regisss/math_qa huggingface dataset:
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 20286 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 15 % , e ) 12 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 20286 / - - 17640 / - = rs . 2646 / - rate of interest = ( 2646 / 17640 ) × ( 100 / 1 ) = > 15 % answer : option d"
Answer: d
Problem: david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 600 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 4,800 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 2400 , b ) 3600 , c ) 3000 , d ) 2800 , e ) 2500
Rationale: let the rate be x , then population of the bacteria after each hour can be given as 600,600 x , 600 ( x ^ 2 ) , 600 ( x ^ 3 ) now population at 4 pm = 4800 thus we have 600 ( x ^ 3 ) = 4800 = 8 thus x = 2 therefore population at 3 pm = 600 ( 4 ) = 2400 answer : a
Answer: a
Problem: 5 years ago , the average age of a , b , c and d was 45 years . with e joining them now , the average of all the 5 is 50 years . the age of e is ?
Options: a ) 50 , b ) 47 , c ) 48 , d ) 49 , e ) 46
Rationale: solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a
Answer: a
Problem: sandy bought 65 books for $ 1180 from one shop and 55 books for $ 860 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21
Rationale: "average price per book = ( 1180 + 860 ) / ( 65 + 55 ) = 2040 / 120 = $ 17 the answer is c ."
Answer: c
Problem: there are 15 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are to be chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 1 / 3 , b ) 7 / 22 , c ) 1 / 9 , d ) 7 / 66 , e ) 2 / 45
Rationale: "total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d ."
Answer: d
Problem: a cistern can be filled by a tap in 4 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 ) 6 hr , b ) 5.6 hr , c ) 9.5 hr , d ) 7.2 hr , e ) 4 hr
Rationale: "net part filled in 1 hour 1 / 4 - 1 / 9 = 5 / 36 the cistern will be filled in 36 / 5 hr = 7.2 hr answer is d"
Answer: d
Problem: approximately how many cubic feet of water are needed to fill a circular swimming pool that is 40 feet across and 7 feet deep ?
Options: a ) 700 , b ) 1500 , c ) 3000 , d ) 5000 , e ) 9000
Rationale: "answer should be e . v = \ pir ^ 2 h = \ pi * 20 ^ 2 * 7 = approximately 9000"
Answer: e
Problem: in a graduate physics course , 70 percent of the students are male and 40 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ?
Options: a ) 2 / 7 , b ) 5 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 / 3
Rationale: "let assume there are 100 students of which 70 are male and 30 are females if 40 are married then 60 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 40 is the total number of students who are married and out of that 20 are males then the remaining 20 will be females who are married . total females = 30 married females = 20 then single females = 30 - 20 = 10 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ e ]"
Answer: e
Problem: ( 3 x + 2 ) ( 2 x - 1 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "expanding we have 6 x ^ 2 - 3 x + 4 x - 2 6 x ^ 2 + x - 2 taking coefficients , a = 6 , k = 1 , n = - 2 therefore a - n + k = 6 - ( - 2 ) + 1 = 8 + 1 = 9 the answer is c ."
Answer: c
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 600 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 710 , c ) 1000 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 600 100 % of oranges = ( 600 × 100 ) / 6 = 1000 total oranges = 1000 answer : c"
Answer: c
Problem: if the sides of a triangle are 196 cm , 81 cm and 277 cm , what is its area ?
Options: a ) 5000 , b ) 5656 , c ) 7878 , d ) 7900 , e ) 7938
Rationale: "the triangle with sides 196 cm , 81 cm and 277 cm is right angled , where the hypotenuse is 277 cm . area of the triangle = 1 / 2 * 81 * 196 = 7938 cm 2 answer : option e"
Answer: e
Problem: what is the average ( arithmetic mean ) of 10 , 2030 , 4050 , 6070 , 8090 ?
Options: a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50
Rationale: so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e .
