multiply eq 1 by 5 and eq 2 by 3 60 x + 50 y = 42 * 5 60 x + 45 y = 70 * 3 subtracting 1 from 2 5 y = 210 - 210 y = 0 therefore x = 3.5 difference in price = 3.5 c"
Answer: c
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Problem: the least number which when divided by 2 , 3 , 5 and 6 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 16 , b ) 63 , c ) 73 , d ) 83 , e ) none of these
Rationale: "explanation : l . c . m of 2 , 3 , 5 , 6 = 30 therefore required number is of the form 30 k + 3 . least value of k for which ( 30 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 30 x 2 + 3 ) = 63 . answer : b"
Answer: b
Problem: how many 4 - digit numbers ( abcd ) can be formed such that | a – d | = 2 ?
Options: a ) 2000 , b ) 1900 , c ) 1800 , d ) 1600 , e ) 1,500
Rationale: digit a can be filled in 9 ways ( excluding 0 ) digit b can be filled in 10 ways digit c can be filled in 10 ways digit d can be filled in 2 ways ( because of modulus a - d ) the answer will be 9 * 10 * 10 * 2 = 1800 ans c
Answer: c
Problem: find the smallest number of 6 digits which is exactly divisible by 111 ?
Options: a ) 12000 , b ) 15550 , c ) 100011 , d ) 158993 , e ) 100010
Rationale: "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer b"
Answer: b
Problem: if the mean of numbers 28 , x , 42 , 78 and 104 is 90 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 355 , d ) 423 , e ) 365
Rationale: the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 90 * 5 - - > x = 198 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 198 ) / 5 = 423 . answer : d .
Answer: d
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 12 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 25 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 12 / 60 ) = 5 kmhr speed in still water = 1 / 2 ( 2 + 5 ) = 3.5 kmhr time taken in stationary = 5 / 3.5 = 1 hrs 25 min answer : c"
Answer: c
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 7 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 630 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 7 h is 90 × 7 = 630 km ans . ( e )"
Answer: e
Problem: the average of 64 numbers is 48 . if two numbers namely 35 and 45 are discarded , the average of remaining numbers is ?
Options: a ) 35.5 , b ) 37.5 , c ) 39.5 , d ) 34.5 , e ) 47.9
Rationale: total of 50 numbers = 64 * 48 = 3072 average of 62 numbers = 3072 - ( 45 + 55 ) / 62 = 2972 / 62 = 47.9 answer is e .
Answer: e
Problem: a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 250.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.40
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 250 = > 125 * s = 175 = > s = 1.4 answer e"
Answer: e
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 65 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . age of the youngest child = x = 7 years . d )"
Answer: d
Problem: a toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters , at 10 meters per minute . however , the toy train is defective and it now produces only two different tunes at random . what is the probability that the toy train produces 3 music tunes of the same type ( 1 in _____ ) ?
Options: a ) 3 , b ) 9 , c ) 8 , d ) 4 , e ) 5
Rationale: 1 / 2 ^ 3 = 1 / 8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2 * 1 / 8 = 1 / 4 so ans is 4 answer : d
Answer: d
Problem: evaluate : 56 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 48 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 56 - 12 * 3 * 2 = 56 - 8 = 48 correct answer b"
Answer: b
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 31 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 11 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 31 - 9 = 22 ab = 11 . answer is d ."
Answer: d
Problem: if x , y , and z are positive real numbers such that x ( y + z ) = 132 , y ( z + x ) = 152 , and z ( x + y ) = 180 , then xyz is
Options: a ) 40 , b ) 60 , c ) 160 , d ) 100 , e ) 120
Rationale: xy + xz = 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 152 + 28 xz + zy = yz + yx + 28 xz = yx + 28 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 160 xz = 80 xyz has to be multiple of 80 , only 160 fits in answer = c
Answer: c
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party q . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: s = 100 not ( q and b ) = 35 only q = 20 ( q and b ) / b = 1 / 2 let ( q and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans
Answer: a
Problem: there is enough provisions for 100 girls in a hostel for 50 days . if there were 20 men less , how long will the provision last ?
