regisss/math_qa huggingface dataset:
Problem: of the 19,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 33 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . c"
Answer: c
Problem: two trains are moving in opposite directions @ 60 kmph and 90 kmph . their length are 1.10 km and 0.9 km . the time taken by the slower train to cross faster train in second is ?
Options: a ) 25 sec , b ) 30 sec , c ) 48 sec , d ) 36 sec , e ) 40 sec
Rationale: "relative speed = 60 + 90 = 150 * 5 / 18 = 125 / 3 m / s distance covered = 1.10 + 0.9 = 2 km = 2000 m required time = 2000 * 3 / 125 = 48 sec answer is c"
Answer: c
Problem: how many integers are between 9 and 67 / 5 , inclusive ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "67 / 5 = 13 . xx we are not concerned about the exact value of 67 / 5 as we just need the integers . since the values are small , we can write down the integers . the different integers between 9 and 67 / 5 would be 9 , 10 , 11 , 12,13 total number of integers = 5 option a"
Answer: a
Problem: total 36 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 35 , b ) 36 , c ) 21 , d ) 32 , e ) 26
Rationale: "35 players answer : a"
Answer: a
Problem: a pipe can empty 3 / 4 th of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 1 / 2 , b ) 3 / 7 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7
Rationale: 3 / 4 - - - - 12 ? - - - - - 8 = = > 1 / 2 a
Answer: a
Problem: benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 2 dollars . how many apples does she buy to share them equally between her 6 kids ?
Options: a ) 8 , b ) 30 , c ) 3 , d ) 7 , e ) 10
Rationale: cost of each apple = 2 dollars apples that benny can buy with the amount she has = 360 / 2 = 180 . apples that each kid gets evenly = 180 / 6 = 30 apples . so the answer is b = 30
Answer: b
Problem: in one year , the population , of a village increased by 12 % and in the next year , it decreased by 12 % . if at the end of 2 nd year , the population was 14784 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081
Rationale: "x * 112 / 100 * 88 / 100 = 14784 x * 0.9856 = 14784 x = 14784 / 0.9856 = > 15000 answer : c"
Answer: c
Problem: a grocer has a sale of rs . 5266 , rs . 5744 , rs . 5864 , rs . 6122 and rs . 6588 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5750 ?
Options: a ) 4016 , b ) 4076 , c ) 4816 , d ) 4916 , e ) 5916
Rationale: "total sale for 5 months = rs . ( 5266 + 5744 + 5864 + 6122 + 6588 ) = rs . 29584 . required sale = rs . [ ( 5750 x 6 ) - 34500 ] = rs . ( 34500 - 29584 ) = rs . 4916 . answer : d"
Answer: d
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 20 per square m ?
Options: a ) s . 43000 , b ) s . 19000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 20 * 950 = rs . 19000 b"
Answer: b
Problem: a shipment of 220 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 11 / 76 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 220 which ontains 84 defective phones is = ( 84 / 220 ) probability of chosing one defective phone from a lot of 219 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 219 ) combined probability of series of events = product of the probabilities = ( 84 / 220 ) * ( 83 / 219 ) 84 / 220 is close to ( 21 / 55 ) and ( 83 / 219 ) = ( 36 / 95 ) so answer is ( 21 / 55 ) * ( 36 / 95 ) = ( 11 / 76 ) so , answer will be c"
Answer: c
Problem: after decreasing 20 % in the price of an article costs rs . 600 . find the actual cost of an article ?