Answer: e
Problem: a man swims downstream 100 km and upstream 30 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 2.5 , b ) 3.5 , c ) 4.5 , d ) 5.3 , e ) 3.4
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 30 - - - - 10 us = 3 ? - - - - 1 s = ? s = ( 10 - 3 ) / 2 = 3.5 answer : b"
Answer: b
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 21 , e ) 1322
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 1323 3 b 2 = 1323 b 2 = 441 = 21 ( b > 0 ) b = 21 m . answer : d"
Answer: d
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.3 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.0 , c ) 4.8 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.3 x = 4.8 alternate solution : try to backsolve . initial volume = 4.8 after one hour - - > ( 1 / 4 ) 4.8 = 1.2 after two hours - - > ( 1 / 4 ) 1.2 = 0.3 answer : c"
Answer: c
Problem: the perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 35 , c ) 77 , d ) 54 , e ) 38
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3.5 * 22 / 2 = 38.5 cm 2 answer : e"
Answer: e
Problem: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 6 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.4 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6
Rationale: "index for females = ( 20 - 6 ) / 20 = 7 / 10 = 0.7 index for males = ( 20 - 14 / 20 = 3 / 10 = 0.3 index for females exceeds males by 0.7 - 0.3 = 0.4 answer : a"
Answer: a
Problem: x does a work in 40 days . y does the same work in 60 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 40 y ' s 1 day ' s work = 1 / 60 ( x + y ) ' s 1 day ' s work = ( 1 / 40 + 1 / 60 ) = 1 / 24 both together will finish the work in 24 days . correct option is c"
Answer: c
Problem: the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the sum and the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 14 , e ) 15
Rationale: "let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b"
Answer: b
Problem: 7 carpet - weavers can weave 7 carpets in 7 days . at the same rate , how many carpets would be woven by 14 carpet - weavers in 14 days ?
Options: a ) 14 , b ) 28 , c ) 21 , d ) 35 , e ) none of these
Rationale: explanation : solution : let the required number of carpets be x . more weavers , more carpets ( direct proportion ) more days , more carpets ( direct proportion ) weavers 7 : 14 } : : 7 : x days 7 : 14 . ' . 7 * 7 * x = 14 * 14 * 7 < = > x = 14 * 14 * 7 / 7 * 7 = 28 . answer : b
Answer: b
Problem: what is the speed of the stream if a canoe rows upstream at 6 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 6 ) kmph = 3 kmph . answer c"
Answer: c
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 40 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 45 % , b ) 40 % , c ) 25 % , d ) 28 % , e ) 33.33 %
Rationale: i year best is to give a number to his income , say 100 . . and let saving be x . . so expenditure = 100 - x next year - income = 140 savings = 2 x expenditure = 140 - 2 x . . now 140 - 2 x + 100 - x = 2 ( 100 - x ) . . . 240 - 3 x = 200 - 2 x . . . . . . . . . . . . . . . . x = 40 . . . saving % = 40 / 100 * 100 = 40 % answer : b
Answer: b
Problem: a train passes a station platform in 40 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 180 m , d ) 197 m , e ) 691 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 40 = 15 = > x = 180 m answer : c"
Answer: c
Problem: speed of a boat in standing water is 10 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 20.48 hours , b ) 21.48 hours , c ) 22.48 hours , d ) 23.48 hours , e ) 24.48 hours
Rationale: "speed upstream = 8.5 kmph speed downstream = 11.5 kmph total time taken = 105 / 8.5 + 105 / 11.5 = 21.48 hours answer is b"
Answer: b
Problem: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 587.75 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 787
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1587.75 = > x = 787 e"
Answer: e
Problem: find large number 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 10 as remainder
Options: a ) 1636 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 a"
Answer: a
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every fourth , starting with the fourth , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 66 , b ) 68 , c ) 70 , d ) 64 , e ) 72
Rationale: widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 19 + 24 - 9 = 34 hence , widgets not inspected : 98 - 34 = 64 option d
Answer: d
Problem: what least number must be added to 3000 to obtain a number exactly divisible by 19 ?
