Cheukting/mathqa huggingface dataset:
Question (general): the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 8 , e ) 9 : 10
Rationale: 3 b = 7 c and so b = 7 c / 3 7 a = 2 b and so a = 2 b / 7 = 2 c / 3 a + b = 2 c / 3 + 7 c / 3 = 9 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 9 : 10 the answer is e .
Answer: e
Question (general): what least number must be added to 1170 , so that the sum is completely divisible by 23 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "51 * 23 = 1173 1173 - 1170 = 3 answer : a"
Answer: a
Question (general): in a 500 member association consisting of men and women , exactly 20 % of men and exactly 50 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 149 , b ) 147 , c ) 101 , d ) 143 , e ) 141
Rationale: "solution simple out of 500 20 % are male i . e 100 and 50 % are female i . e 250 , so total homeowner is 350 . now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option . so ans is 101 . ans : c"
Answer: c
Question (physics): two trains 140 m and 160 m long run at the speed of 60 kmph and 48 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 48 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 1 / 30 = 10 sec answer is c"
Answer: c
Question (general): there are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 25 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 192 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 192 / 24 = 17 + 8 = 25 answer : a"
Answer: a
Question (physics): 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 / 4 of all the paint . during the second week , he uses 1 / 7 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 128 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 7 ) * 270 = 38 gallons total paint used = 128 gallons . option b"
Answer: b
Question (gain): the sale price sarees listed for rs . 540 after successive discount is 5 % and 2 % is ?
Options: a ) 288 , b ) 500 , c ) 502 , d ) 540 , e ) 262
Rationale: "540 * ( 95 / 100 ) * ( 98 / 100 ) = 502 answer : c"
Answer: c
Question (other): a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 3 / 28 , d ) 3 / 31 , e ) 5 / 32
Rationale: "p ( both are red ) , = 3 c 2 / 8 c 2 = 6 c 213 c 2 = 3 / 28 c"
Answer: c
Question (gain): company p had 15 percent more employees in december than it had in january . if company p had 480 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 417 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 480 j = 480 / 1.15 j = 48,000 / 115 = 417 thus b is the correct answer ."
Answer: b
Question (general): at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 40 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 26.6
Rationale: "in 40 liters , red = 5 / 8 * 40 = 25 and blue = 15 so , 25 / ( 15 + x ) = 3 / 5 or , x = 26.6 ( answer e )"
Answer: e
Question (general): how many 4 digits number contain the number 2 .
Options: a ) 3170 , b ) 3172 , c ) 3174 , d ) 3168 , e ) 3167
Rationale: "total no . of 4 digit nos are 9000 ( btwn 1000 and 9999 ) . consider the case where the nos contain no 2 in it . so units place can be filled in 9 ways ( 0 , 1,3 , 4,5 , 6,7 , 8,9 ) smlry , tenths place in 9 ways hunderedths place in 9 ways thousands place can be filled in 8 ways only ( because 0 can not come ) so total nos are ( 9000 - ( 8 * 9 * 9 * 9 ) ) = 3168 answer : d"
Answer: d
Question (general): according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 40 , e ) e ) 100
Rationale: its d . total juice rquired = 320 * 6 = 1920 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1920 / 48 = 40 . answer d
Answer: d
Question (general): the largest natural number which exactly divides the product of any 4 consecutive natural numbers is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 120 , e ) none
Rationale: sol . required number = 1 × 2 × 3 × 4 = 24 . answer c
Answer: c
Question (geometry): the area of a circle is increased by 1500 % . by what percent has the diameter of the circle increased ?
Options: a ) 100 % , b ) 500 % , c ) 300 % , d ) 600 % , e ) 800 %
Rationale: "the area of the circle is increased by 1500 % , thus the area is increased 16 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 4 times ( diameter increase 4 times = area increase 16 times ) , which is increase by 500 % . answer : b ."
Answer: b
Question (physics): 16 boys or 24 girls can construct the wall in 6 days . the number of days that 16 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 4 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 16 boys + 12 girls = 16 ã — 6 / 4 + 12 = 24 + 12 = 36 girls 4 days to complete the work answer : option b"
Answer: b
Question (general): 9873 + x = 13800 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3927 , d ) 2337 , e ) none of these
Rationale: "answer x = 13800 - 9873 = 3927 option : c"
Answer: c
Question (other): in a sports club with 40 members , 20 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "20 + 18 = 38 but where as total number is 40 - 5 = 35 therefore answer is 38 - 35 = 3 hence answer is e"
Answer: e
Question (gain): an article is bought for rs . 600 and sold for rs . 300 , find the loss percent ?