Options: a ) 775 , b ) 620 , c ) 53 , d ) 530 , e ) 220
Rationale: "cp * ( 80 / 100 ) = 600 cp = 7.75 * 100 = > cp = 775 answer : a"
Answer: a
Problem: the average score of a cricketer in 2 matches is 27 and in other 3 matches is 32 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 27 + 3 * 32 ) / 2 + 3 = 54 + 96 / 5 = 30 answer is c"
Answer: c
Problem: the number of singles that a baseball player hit increased 18 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 6 percent . if the total number of singles and doubles that she hit increased 3 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 1 : 3 , b ) 4 : 5 , c ) 1 : 5 , d ) 2 : 5 , e ) 3 : 5
Rationale: "soln : - 1.18 s + 0.94 d = 1.03 [ s + d ] 0.15 s = 0.09 d s / d = 3 / 5 answer : e"
Answer: e
Problem: if a and d are both integers , a > d , and - 3 c > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that a > d and a < - 6.33 , the largest value of a can be - 7 while if a = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < a and a = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 6 inches on a side and costs $ 10 , and a large pizza that measures 9 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 9 square inches , b ) 10 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 6 * 6 = 36 ) for the small pizza and ( 9 * 9 = 81 ) for the large pizza . in total sq inches that would be ( 36 + 81 ) * 2 = 234 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 81 = 243 sq inches . hence , the difference is 9 square inches more ( 243 - 234 ) . the correct answer is a"
Answer: a
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 20 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 12.6 , b ) 1.21 , c ) 1.25 , d ) 12.4 , e ) 12.7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 20 ? - - - 1 = > rs . 1 100 - - - 80 ? - - - 1 = > rs . 1.25 answer : c"
Answer: c
Problem: john found that the average of 15 numbers is 40 . if 12 is added to each number then the mean of number is ?
Options: a ) 52 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 52 option a"
Answer: a
Problem: a and b together can do a piece of work in 2 days . if a alone can do the same work in 22 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 2 – 1 / 22 = 0.45 days answer : b"
Answer: b
Problem: if 1 / ( x + 3 ) + 1 / ( x - 3 ) = 1 / ( x + 3 ) , what is the value of x ?
Options: a ) 2 , b ) 3 , c ) - 1 , d ) - 2 , e ) - 3
Rationale: "if we solve the question , we get x = - 3 . option : e"
Answer: e
Problem: the area of a square field is 1600 km 2 . how long will it take for a horse to run around at the speed of 16 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 1600 km 2 . then , each side of field = √ 1600 = 40 km distance covered by the horse = perimeter of square field = 40 × 4 = 160 km ∴ time taken by horse = distances / peed = 160 / 16 = 10 h answer b
Answer: b
Problem: how many 4 - digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ? .
Options: a ) 400 , b ) 1728 , c ) 108 , d ) 216 , e ) 432
Rationale: the number of ways u can chose two digits from 9 digits is 9 c 2 = ( 9 * 8 ) / 2 . and the no of ways u can arrange two digits like asked is 4 c 2 = ( 4 * 3 ) / 2 . total ways is 36 * 6 = 216 . answer : d
Answer: d
Problem: the charge for a single room at hotel p is 50 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 45 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: p = 0.5 r = 0.9 g r = 0.9 g / 0.5 = 1.8 * g thus r is 80 % greater than g . the answer is d .
Answer: d
Problem: 0.009 / x = 0.03 . find the value of x
Options: a ) 0.0003 , b ) 0.03 , c ) 0.3 , d ) 3 , e ) 30
Rationale: "x = 0.009 / 0.03 = 0.3 answer : c"
Answer: c
Problem: a man rows his boat 90 km downstream and 70 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 3.5 kmph , d ) 4.5 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 70 / ( 3 ) = 23 kmph the speed of the stream = ( 30 - 23 ) / 2 = 3.5 kmph answer : c"
Answer: c
Problem: one night 18 percent of the female officers on a police force were on duty . if 180 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 180 number of female officers on duty on that night = 180 / 2 = 90 ( 18 / 100 ) * f = 90 = > f = 500 answer d"
Answer: d
Problem: there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 24 plants . how many birches and roses were planted ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of roses . then the number of birches is 24 − x , and the number of boys is 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 216 − 72 = 8 x 1448 = x x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . so answer is d ."
Answer: d
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,900 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,900 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.9 so , answer is d ."