Options: a ) 2 , b ) 1 , c ) 4 , d ) 18 , e ) 17
Rationale: "on dividing 3000 by 19 , we get 17 as remainder .  number to be added = ( 19 - 17 ) = 2 . answer a 2"
Answer: a
Problem: the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.45 p ( b ) = 0.55 ans : e"
Answer: e
Problem: the length of the bridge , which a train 130 metres long and travelling at 36 km / hr can cross in 45 seconds , is :
Options: a ) 320 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 240 m
Rationale: "speed = [ 36 x 5 / 18 ] m / sec = 10 m / sec time = 45 sec let the length of bridge be x metres . then , ( 130 + x ) / 45 = 10 = > 130 + x = 450 = > x = 320 m . answer : a"
Answer: a
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelled in the first one hour was 35 kms , what was the total distance travelled in 12 hours ?
Options: a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
Rationale: "total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . upto 12 terms ) . this is an a . p . with first term , a = 35 , number of terms , n = 12 , common difference d = 2 required distance = 12 / 2 ( 2 * 35 + ( 12 - 1 ) * 2 ) = 6 ( 70 + 22 ) = 552 km . correct option : c"
Answer: c
Problem: evaluate : 11110 + 24 * 3 * 10 = ?
Options: a ) 90111 , b ) 52631 , c ) 11190 , d ) 65321 , e ) 11133
Rationale: "according to order of operations , 24 ? 3 ? 10 ( division and multiplication ) is done first from left to right 24 / 2 = 8 * 10 = 80 hence 11110 + 24 * 3 * 10 = 11110 + 80 = 11190 correct answer c"
Answer: c
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 15 candidates . she plans to have one working interview with 3 of the 15 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 360 , e ) 333
Rationale: "360 . answer d"
Answer: d
Problem: what is the difference between the largest number and the least number written with the digits 6 , 3 , 2 , 5 ?
Options: a ) 6084 , b ) 4176 , c ) 2077 , d ) 2721 , e ) 1812
Rationale: "explanation : 2356 6532 - - - - - - - - - - - - 4176 answer : b"
Answer: b
Problem: a money lender lent rs . 1000 at 4 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.2 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 4 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.2 answer a
Answer: a
Problem: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 46
Rationale: "n = 4 k + 1 = 5 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 5 j + 4 . 1 , 5 , 9 = 5 ( 1 ) + 4 the next such number is 9 + 4 * 5 = 29 . 9 + 29 = 38 the answer is c ."
Answer: c
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 86 , d ) 92 , e ) 106
Rationale: divisor = ( 6 * 3 ) + 7 = 25 5 * quotient = 25 quotient = 5 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 5 ) + 6 = 106 . e )
Answer: e
Problem: a and b together can do a piece of work in 8 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.075 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 8 – 1 / 22 = 0.075 days answer : a"
Answer: a
Problem: circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 60 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 8 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 14 , e ) e ) 12
Rationale: "gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 60 rotations per 60 seconds - - 6 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 4 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 4 units . required net difference should be 8 rotations = > 2 ( 6 seconds later ) = = > 12 seconds . answer : e"
Answer: e
Problem: for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 90 θ 33 ) θ 17 ) - ( 97 θ ( 33 θ 17 ) ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: ( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 97 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 97 divided by 16 is 1 . 7 - 1 = 6 . answer : d .
Answer: d
Problem: what is the range of all the roots of | x ^ 2 - 3 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 3 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 3 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 3 or x = 1 i guess range is 3 - 1 = 2 c"
Answer: c
Problem: if 1,000 microns = 1 decimeter , and 1,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 1,000 , b ) 100 , c ) 1 , 000,000 , d ) 10 , e ) 10,000
Rationale: "given that 1,000 microns = 1 decimeter = 1,000 , 000,000 angstroms so , 1 micron = 1,000 , 000,000 / 1,000 = 1 , 000,000 answer : c"
Answer: c
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of $ 8400 ?
Options: a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13
Rationale: "required difference = [ 3 1 / 2 % of $ 8400 ] – [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a ."
Answer: a
Problem: the sum of three consecutive numbers is 63 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 22 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 63 3 x = 60 x = 20 greatest number , ( x + 2 ) = 22 . answer : d"
Answer: d
Problem: machine p and machine q are each used to manufacture 770 sprockets . it takes machine p 10 hours longer to produce 770 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 770 / x = 770 / 1.1 x + 10 1.1 ( 770 ) = 770 + 11 x 11 x = 77 x = 7 the answer is c ."