Options: a ) 12 % , b ) 16 % , c ) 19 % , d ) 50 % , e ) 60 %
Rationale: "600 - - - - 300 100 - - - - ? = > 50 % answer : d"
Answer: d
Question (other): the ratio of 2 numbers is 1 : 2 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 50 , e ) 40
Rationale: "let the numbers be x and 2 x their h . c . f . = 10 so the numbers are 1 * 10 , 2 * 10 = 10,20 l . c . m . = 20 answer is b"
Answer: b
Question (physics): a 300 m long train crosses a platform in 33 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 286 m , b ) 250 m , c ) 277 m , d ) 278 m , e ) 267 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 33 = 50 / 3 = > x = 250 m . answer : b"
Answer: b
Question (physics): youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 14 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 21
Rationale: please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 840 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 840 - - - - > 40 x = 840 - > x = 21 . option e
Answer: e
Question (gain): what sum of money will produce rs . 60 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 337 , b ) 429 , c ) 266 , d ) 288 , e ) 211
Rationale: "60 = ( p * 4 * 7 / 2 ) / 100 p = 429 answer : b"
Answer: b
Question (physics): a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 45 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 34 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 : 34 pm . the correct answer is d ."
Answer: d
Question (physics): an woman sitting in a train which is travelling at 25 kmph observes that a goods train travelling in a opposite direction , takes 3 seconds to pass him . if the goods train is 140 m long , find its speed .
Options: a ) 141 , b ) 142 , c ) 143 , d ) 144 , e ) 145
Rationale: "relative speed = ( 140 / 3 ) m / s = ( 140 / 3 ) * ( 18 / 5 ) = 168 kmph speed of goods train = 168 - 25 = 143 kmph answer is c"
Answer: c
Question (physics): on a trip , a cyclist averaged 12 miles per hour for the first 18 miles and 10 miles per hour for the remaining 18 miles . if the cyclist returned immediately via the same route and took a total of 7.3 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 8.4 , b ) 8.6 , c ) 8.8 , d ) 9 , e ) 9.2
Rationale: "the time to go 36 miles was 18 / 12 + 18 / 10 = 1.5 + 1.8 = 3.3 hours . the average speed for the return trip was 36 miles / 4 hours = 9 mph . the answer is d ."
Answer: d
Question (geometry): there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure q in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = q = 10 ans e ."
Answer: e
Question (physics): in covering a distance of 30 km , arun takes 2 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the speed of arun = x kmph and the speed of anil = y kmph distance = 30 km we know that distancespeed = timehence 30 x − 30 y = 2 . . . . . . . . . . . ( equation 1 ) 30 y − 302 x = 1 . . . . . . . . . . . ( equation 2 ) equation 1 + equation 2 ⇒ 30 x − 302 x = 3 ⇒ 302 x = 3 ⇒ 15 x = 3 ⇒ 5 x = 1 ⇒ x = 5 hence arun ' s speed = 5 kmph answer : b"
Answer: b
Question (physics): the racing magic takes 150 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 150 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 150 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 2 * 450 = 900 seconds = 15 mins answer e"
Answer: e
Question (physics): the sector of a circle has radius of 21 cm and central angle 144 o . find its perimeter ?
Options: a ) 80 cm , b ) 82 cm , c ) 90 cm , d ) 94.8 cm , e ) 95 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 52.8 + 42 = 94.8 cm answer : d"
Answer: d
Question (general): a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 300 , e ) 420
Rationale: maximum number of soap boxes that can be placed in each carton = volume of each carton / volume of each box = ( 25 * 42 * 60 ) / ( 7 * 6 * 5 ) = 300 answer : d
Answer: d
Question (other): how many multiples of 10 are there between 100 and 10000 ( both are inclusive ) ?
Options: a ) 456 , b ) 789 , c ) 991 , d ) 1020 , e ) 1100
Rationale: "the answer is ( 10000 - 100 ) / 10 + 1 = 991 answer is c"
Answer: c
Question (physics): there are 20 poles with a constant distance between each pole . a car takes 25 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 43.1543 , b ) 43.1818 , c ) 43.45128 , d ) 43.41288 , e ) 43.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 25 seconds 1 pole ( 25 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 25 / 11 ) seconds = 43.1818 seconds answer : b"
Answer: b
Question (general): if x > 0 , x / 25 + x / 20 is what percent of x ?
Options: a ) 5 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 25 + 100 / 20 = 4 + 5 = 9 9 is 9 % of 100 = a ."
Answer: a
Question (other): two numbers are in the ratio of 5 : 7 . if 25 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 25 ) : ( 7 x - 25 ) = 5 y : 9 y 5 x - 25 = 5 y 7 x - 25 = 9 y 175 - 125 = 45 y - 35 y 50 = 10 y y = 5 5 x - 25 = 25 x = 10 the two numbers are 5 x and 7 x which are 50 and 70 . the answer is b ."