Answer: d
Problem: if shares of two persons in profits are rs . 400 and rs . 1200 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: profit = time * capital so 400 : 1200 = 1 : 3 answer : d
Answer: d
Problem: rectangular tile each of size 60 cm by 56 cm must be laid horizontally on a rectangular floor of size 560 cm by 240 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 54 , c ) 47 , d ) 40 , e ) 45
Rationale: "area of tile = 60 * 56 = 3360 area of floor = 560 * 240 = 134400 no of tiles = 134400 / 3360 = 40 so , the no of tile = 40 answer : d"
Answer: d
Problem: the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is
Options: a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) none
Rationale: "solution let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 × 495 ‹ = › x 2 - 100 x + 2475 = 0 . ‹ = › ( x - 55 ) ( x - 45 ) = 0 . x = 55 or x = 45 . therefore , the numbers are 45 and 55 . required difference = ( 55 - 45 ) = 10 . answer a"
Answer: a
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 9 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 304 , e ) 320
Rationale: 4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 9 - s , 9 x 9 x 4 * 1 * 4 * 1 = 16 . thus there are 320 - 16 = 304 such numbers . answer : d .
Answer: d
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 45 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 88 , e ) 75
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 45 3 x = 45 = > x = 15 = > smaller number = 5 x = 75 . answer : e"
Answer: e
Problem: the sum of ages of 4 children born 2 years different each is 36 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 17
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 36 4 x = 24 x = 6 . x + 6 = 6 + 6 = 12 answer : d"
Answer: d
Problem: if ajay completes a certain work in 8 days and vijay can complete the same work in 24 days , find the time in which the work will be completed if both ajay and vijay work together .
Options: a ) 6 days , b ) 9 days , c ) 2 days , d ) 7 days , e ) 1 days
Rationale: explanation : on working together ajay and vijay can complete the work in ( 8 * 24 ) / ( 8 + 24 ) = 192 / 32 = 6 days answer : a
Answer: a
Problem: the length of the diagonal of a square is 12 cm . find its area and perimeter .
Options: a ) 31.84 cm
b ) 33.84 cm
c ) 35.84 cm
d ) 38.84 cm
e ) 38.92 cm
Rationale: diagonal of a square = 12 cm area of square = 1 / 2 ( d ) ² = 1 / 2 ( 12 ) ² = 1 / 2 × 12 × 12 = 72 side of a square = √ area = √ 72 = √ ( 2 × 2 × 2 × 3 × 3 ) = 2 × 3 √ 2 = 6 × 1.41 = 8.46 cm perimeter of square = 4 × 8.46 = 33.84 cm answer option : b
Answer: b
Problem: a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 14 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 12.05 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 14 = 12.05 cm answer is b"
Answer: b
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 9 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 104 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 9 ) * 360 = 40 gallons . remaning paint = 320 gallons paint used in the second week = ( 1 / 5 ) * 320 = 64 gallons total paint used = 104 gallons . option c"
Answer: c
Problem: what is the sum of 59 consecutive integers from - 29 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 29 , c ) - 30 , d ) 0 , e ) 60
Rationale: "from - 29 to - 1 - - > 29 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 29 to + 29 sum will be zero for total 59 nos . sum of these 59 nos . = 0 . d is the answer ."
Answer: d
Problem: if an integer n is to be selected at random from 1 to 400 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 8 , either n or n + 1 has to be a multiple of 8 . thus n must be of the form 8 k or 8 k - 1 . the probability is 2 / 8 = 1 / 4 . the answer is a ."
Answer: a
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 185 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 2 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 185 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 185 m ) / ( w + m ) = 180 170 w + 185 m = 180 w + 180 m 5 m = 10 w m = 2 w m / w = 2 / 1 the ratio of men to women is 2 to 1 . d"
Answer: d
Problem: a and b start walking towards each other at 6 pm at speed of 4 kmph and 6 kmph . they were initially 18 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 7 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 18 / 6 + 3 = 18 / 9 = 2 hrs after 6 pm = 8 pm answer is a"
Answer: a
Problem: calculate the l . c . m of 5 / 6 , 4 / 7 , 9 / 10 , 8 / 9 is :
Options: a ) 560 , b ) 364 , c ) 320 , d ) 330 , e ) 360
Rationale: "required l . c . m = l . c . m . of 5 , 4 , 9 , 8 / h . c . f . of 6 , 7 , 10 , 9 = 360 / 1 = 360 answer is e"
Answer: e
Problem: find the least positive integer divisible by each of the integers between 5 through 10 ( including 10 ) .