Answer: c
Problem: the c . p of 20 books is equal to the s . p of 30 books . find his gain % or loss % ?
Options: a ) 63.33 % , b ) 34.33 % , c ) 33.33 % , d ) 31.33 % , e ) 36.33 %
Rationale: explanation : 20 cp = 30 sp 30 - - - 10 cp loss 100 - - - ? = > 33.33 % loss answer : c
Answer: c
Problem: weights of two friends ram and shyam are in the ratio 3 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 18 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 3 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 3 / 5 or , x = 18 % . answer : option a"
Answer: a
Problem: in the manufacture of a certain product , 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.28 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 7 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 7 / 100 ) * 100 % = ( 28 / 10000 ) * 100 % = ( 28 / 100 ) % = . 28 % answer b"
Answer: b
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 7 students ?
Options: a ) 14 years , b ) 17 years , c ) 19 years , d ) 38 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 7 = 38 years . answer d"
Answer: d
Problem: a trader bought a car at 30 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 26 % , c ) 12 % , d ) 32 % , e ) 15 %
Rationale: "original price = 100 cp = 70 s = 70 * ( 180 / 100 ) = 126 100 - 126 = 26 % answer : b"
Answer: b
Problem: a boy goes to his school from his house at a speed of 3 km / hr and return at a speed of 2 km / hr . if he takes 5 hours in going and coming , the distance between his house and school is ?
Options: a ) 5 km , b ) 6 km , c ) 10 km , d ) 12 km , e ) 8 km
Rationale: average speed = 2 * 3 * 2 / 3 + 2 = 12 / 5 km / hr distance traveled = 12 / 5 * 5 = 12 km distance between house and school = 12 / 2 = 6 km answer is b
Answer: b
Problem: how many seconds will a 600 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 700 , b ) 288 , c ) 500 , d ) 277 , e ) 121
Rationale: let length of tunnel is x meter distance = 600 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 600 + x = ( 65 / 3 ) * 60 600 + x = 20 * 65 = 1300 x = 1300 - 600 = 700 meters answer : a
Answer: a
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?
Options: a ) 12 hours , b ) 10 hours , c ) 6 hours , d ) 8 hours , e ) 4 hours
Rationale: a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 c ' s 1 hour work = ( 7 / 12 - 1 / 2 ) = 1 / 12 c alone will take 12 hours to do the work . answer : a
Answer: a
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 60 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 25 , c ) 35 , d ) 40 , e ) 55
Rationale: "total = 75 books . 60 % of books that were loaned out are returned - - > 100 % - 60 % = 40 % of books that were loaned out are not returned . now , there are 68 books , thus 75 - 65 = 10 books are not returned . { loaned out } * 0.4 = 10 - - > { loaned out } = 25 . answer : b ."
Answer: b
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?
Options: a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Problem: albert is 2 times mary ’ s age and 4 times as old as betty . mary is 12 years younger than albert . how old is betty ?
Options: a ) 6 , b ) 12 , c ) 10 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 12 m = 12 a = 24 a = 4 b , and so b = 6 the answer is a ."
Answer: a
Problem: what is the next number : 2 , 10 , 82 , __
Options: a ) 630 , b ) 730 , c ) 830 , d ) 848 , e ) 900
Rationale: "3 ^ 0 + 1 = 2 3 ^ 2 + 1 = 10 3 ^ 4 + 1 = 82 3 ^ 6 + 1 = 730 the answer is b ."
Answer: b
Problem: the wages earned by robin is 40 % 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 ) 23 % , b ) 18.75 % , c ) 28.57 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 140 and $ 160 respectively . charles earns $ 40 more than robin who earns $ 140 . therefore , charles ' wage is 40 / 140 * 100 = 28.57 % . the correct choice is ( c )"
Answer: c
Problem: marts income is 50 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 90 % , e ) e ) 64 %
Rationale: m = ( 150 / 100 ) t t = ( 60 / 100 ) j = > m = ( 90 / 100 ) j answer d .