Options: a ) 250 , b ) 255 , c ) 260 , d ) 265 , e ) 270
Rationale: we have , m 1 d 1 = m 2 d 2 100 * 50 = 20 * d 2 d 2 = 100 * 50 / 20 = 250 days . answer : a
Answer: a
Problem: at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years arun ' s age will be 26 years . what is the age of the deepak ?
Options: a ) 15 , b ) 20 , c ) 18 , d ) 22 , e ) 35
Rationale: "let the present age of arun and deepak be 4 x and 3 x 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a"
Answer: a
Problem: what is the greatest integer m for which the number 40 ! / 14 ^ m is an integer ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: 14 ^ m = 2 ^ m * 7 ^ m . let ' s figure out how many 7 ' s are in the prime factorization of 40 ! the multiples of 7 are : 7 , 14 , 21 , 28 , 35 . thus 7 ^ 5 will divide 40 ! but 7 ^ 6 will not . clearly 2 ^ 5 will divide 40 ! so m = 5 is the largest possible integer . the answer is d .
Answer: d
Problem: the price of a book is increased from $ 300 to $ 480 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 480 â € “ rs 300 = rs 180 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 180 300 ) * 100 = 60 % e"
Answer: e
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 21 ) both lie on the line defined by the equation x = ( y / 7 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x = ( y / 7 ) - ( 2 / 5 ) , and so y = 7 x + 14 / 5 . the slope is 7 . ( n + 21 - n ) / ( m + p - m ) = 7 p = 3 the answer is c .
Answer: c
Problem: let a be the event that a randomly selected two digit number is divisible by 10 and let b be the event that a randomly selected two digit number is divisible by 5 . what is p ( a and b ) ?
Options: a ) 1 / 50 , b ) 1 / 30 , c ) 1 / 15 , d ) 1 / 10 , e ) 1 / 5
Rationale: p ( a and b ) = 1 / 10 * 1 / 5 = 1 / 50 the answer is a .
Answer: a
Problem: in a group of cows and hens , the number of legs are 12 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 12 2 x = 12 x = 6 . answer : b"
Answer: b
Problem: find the least number which when divided by 12,24 , 36,42 leaves remainder 9,21 , 33,39 respectively .
Options: a ) 499 , b ) 501 , c ) 452 , d ) 365 , e ) 325
Rationale: "the difference of 12 - 9 = 3 , 24 - 21 = 3 , 36 - 33 = 3 , 42 - 39 = 3 lcm of 12,24 , 36,42 = 504 required number = 504 - 3 = 501 answer is b"
Answer: b
Problem: the difference between a 6 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 3 , b ) 92439 , c ) 30813 , d ) 10271 , e ) 10272
Rationale: another approach is to test a number . let ' s say the original number is 123004 so , the reversed number is 400321 the difference = 400321 - 123004 no check the answer choices 277317 is a multiple of 3,92439 , 30813,10271 10272 is not a multiple of 277317 answer : e
Answer: e
Problem: sandy is younger than molly by 12 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 12 s / m = 7 / 9 9 s = 7 m 9 ( m - 12 ) = 7 m m = 54 the answer is c ."
Answer: c
Problem: two pipes can fill a tank in 20 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 5 minutes , b ) 17 minutes , c ) 15 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 20 + 1 / 15 - 1 / 45 = ( 9 + 12 - 4 ) / 180 = 17 / 180 so , the tank becomes full in 5 minutes . answer : a"
Answer: a
Problem: the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 10 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 17 %
Rationale: "the original output increases by 10 % and then 10 % . total % change = a + b + ab / 100 total % change = 10 + 10 + 10 * 10 / 100 = 21 % now , you want to change it to 0 , so , 0 = 21 + x + 21 x / 100 x = - 21 ( 100 ) / 121 = 17 % approximately answer is e"
Answer: e
Problem: a company recently conducted a survey and found that 25,000 of its customers live in rural areas . if the number of customers who live in urban areas is 120 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 50,000 , b ) 55,000 , c ) 60,000 , d ) 65,000 , e ) 70,000
Rationale: "the number of customers in urban areas is 25,000 + 1.2 * 25,000 = 55,000 . the answer is b ."