Options: a ) 560 , b ) 380 , c ) 900 , d ) 2560 , e ) 2520
Rationale: the integer should be divisible by : 5 , 6 , 7 , 89 , and 10 . the least common multiple of these integers is lcm = 420 . answer : 5 * 3 ^ 2 * 7 * 2 ^ 3 the answer is e )
Answer: e
Problem: a number when divided by a divisor leaves a remainder of 25 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 38 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 25 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 38 as d is also integer and 38 is a prime number , the d should be 38 to satisfy the above equation . hence answer is ' d '"
Answer: d
Problem: dexter and prexter are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1000 m . dexter crosses 50 m in 2 min and prexter in 3 min 15 sec . each time they meet / cross each other , they do handshake ' s . how many such handshake ' s will happen if they start from the same end at the same time ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: explanation : when dexter completes second round , they do handshake once . now for every round which dexter completes , there will be one hand shake as the ratio of speed is 13 : 8 . d and p will meet at the pool end only after d completes 26 rounds . in the 20 th round , d finish the race and the total handshake ' s will be : 20 − 1 = 19 . answer : c
Answer: c
Problem: find the average of all numbers between 6 and 34 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 10 + 15 + 20 + 25 + 305 ) = 1005 = 20 answer : option b"
Answer: b
Problem: two numbers are less than third number by 35 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 33 % , d ) 41 % , e ) 42 %
Rationale: "let the third number is x . then first number = ( 100 - 35 ) % of x = 65 % of x = 65 x / 100 second number is ( 63 x / 100 ) difference = 65 x / 100 - 63 x / 100 = x / 50 so required percentage is , difference is what percent of first number ( x / 50 * 100 / 65 x * 100 ) % = 33 % answer : c"
Answer: c
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 8 more than 1 / 4 of the fine and peter paid $ 8 less than 1 / 3 of the fine , leaving pay $ 15 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 70 , b ) $ 72 , c ) $ 73 , d ) $ 74 , e ) $ 75
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 8 ] + [ ( 1 / 3 ) f – 8 ] + [ ( 1 / 2 ) f – 15 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 15 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 180 12 f = 13 f – 180 – f = – 180 f = 180 well , if the fine cost $ 180 , then sam paid the part not covered by joe or peter . half the fine is $ 90 , and sam paid $ 15 less than this : $ 75 answer = e"
Answer: e
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 2 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c
Answer: c
Problem: a man gains 60 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 320 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 160 / 100 ) x = 8 x / 5 new s . p . = 2 ( 8 x / 5 ) = 16 x / 5 profit = 16 x / 5 - x = 16 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 16 x / 5 ) * ( 1 / x ) * 100 = 320 % option b"
Answer: b
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 54 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 54 ⇔ 9 ( x - y ) = 54 ⇔ x - y = 6 answer c
Answer: c
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 40 : 70 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 720
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 2 : 40 : 70 initial soap : alcohol = 2 / 40 = 2 : 40 after doubled soap : alcohol = 2 * 2 / 40 = 4 : 40 initial soap : water = 2 / 70 = 2 : 70 after halved soap : water : 1 / 2 * 2 / 70 = 1 / 70 = 1 : 70 after soap : alcohol : water - - > 4 : 40 : 280 - - > 1 : 10 : 70 given alcohol 100 cubic centimeter . ratio is 10 : 100 : 700 ( 1 : 10 : 70 ) for 100 cubic centimeter of alcohol - - - 700 cubic cm water is required . answer - d"
Answer: d
Problem: a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4991 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer : d"
Answer: d
Problem: if rs . 420 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 600 , e ) s . 585
Rationale: 80 = ( 420 * 4 * r ) / 100 r = 7.14 % i = ( 420 * 6 * 7.14 ) / 100 = 180 420 + 180 = 600 answer : d
Answer: d
Problem: what is the ratio of 3 / 7 to the product 2 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 9 : 98 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "3 / 7 / 14 / 3 = 9 / 98 . . . imo option b ."