Answer: d
Problem: what least number should be subtracted from 13601 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13601 ÷ 87 = 156 , remainder = 29 hence 29 is the least number which can be subtracted from 13601 such that the remainder is divisible by 87 answer is b"
Answer: b
Problem: if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?
Options: a ) 45 ° , b ) 30 ° , c ) 22.5 ° , d ) 18 ° , e ) 11.25 °
Rationale: thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 ° answer = ( e )
Answer: e
Problem: if the average ( arithmetic mean ) of x and y is 80 , and z – x = 100 , what is the average of y and z ?
Options: a ) 140 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "x + y / 2 = 80 = > x + y = 160 x = z - 100 . . . sub this value z - 100 + y = 160 = > z + y = 260 = > z + y / 2 = 130 answer : e"
Answer: e
Problem: the area of a triangle is with base 2 m and height 5 m ?
Options: a ) 11 , b ) 10 , c ) 787 , d ) 122 , e ) 5
Rationale: "1 / 2 * 2 * 5 = 5 m 2 answer : e"
Answer: e
Problem: the ratio of 2 numbers is 2 : 8 and their h . c . f . is 40 . their l . c . m . is ?
Options: a ) 400 , b ) 120 , c ) 80 , d ) 320 , e ) 40
Rationale: "let the numbers be 2 x and 8 x their h . c . f . = 40 so the numbers are 2 * 40 , 8 * 40 = 80 , 320 l . c . m . = 320 answer is d"
Answer: d
Problem: if n divided by 3 has a remainder of 2 , what is the remainder when 2 times n is divided by 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 0
Rationale: "as per question = > n = 3 p + 2 for some integer p hence 2 n = > 6 q + 4 = > remainder = > 1 for some integer q hence a"
Answer: a
Problem: ramu bought an old car for rs . 38000 . he spent rs . 12000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 17 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 29.8 %
Rationale: "total cp = rs . 38000 + rs . 12000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : e"
Answer: e
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 10 sec , e ) 11.25 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 90 + 70 = 160 * 5 / 18 = 400 / 9 t = 500 * 9 / 400 = 11.25 sec answer : option e"
Answer: e
Problem: the mass of 1 cubic meter of a substance is 200 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.25 , c ) 8.0 , d ) 12.5 , e ) 5.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 200 kg / 1 m ^ 3 = 800 kg / m ^ 3 or 1 g / 5 cm ^ 3 = 0.2 g / cm ^ 3 . next , ask yourself if 200,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 800,000 = 10 / 2 = 5 cubic centimeters . answer is e"
Answer: e
Problem: alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 6400 , his gain percent is ?
Options: a ) 5.45 % , b ) 16.36 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 6400 gain = 6400 - 5500 = $ 900 gain % = 900 / 5500 * 100 = 16.36 % answer is b"
Answer: b
Problem: 3251 + 587 + 369 - ? = 3007
Options: a ) 1250 , b ) 1300 , c ) 1375 , d ) 1200 , e ) none of them
Rationale: let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d
Answer: d
Problem: the manufacturer ’ s suggested retail price ( msrp ) of a certain item is $ 60 . store a sells the item for 20 percent more than the msrp . the regular price of the item at store b is 30 percent more than the msrp , but the item is currently on sale for 10 percent less than the regular price . if sales tax is 5 percent of the purchase price at both stores , what is the result when the total cost of the item at store b is subtracted from the total cost of the item at store a ?
Options: a ) $ 0 , b ) $ 0.63 , c ) $ 1.80 , d ) $ 1.89 , e ) $ 2.10
Rationale: msrp = 60 price at store a = 60 ∗ 120100 = 72 = 60 ∗ 120100 = 72 price at store b = 60 ∗ 130100 ∗ 90100 = 70.2 = 60 ∗ 130100 ∗ 90100 = 70.2 difference = 72.0 - 70.2 = 1.8 sales tax applicable = 5 % on both = 1.8 + 0.09 = 1.89 answer = d
Answer: d
Problem: in business , a and c invested amounts in the ratio 3 : 2 , whereas the ratio between amounts invested by a and b was 3 : 4 , if rs 30,000 was their profit , how much amount did b receive .