Answer: b
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 142 m length ?
Options: a ) 82.1 sec . , b ) 12.6 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 142 = 252 m . required time = 252 / 20 = 12.6 sec . answer : b"
Answer: b
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration q of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration q would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Problem: in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 4.5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 110 * 95 = 10,450 , which is 4.5 % greater than the actual area . answer : d ."
Answer: d
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 4 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 4 * 3 * 1 ) / 3 = 12 / 3 = 4 e"
Answer: e
Problem: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 760 , b ) $ 750 , c ) $ 810 , d ) $ 800 , e ) $ 780
Rationale: 50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 5 ) + 30 ( 5 + 4 ) + 20 ( 5 + 4 + 4 ) = 250 + 270 + 260 = 780 answer - e
Answer: e
Problem: 0.2 x 0.7 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.14 , e ) none of these
Rationale: "explanation : 2 x 7 = 14 . sum of decimal places = 2 0.2 x 0.7 = 0.14 answer - d"
Answer: d
Problem: the cost price of a radio is rs . 1860 and it was sold for rs . 1340 , find the loss % ?
Options: a ) 18 % , b ) 12 % , c ) 22 % , d ) 27 % , e ) 21
Rationale: "1860 - - - - 520 100 - - - - ? = > 27 % answer : d"
Answer: d
Problem: in a kilometer race , a beats b by 16 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 716 sec , e ) 615 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 16 = 625 sec . time taken by a = 625 - 10 = 615 sec . answer : e"
Answer: e
Problem: if 15 students in a class average 75 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 81 % , b ) 82 % , c ) 83 % , d ) 84 % , e ) 85 %
Rationale: "( 15 * 75 + 10 * 95 ) / 25 = 83 % the answer is c ."
Answer: c
Problem: a boat crossed a lake from north to west at the speed of 5 km / h , entered a river and covered twice as much distance going upstream at 4 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.6 km / h that day , what was its approximate downstream speed ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 8
Rationale: one way of solving this is : speed of boat on still water ( lake ) = 5 kmph speed upstream = 4 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 5 + 1 = 6 kmph ans is c
Answer: c
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 50 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 110 % , d ) 120 % , e ) 150 %
Rationale: "x discount on pony jeans , ( 0.5 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.5 - x ) + 2 * 18 x = 9 - - > x = 1.5 = 150 % answer : e ."
Answer: e
Problem: a shopkeeper forced to sell at cost price , uses a 750 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 33.33 % , d ) 12 % , e ) none of these
Rationale: shopkeeper sells 750 g instead of 1000 g . so , his gain = 1000 - 750 = 250 g . thus , % gain = ( 250 * 100 ) / 750 = 33.33 % . answer : option c
Answer: c
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 9 : 1 . if 90 % of the toyota bought and 10 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 82 % , b ) 64 % , c ) 28 % , d ) 69 % , e ) 80 %
Rationale: "let total no of vehicles bought be 100 , toyota 90 and honda 10 , so total number of suv ' s bought for toyota and honda respectively 90 * 90 / 100 = 81 and 10 * 10 / 100 = 1 so total 82 suv ' s were bought out of 100 vehicles bought . . so required % is 82 % answer : a"
Answer: a
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 171 ( p ) ( p - 1 ) = 342 = 19 * 18 p = 19 the answer is e ."
Answer: e
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 / 10 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 / 1000 n = 10 satisfies this . d
Answer: d
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 3 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 180 x = 90 min answer : c"
Answer: c
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 56 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 39 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 56 = 392 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 392 - 780 = 39 . answer : a"
Answer: a
Problem: a student got twice as many sums wrong as he got right . if he attempted 75 sums in all , how many did he solve correctly ?