Answer: b
Problem: if 40 % of a number exceeds 20 % of it by 12 , then find the number ?
Options: a ) 60 , b ) 50 , c ) 47 , d ) 55 , e ) 80
Rationale: "use the elimination method to find the correct option . of all the options only 60 fits 40 % of 60 = 24 20 % of 60 = 12 24 - 12 = 12 required number is 60 . answer : a"
Answer: a
Problem: a discount electronics store normally sells all merchandise at a discount of 5 percent to 25 percent off the suggested retail price . if , during a special sale , an additional 25 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 300 before any discount ?
Options: a ) $ 130.00 , b ) $ 160.75 , c ) $ 168.75 , d ) $ 182.00 , e ) $ 168.00
Rationale: "original price : 300 $ max first discount = - 25 % thus : 300 â ˆ — ( 1 â ˆ ’ 25 / 100 ) = 225 second discount on the discounted price = - 25 % thus : 225 â ˆ — ( 1 â ˆ ’ 25 / 100 ) = 168.75 answer c"
Answer: c
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is :
Options: a ) 120 m , b ) 140 m , c ) 240 m , d ) 300 m , e ) none
Rationale: "sol . speed = [ 12 / 10 * 60 ] km / hr = [ 72 * 5 / 18 ] m / sec = 20 m / sec . length of the train = ( speed * time ) = ( 20 * 6 ) m = 120 m . answer a"
Answer: a
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.20 lacs . how many workers were they ?
Options: a ) 220 , b ) 400 , c ) 500 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 320000 - 300000 ) = 20000 n = 20000 / 50 = 400 b"
Answer: b
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 2 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) none of these , d ) 78 , e ) 90
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 2 can be arranged as 12 or 21 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : c"
Answer: c
Problem: if a rectangular billboard has an area of 130 square feet and a perimeter of 46 feet , what is the length of each of the longer sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 130 and a perimeter of 46 . we ' re asked for the length of one of the longer sides of the rectangle . since the answers are all integers , and the area is 130 , the shorter side will almost certainly be closer to 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 130 , if . . . the shorter side = 10 . . . the area = 130 / 10 = 13 = the longer side perimeter = 10 + 10 + 13 + 13 = 46 d"
Answer: d
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 100 metres , d ) 228 metres , e ) 150 metres
Rationale: "speed = 60 x 5 / 18 m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 3 x 6 m = 100 m . option c"
Answer: c
Problem: find the greatest number which on dividing 3815 and 4521 , leaves a reminder of 31 and 33 respectively
Options: a ) 88 , b ) 56 , c ) 89 , d ) 86 , e ) 96
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 3815 - 31 ) and ( 4521 - 33 ) = hcf ( 3784 , 4488 ) = 88 option a"
Answer: a
Problem: 16 men can complete a piece of work in 28 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 22.4 days , d ) 88 days , e ) 44 days
Rationale: "16 * 28 = 20 * x = > x = 22.4 days answer : c"
Answer: c
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 5 : 4 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 26 = 5 : 4 answer : c"
Answer: c
Problem: two sides of a triangle have lengths x and w and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to w ?
Options: a ) a ) 2 : 3
b ) b ) 3 : 4
c ) c ) 4 : 3
d ) d ) 3 : 2
e ) e ) 2 : 1
Rationale: ahhhh . . . . my bad . thank you , you ' re correct . 8 x = 6 w - - > x / w = 3 / 4 . actually b is the right answer .