Options: a ) 1235 , b ) 62896 , c ) 6666 , d ) 8974 , e ) 5626
Rationale: "explanation : a : b = 3 : 4 = 3 : 4 = > a : c = 3 : 2 = 3 : 2 = > a : b : c = 3 : 4 : 2 c share = ( 2 / 9 ) * 30000 = 6666 option c"
Answer: c
Problem: if the selling price of 100 articles is equal to the cost price of 63 articles , then the loss or gain percent is :
Options: a ) 39 % , b ) 36 % , c ) 35 % , d ) 40 % , e ) 37 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 63 . loss % = 37 / 100 * 100 = 37 % answer : e"
Answer: e
Problem: rs . 1775 is divided amongst a , b , c so that 5 times a ' s share , 3 times b ' s share and 7 times c ' s share are all equal . find c ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 716 , e ) 375
Rationale: a + b + c = 590 5 a = 3 b = 7 c = x a : b : c = 1 / 5 : 1 / 3 : 1 / 7 = 21 : 35 : 15 15 / 71 * 1775 = rs . 375 answer : e
Answer: e
Problem: n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 4 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "n ^ ( n / 2 ) = 4 apply log n / 2 logn = log 4 nlogn = 2 log 4 = log 4 ^ 2 = log 16 logn = log 16 now apply antilog n = 16 / n now n = 4 . answer : c"
Answer: c
Problem: a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 120 , c ) 90 , d ) 85 , e ) 30
Rationale: "won 50 % of the first 60 games means it won 30 games . let the number of remaining games played be x . hence the number of remaining games won is 0.8 x . so the equation for winning can be written as : 30 + 0.8 x = 0.6 ( 60 + x ) x = 30 total games played = 60 + 30 = 90 option c ."
Answer: c
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 23 - 9 = 14 ab = 7 . answer is c ."
Answer: c
Problem: a person buys an article at $ 380 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 445 , b ) 449 , c ) 475 , d ) 740 , e ) 460
Rationale: "c 475 cost price = $ 380 profit = 25 % of 380 = $ 95 selling price = cost price + profit = 380 + 95 = 475"
Answer: c
Problem: in certain code ' twice ' is written as ' 34 $ 5 δ ' and ' wears ' is written as ' 4 δ 29 % ' . how is ' seat ' written in that code ?
Options: a ) 22 , b ) 23 , c ) 697 , d ) 66 p , e ) 82
Rationale: answer : option b
Answer: b
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12.5 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.36 % , e ) 10.8 %
Rationale: "12.5 = 1.1 * x x = 11.36 % answer d )"
Answer: d
Problem: two pipes a and b can fill a cistern in 10 and 15 minutes respectively . both fill pipes are opened together , but at the end of 3 minutes , ‘ b ’ is turned off . how much time will the cistern take to fill ?
Options: a ) 6 min , b ) 8 min , c ) 10 min , d ) 12 min , e ) none of these
Rationale: in one min , ( a + b ) fill the cistern = 1 ⁄ 10 + 1 ⁄ 15 = 1 ⁄ 6 th in 3 min , ( a + b ) fill the cistern = 3 ⁄ 6 = 1 ⁄ 2 th remaining part = 1 - 1 ⁄ 2 = 1 ⁄ 2 ∵ 1 ⁄ 10 th part filled by a in one min . ∴ 1 ⁄ 2 nd part filled by a in 10 × 1 ⁄ 2 = 5 min . ∴ total time = 3 + 5 = 8 min . answer b
Answer: b
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 8 km ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 8 / 2 = 4 hours . the answer is d ."
Answer: d
Problem: find the simple interest on rs . 945 for 5 months at 4 paisa per month ?
Options: a ) s . 325 , b ) s . 500 , c ) s . 200 , d ) s . 189 , e ) s . 211
Rationale: "explanation : i = ( 945 * 5 * 4 ) / 100 = 189 answer : option d"
Answer: d
Problem: find a sum for first 8 prime numbers ?