Options: a ) 25 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 75 3 x = 75 x = 25 . answer : a"
Answer: a
Problem: how much water should be added to 12 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 28 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 12 + x ) ) ) 2 = 5 % * ( 12 + x ) - - - - - - - - > x = 28 ans a
Answer: a
Problem: a sum of money lent out at s . i . amounts to rs . 710 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 586 , c ) s . 540 , d ) s . 740 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 710 ) = rs . 310 . s . i . for 2 years = 310 / 5 * 2 = rs . 124 . principal = ( 710 - 124 ) = rs . 586 . answer : b"
Answer: b
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 15,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 4965 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 15000 . t = 3 years and r = 10 % p . a . c . i . = rs . 15000 x 1 + 10 3 - 1 100 = rs . 15000 x 331 1000 = 4965 . d"
Answer: d
Problem: the overall age of x and y is 10 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 10 , c ) 12 , d ) 17 , e ) 19
Rationale: "b 10 ( x + y ) â € “ ( y + z ) = 10 x â € “ z = 10"
Answer: b
Problem: a bag contains 15 red jellybeans and 15 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 10 answer : option e"
Answer: e
Problem: if the simple interest on a sum of money for 6 years at 12 % per annum is rs . 700 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) 746.77 , b ) 945.77 , c ) 946.77 , d ) 246.77 , e ) 926.77
Rationale: "sum = ( 700 * 100 ) / ( 6 * 12 ) = rs . 972.22 c . i . on rs . rs . 972.22 for 6 years at 12 % = rs . 1 , 918.99 . = rs . 1 , 918.99 - 972.22 = rs . 946.77 answer : c"
Answer: c
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 52 , then how old is b ?
Options: a ) 17 years , b ) 20 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 52 5 x = 50 = > x = 10 hence , b ' s age = 2 x = 20 years . answer : b"
Answer: b
Problem: a man ' s age is 125 % of what it was 10 years ago , but 83 x 1 / 3 % of what it will be after 10 years . what is his present age ?
Options: a ) 20 , b ) 60 , c ) 50 , d ) 70 , e ) 80
Rationale: c 50 let the age before 10 years = x then , 125 x / 100 = x + 10 ⇒ 125 x = 100 x + 1000 ⇒ x = 1000 / 25 = 40 present age = x + 10 = 40 + 10 = 50
Answer: c
Problem: when average age of 20 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 20 numbers = 0 . sum of 20 numbers ( 0 x 20 ) = 0 . it is quite possible that 19 of these numbers may be positive and if their sum is a then 20 th number is ( - a ) answer is 19 ( b )"
Answer: b
Problem: 5301 x 13 = ?
Options: a ) 89136 , b ) 31986 , c ) 68910 , d ) 53113 , e ) 68913
Rationale: "append 0 before and after : 053010 calculation : 1 x 3 + 0 = 3 ( take 3 as ones digit of the product ) 0 x 3 + 1 = 1 ( take 1 tens digit of the product ) 3 x 3 + 0 = 9 ( take 9 hundreds digit of the product ) 5 x 3 + 3 = 18 ( take 8 as thousands digit of the product , carry over 1 ) 0 x 3 + 5 = 5 ; 5 + 1 = 6 ( take 6 as ten thousands digits of the product ) so , 5301 x 13 = 68913 answer is e ."
Answer: e
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 9.2 hrs
Rationale: "net part filled in 1 hour = 1 / 3 - 1 / 9 = 2 / 9 therefore the cistern will be filled in 9 / 2 hours or 4.5 hours . answer : a"
Answer: a
Problem: a river 8 m deep and 25 m wide is flowing at the rate of 8 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 26666 , b ) 26166 , c ) 29666 , d ) 22666 , e ) 26699
Rationale: "rate of water flow - 8 kmph - - 8000 / 60 - - 133.33 m / min depth of river - - 8 m width of river - - 25 m vol of water per min - - 133.33 * 8 * 25 - - - 26666 answer a"
Answer: a
Problem: among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 168 using your analysis : we see that the total number of students who study either maths or sociology = 176 + 224 - 168 = 232 so , in the image we know that the number of students in the zone with the black boundary = 232 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 232 + b + w = 400 or , b + w = 400 - 232 = 168 that is , b = 168 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 168 d"
Answer: d
Problem: each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 12 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 12 , the ratio of 10 - pound boxes : 20 - pound boxes should be 4 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 4 : 1 , the number of 20 - pound boxes must be 1 . we need to remove 15 of the 20 - pound boxes . the answer is e ."