Answer: b
Problem: a man deposits $ 2000 in a bank at 4 % per annum and $ 3000 in uti at 14 % per annum . find the rate of interest for the whole sum .
Options: a ) 15 % , b ) 18 % , c ) 11 % , d ) 17 % , e ) 10 %
Rationale: following the above formula , we have the rate of interest for the whole sum = ( 2000 * 4 ) + ( 3000 * 14 ) / 2000 + 3000 = 50000 / 5000 = 10 % . answer is d
Answer: d
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 55.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 25.5 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 55 = 14 $ ( 14 / 55 ) * 100 = 25.5 % answer : a"
Answer: a
Problem: convert 30 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 52800 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 30 miles = 30 * 1760 = 52800 yards answer is c"
Answer: c
Problem: a garrison of 2000 men has provisions for 65 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1893 , c ) 1979 , d ) 3000 , e ) 1278
Rationale: "2000 - - - - 65 2000 - - - - 50 x - - - - - 20 x * 20 = 2000 * 50 x = 5000 2000 - - - - - - - 3000 answer : d"
Answer: d
Problem: in what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 6 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 2 sec
Rationale: "t = 70 / 36 * 18 / 5 = 7 sec answer : b"
Answer: b
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 20 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 192 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 20 emlpoyee paid = . 8 * 240 = 192 $ answer c"
Answer: c
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 5 ?
Options: a ) 897 , b ) 98,910 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 5 seeing the options after dividing and finding the reminder of 2 my answer was b
Answer: b
Problem: the speed of a train is 72 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 20 kmph , b ) 28 kmph , c ) 25 kmph , d ) 22 kmph , e ) 24 kmph
Rationale: "72 * 20 / 60 = 24 kmph answer : e"
Answer: e
Problem: a math teacher has 27 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 9
b ) 10
c ) 11
d ) 12
e ) 13
Rationale: a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 27 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 27 - 17 = 10 answer ( b )
Answer: b
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 45 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 28 , d ) 66 , e ) 99
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 45 / 5 = 9 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 9 = 99 secs . answer : e"
Answer: e
Problem: the total marks obtained by a student in mathematics and physics is 70 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 45 , c ) 27 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 70 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 70 + 20 ) / 2 = 45 . answer : b"
Answer: b
Problem: the ratio of the money with ravi and giri is 6 : 7 and that with giri and kiran is 6 : 15 . if ravi has $ 36 , how much money does kiran have ?
Options: a ) $ 36 , b ) $ 42 , c ) $ 60 , d ) $ 75 , e ) $ 105
Rationale: rita : sita : kavita 6 : 7 6 : 15 36 : 42 : 105 the ratio of money with ravi , giri and kiran is 36 : 42 : 105 we see that 36 = $ 36 then 105 = $ 105 answer is e
Answer: e
Problem: ( 3 x + 2 ) ( 2 x - 7 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 3 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: expanding we have 6 x ^ 2 - 21 x + 4 x - 14 6 x ^ 2 - 17 x - 14 taking coefficients , a = 6 , k = - 17 , n = - 14 therefore a - n + k = 6 - ( - 14 ) - 17 = 20 - 17 = 3 the answer is a .
Answer: a
Problem: how many positive integers h between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Problem: if the sides of a triangle are 91 cm , 84 cm and 35 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 1470 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 91 cm , 84 cm and 35 cm is right angled , where the hypotenuse is 91 cm . area of the triangle = 1 / 2 * 84 * 35 = 1470 cm 2 answer : b"
Answer: b
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 28 ) ?
Options: a ) 2 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "f ( 28 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 16 marks , what was the maximum marks he could have got ?
Options: a ) 643 , b ) 677 , c ) 760 , d ) 767 , e ) 832
Rationale: if mike had scored 16 marks more , he could have scored 30 % therefore , mike required 212 + 16 = 228 marks let the maximum marks be m . then 30 % of m = 228 ( 30 / 100 ) × m = 228 m = ( 228 × 100 ) / 30 m = 22800 / 30 m = 760 answer : c
Answer: c
Problem: a student completes a 3 part exam as follows . the student completes sections a in 18 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 6 : 5 , d ) 7 : 6 , e ) 8 : 7
Rationale: "the time spent on section b and section c is 21 minutes each . the ratio of c to a is 21 : 18 = 7 : 6 the answer is d ."