Options: a ) 22 , b ) 28 , c ) 59 , d ) 77 , e ) 84
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d
Answer: d
Problem: a jogger running at 9 km / hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 41 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 290 + 120 = 410 m . time taken = 410 / 10 = 41 sec . answer : e"
Answer: e
Problem: if you write down all the numbers from 1 to 100 , then how many times do you write 1 ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : explanation : clearly , from 1 to 100 , there are ten numbers with 1 as the unit ' s digit - 1 , 11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91 ; and ten numbers with 1 as the ten ' s digit - 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 100 so , required number = 10 + 11 = 21 . answer : d"
Answer: d
Problem: working simultaneously and independently at an identical constant rate , 20 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 8 days ?
Options: a ) 30 , b ) 32 , c ) 35 , d ) 38 , e ) 40
Rationale: "the rate of 20 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 20 * ( x / 4 ) = x / 80 units per day ; now , again as { time } * { combined rate } = { job done } then 8 * ( m * x / 80 ) = 3 x - - > m = 30 . answer : a ."
Answer: a
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive .
Options: a ) 220 , b ) 364 , c ) 410 , d ) 424 , e ) 450
Rationale: we ' re dealing with a sequence of consecutive odd integers : 13 to 31 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 31 = 44 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 29 = 44 now we have proof that there is no middle term . we have 5 bunches of 44 5 ( 44 ) = 220 a
Answer: a
Problem: find the l . c . m of 15 , 18 , 28 and 30 .
Options: a ) 1800 , b ) 1260 , c ) 1460 , d ) 1600 , e ) 960
Rationale: "explanation : 2 x 3 x 5 x 3 x 14 = 1260 answer : option b"
Answer: b
Problem: if o is the center of the circle in the figure above and the area of the unshaded sector is 5 , what is the area of the shaded region ?
Options: a ) 25 / √ π
b ) 30 / √ π
c ) 20
d ) 25
e ) 30
Rationale: 60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d
Answer: d
Problem: the smallest value of n , for which 2 n is not a prime number , is
Options: a ) 2 , 3,4 , b ) 1 , 3,5 , c ) 2 , 5,6 , d ) 4 , 8,9 , e ) 12 , 14,16
Rationale: "( 2 ã — 1 ) = 2 . ( 2 ã — 2 ) = 4 . ( 2 ã — 3 ) = 6 . ( 2 ã — 4 ) = 8 . which is not prime , n = 2 , 3,4 . answer : a"
Answer: a
Problem: if a mixture is 5 ⁄ 9 alcohol by volume and 4 ⁄ 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 5 / 4 , d ) 6 / 4 , e ) 7 / 4
Rationale: "should be a sub - 600 level q . . volume = { 5 / 9 } / { 4 / 9 } = 5 / 4 c"
Answer: c
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 8 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 8 = ( r - 12 ) / r 4 r = 8 r - 96 r = 24 the answer is b ."
Answer: b
Problem: s = { 12 , 35 , 69 } t = { 45 , 67 , 13 } what is the probability that x chosen from s and y chosen from t will result x * y = even
Options: a ) 5 / 9 , b ) 3 / 2 , c ) 1 / 2 , d ) 5 / 6 , e ) 6 / 5
Rationale: p : the probability that x * y is even , then p = 1 - p ( x * y is odd ) p ( x * y odd ) = p ( x odd ) * p ( y odd ) = 4 / 6 * 4 / 6 = 16 / 36 = 4 / 9 and p = 1 - 4 / 9 = 5 / 9 option : a
Answer: a
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 110 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 11 / 48,000 , b ) 1 / 8,100 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 110 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 110 / 800 * 1 / 600 = 311 / 48,000 . answer : a ."