Answer: e
Problem: if n is a positive integer and n ^ 2 is divisible by 264 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 48 , is n divisible by 48 ? no . so , n is not always divisible by 48 . e"
Answer: e
Problem: ramesh purchased a refrigerator for rs . 17500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 24475 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 17,500 discount offered = 20 % marked price = 17500 * 100 / 80 = rs . 21875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 21875 + 375 = rs . 22250 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 22250 * 110 / 100 = rs . 24475 answer : c"
Answer: c
Problem: harkamal purchased 3 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 700 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 3 kg grapes = 70 × 3 = 210 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 210 + 490 = 700 a"
Answer: a
Problem: the wages earned by robin is 35 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 25.92 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 135 and $ 160 respectively . charles earns $ 35 more than robin who earns $ 135 . therefore , charles ' wage is 35 / 135 * 100 = 25.92 % . the correct choice is ( a )"
Answer: a
Problem: if log 1087.5 = 4.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 60 , b ) 28 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 4087.5 + 1 ) = 10 ( 4.9421 + 1 ) = 10 ( 5.9421 ) = 59.421 x = antilog ( 59.421 ) therefore , number of digits in x = 60 . answer : a"
Answer: a
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 70 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 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 70 % , 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 is 40 % of 80 hence , d is the answer"
Answer: d
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 210 / 7.5 + 210 / 10.5 ] hours = 48 hours . answer d"
Answer: d
Problem: q ' = 3 q - 3 , what is the value of ( 4 ' ) ' ?
Options: a ) 48 , b ) 57 , c ) 66 , d ) 72 , e ) 81
Rationale: "( 4 ' ) ' = ( 3 * 4 - 3 ) ' = 9 ' = 9 * 9 - 9 = 72 answer d"
Answer: d
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is $ 50 , what is the compound interest on the same at the same rate and for the same time ?
Options: a ) $ 50 , b ) $ 51.5 , c ) $ 52 , d ) $ 52.5 , e ) $ 51.25
Rationale: "sum = 50 x 100 / ( 2 x 5 ) = 500 = 500 x ( 1 + 5 / 100 ) ^ 2 = 500 x 21 / 20 x 21 / 20 = 551.25 . c . i = 551.25 - 500 = 51.25 . answer e ) $ 51.25"
Answer: e
Problem: a train running at the speed of 180 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 288 meter , e ) 450 meter
Rationale: "speed = 180 * ( 5 / 18 ) m / sec = 50 m / sec length of train ( distance ) = speed * time ( 50 ) * 9 = 450 meter answer : e"
Answer: e
Problem: the cost of 2 chairs and 3 tables is rs . 1700 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 500
Rationale: "explanation : 2 c + 3 t = 1700 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 500 = > t - c = 500 answer : e"
Answer: e
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 5 seconds than it was moving after 3 seconds ?
Options: a ) 4 , b ) 9 , c ) 15 , d ) 20 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 therefore z ( 7 ) - z ( 3 ) = 35 - 15 = 20 km / hr option d"
Answer: d
Problem: consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ?
Options: a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these
Rationale: "explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 * 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer : c"
Answer: c
Problem: the present ages of reena and usha are 24 and 36 yr . respectively . what was the ratio between the ages of usha and reena respectively 8 yr ago ?
Options: a ) 7 : 4 , b ) 4 : 7 , c ) 11 : 8 , d ) 8 : 11 , e ) 9 : 12
Rationale: required ratio = ( 36 - 8 ) / ( 24 - 8 ) = 28 / 16 = 7 : 4 answer : a
Answer: a
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 24 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 292 , e ) 312
Rationale: so 12.2 * 24 = 292 . . imo option d is correct answer . .
Answer: d
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds . what is the length of the platform in meters ?
Options: a ) 200 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 20 * 20 = 400 = length of train length of platform = 600 - 400 = 200 answer : a"
Answer: a
Problem: what is the 20 - fourth decimal to the right in the fraction 35 / 36 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 35 / 36 = 0.97222222222 . . . the answer is b .
Answer: b
Problem: a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 10 : 00 a . m . ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 10
Rationale: sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour and 5 times in next hour . hence , they cross each other 10 times before 10 : 00 a . m . answer e
Answer: e