Answer: d
Problem: . a car covers a distance of 742 km in 7 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 148 , d ) 150 , e ) 159
Rationale: "742 / 5 = 148 kmph answer : c"
Answer: c
Problem: how many bricks each measuring 20 cm x 10 cm x 8 cm , will be needed to build a wall 10 m x 8 m x 24.5 m
Options: a ) 12250 , b ) 13400 , c ) 12500 , d ) 14340 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 1000 x 800 x 24.5 ) / ( 20 x 10 x 8 ) = 12250 answer : a"
Answer: a
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 2,000 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 ) 19,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 2,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 2,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 160 = 0.10 x combine terms and subtract 0.08 x from both sides : 390 = 0.02 x divide both sides by 0.02 : 19,500 = x your answer is a ."
Answer: a
Problem: if 45 % of z is 120 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 120 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 120 / 100 ) * ( 3 / 4 ) x i . e . z = ( 120 * 3 ) x / ( 45 * 4 ) i . e . z = ( 2 ) x = ( 200 / 100 ) x i . e . z is 200 % of x answer : option a"
Answer: a
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 13,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000
Rationale: answer equals d in 48 years . i thought by 50 th year it would reach 100,500 . options should have been separated more widely for clarity .
Answer: d
Problem: what is the square root of 81 ?
Options: a ) 2 , b ) 8 , c ) 12 , d ) 9 , e ) 16
Rationale: "9 x 9 = 81 answer d"
Answer: d
Problem: how is 4 % expressed as a decimal fraction ?
Options: a ) 0.4 , b ) 0.04 , c ) 0.004 , d ) 0.0004 , e ) 4
Rationale: "4 / 100 = 0.04 answer : b"
Answer: b
Problem: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 128 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 72 , e ) 80
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 128 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 128 . so 1 part corresponds to 128 / 8 = 16 and so 5 parts correspond to 5 * 16 = 80 . e"
Answer: e
Problem: i remember during the school days , the teacher asked the class ` ` can you tell me the sum of the first 50 odd numbers ? ` ` . i ran quickly to the teacher and told her ` ` the answer is 2500 ' ' . the teacher replied ` ` lucky guess ' ' . she then asked me ` ` can you tell me the sum of first 75 odd numbers ? ` ` . i wait for approx 10 seconds and replied with the correct answer . how can i answer so quickly and whats the correct answer ?
Options: a ) 5624 , b ) 5625 , c ) 5626 , d ) 5627 , e ) none
Rationale: solution : 5625 n ^ 1 75 * 75 = 5625 ( sum of first 75 odd numbers ) . 50 * 50 = 2500 ( sum of first 50 odd numbers ) . answer b
Answer: b
Problem: in one hour , a boat goes 11 km along the stream and 7 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 7 ) km / hr = 9 kmph . answer d"
Answer: d
Problem: the average of first five prime numbers greater than 10 is ?
Options: a ) 16.6 , b ) 12.9 , c ) 31.3 , d ) 19.2 , e ) 15.7
Rationale: "11 + 13 + 17 + 19 + 23 = 83 / 5 = 16.6 answer : a"
Answer: a
Problem: following an increase in prices , the price of a candy box was 15 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 16
Rationale: "price of candy before price increase = 15 / 1.25 = 12 price of soda before price increase = 6 / 1.5 = 4 total price = 12 + 4 = 16 e is the answer"
Answer: e
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 20 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 20 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 20 pm + 2 hrs = 6 : 20 pm answer : d . 6 : 20"
Answer: d
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 56 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 72.28 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 56 = 2530 correct average = 2530 / 35 = 72.28 answer : b"
Answer: b