Answer: a
Problem: a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 1 / 3 , e ) 1
Rationale: "probability = ( favorable cases ) / ( total number of cases ) total number of ways in which a person can ride car = 3 * 3 * 3 = 27 ( in first ride he has 3 options to sit , in second right again he has 3 seats available to sit and so on ) number of favorable cases , i . e . , when he rides on different cars ; he can choose seat car in 3 ways in his 1 st ride . he can choose seat car in 2 ways in his 2 nd ride . he can choose seat car in 1 ways in his 3 rd ride . so , 3 * 2 * 1 = 6 ways thus , probability of choosing different seats = 6 / 27 = 2 / 9 answer : c"
Answer: c
Problem: of the 100 people in a room , 4 / 5 are women . if 3 / 5 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: "women = 4 / 5 * 100 = 80 married = 3 / 5 * 100 = 60 unmarried = 40 max ( un - married women ) = 40 e"
Answer: e
Problem: one copy machine can make 25 copies a minute , and a second copy machine makes 35 copies a minute . if the two copiers work together , how long would it take them to make 4,800 copies ?
Options: a ) 30 minutes , b ) 40 minutes , c ) 60 minutes , d ) 70 minutes , e ) 80 minutes
Rationale: "total work done by both machines in a minute = 25 + 35 = 60 copies total number of copies required = 6000 time = 4800 / 60 = 80 mins answer e"
Answer: e
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 20 gallons of water and 40 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 300 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 40 gallons salt is added and 20 gallons of water is added . so salt now becomes - > ( 0.2 x + 40 ) and water - - > ( 0.6 x + 20 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 40 ) = ( 0.6 x + 20 ) / 2 = > 0.4 x + 80 = 0.6 x + 20 = > 0.2 x = 60 solving , x = 300 answer : a"
Answer: a
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area w covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads w = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 53 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: "annie earned 40 x + 13 ( 2 x ) = 66 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 66 x ( 1.5 x ) ( h ) = 81 x h = 54 hours the answer is d ."
Answer: d
Problem: the diagonals of a rhombus are 18 cm and 22 cm . find its area ?
Options: a ) 277
b ) 266
c ) 198
d ) 288
e ) 212
Rationale: 1 / 2 * 18 * 22 = 198 answer : c
Answer: c
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 25 % chemical x and 75 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 28 % , b ) 32 % , c ) 36 % , d ) 40 % , e ) 44 %
Rationale: the amount of chemical x in the solution is 20 + 0.25 ( 80 ) = 40 liters . 40 liters / 100 liters = 40 % the answer is d .
Answer: d
Problem: a number increased by 20 % gives 600 . the number is
Options: a ) 250 , b ) 400 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 600 ( 120 × 5 = 600 ) 100 % - - - - - - - > 500 ( 100 × 5 = 500 ) d )"
Answer: d
Problem: when a laptop is sold for rs . 49,000 , the owner loses 30 % . at what price must that laptop be sold in order to gain 30 % ?
Options: a ) 87000 , b ) 88000 , c ) 89000 , d ) 90000 , e ) 91000
Rationale: 70 : 49000 = 130 : x x = ( 49000 x 130 ) / 70 = 91000 . hence , s . p . = rs . 91,000 . answer : option e
Answer: e
Problem: if a and b together can finish a work in 16 days . a can finish same work alone in 24 days then b alone can finish same work alone in how many days ?
Options: a ) 30 days , b ) 48 days , c ) 40 days , d ) 36 days , e ) 50 days
Rationale: ( a + b ) work in 1 day = 1 / 16 , a work in 1 day = 1 / 24 b work in 1 day = [ 1 / 16 - 1 / 24 ] = 1 / 48 . b alone can finish same work in 48 days . answer b
Answer: b
Problem: if 5 a + 7 b = m , where a and b are positive integers , what is the largest possible value of m for which exactly one pair of integers ( a , b ) makes the equation true ?
Options: a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74
Rationale: 5 * a 1 + 7 * b 1 = m 5 * a 2 + 7 * b 2 = m 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 toawe will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 froma , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer
Answer: d
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 15 % ?
Options: a ) 32.8 % , b ) 37.6 % , c ) 38.5 % , d ) 17.5 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 85 gain % = 21 / 64 * 100 = 32.8 % . answer : a"
Answer: a
Problem: the calendar of the year 2028 can be used again in the year ?
Options: a ) 2041 , b ) 1951 , c ) 2056 , d ) 1971 , e ) 1973
Rationale: "explanation : given year 2028 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2028 + 28 = 2056 answer : c"
Answer: c