Answer: b
Question (general): two employees x and y are paid a total of rs . 572 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 260 , e ) s . 300
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 572 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 572 ⇒ y [ 12 / 10 + 1 ] = 572 ⇒ 22 y / 10 = 572 ⇒ 22 y = 5720 ⇒ y = 5720 / 22 = 520 / 2 = rs . 260 d"
Answer: d
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 3 / 7 of the mice are white . if therare 24 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 12 , e ) 20
Rationale: "let total number of mice = m number of white mice = 3 / 7 m number of brown mice = 4 / 3 m = 18 = > m = 18 answer c"
Answer: c
Question (other): how many of the positive factors of 42 , 104 and how many common factors are there in numbers ?
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 42 - 1,2 , 3,6 , 7,14 , 21,42 factors of 104 - 1,2 , 4,8 , 13,26 , 52,104 comparing both , we have two common factors of 40 and 104 - 1,2 , answer ( b )"
Answer: b
Question (general): a batsman scored 130 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 45 % , c ) 53 ( 11 / 13 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 130 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 130 - 60 = 70 required % = ( 70 / 130 ) × 100 = 700 / 13 = 53 ( 11 / 13 ) % answer : option c"
Answer: c
Question (gain): a sum of money at simple interest amounts to $ 815 in 3 years and to $ 854 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "b $ 698 s . i . for 1 year = $ ( 854 - 815 ) = $ 39 . s . i . for 3 years = $ ( 39 x 3 ) = $ 117 . principal = $ ( 815 - 117 ) = $ 698 ."
Answer: b
Question (physics): along a yard 434 metres long , 32 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 14 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "explanation : 32 trees have 31 gaps between them , required distance ( 434 / 31 ) = 14 option a"
Answer: a
Question (gain): a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 300 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 20289 , d ) 20027 , e ) 15000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 300 = > x = 15000 answer : e"
Answer: e
Question (general): the product of a and b is equal to 11 more than twice the sum of a and b . if b = 7 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "given : ab = 2 ( a + b ) + 11 and b = 7 hence 7 a = 2 a + 14 + 11 5 a = 25 , a = 5 ( a potential trap . do not get excited here . we need to find b - a , not a ) b - a = 7 - 5 = 2 correct option : a"
Answer: a
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 5 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 50 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 5 = 42 members have not passed the test , thus 0.7 * total = 35 - - > total = 50 . answer : c ."
Answer: c
Question (physics): a is 2 times as fast as b . a alone can do the work in 20 days . if a and b work on alternative days , beginning with a , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 24 , e ) 26
Rationale: "a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days since they alternate on days , it will take them double this time so total time = 13 * 2 = 26 days so answer is e"
Answer: e
Question (other): how many different positive integers are factors of 125 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "125 = 5 * 25 answer : b"
Answer: b
Question (general): what is the greatest integer m for which the number 30 ! / 10 ^ m is an integer ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 30 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 . thus 5 ^ 7 will divide 30 ! but 5 ^ 8 will not . clearly 2 ^ 7 will divide 30 ! so m = 7 is the largest possible integer . the answer is a ."
Answer: a
Question (general): the smallest 5 digit number exactly divisible by 41 is ?
Options: a ) 10003 , b ) 10004 , c ) 10007 , d ) 10009 , e ) 10010
Rationale: "the smallest 5 - digit number = 10000 . 41 ) 10000 ( 243 82 - - - 180 164 - - - - 160 123 - - - 37 - - - required number = 10000 + ( 41 - 37 ) = 10004 . option b"
Answer: b
Question (general): 9 men are equal to as many women as are equal to 7 boys . all of them earn rs . 216 only . men ’ s wages are ?
Options: a ) 6 , b ) 5 , c ) 2 , d ) 8 , e ) 2
Rationale: "9 m = xw = 7 b 9 m + xw + 7 b - - - - - 216 rs . 9 m + 9 m + 9 m - - - - - 216 rs . 27 m - - - - - - 216 rs . = > 1 m = 8 rs . answer : d"
Answer: d
Question (physics): the speed at which a man can row a boat in still water is 20 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 80 metres ?
Options: a ) 10.51 , b ) 11.51 , c ) 9.51 , d ) 13.51 , e ) 15.51
Rationale: speed of the boat downstream = 20 + 4 = 24 kmph = 24 * 5 / 18 = 6.66 m / s hence time taken to cover 70 m = 70 / 6.66 = 10.51 seconds . answer : a
Answer: a
Question (geometry): the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 360 m , its area is ?
Options: a ) 180 , b ) 882 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 360 = > x = 12 a = 60 , b = 144 , c = 156 s = ( 60 + 144 + 156 ) / 2 = 180 answer : a"
Answer: a
Question (general): the cost of 2 chairs and 3 tables is rs . 1800 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 600
Rationale: "explanation : 2 c + 3 t = 1800 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 600 = > t - c = 600 answer : e"
Answer: e
Question (gain): jim is able to sell a hand - carved statue for $ 670 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20
Rationale: "670 is the final price that is the selling price . now suppose , x is the cost price . therefore 670 = 1.35 * x now while doing x = 670 / 1.35 calculation . i saw that the answer choices begin with 5 . so i did 135 * 5 = 675 . as 670 is less than 675 . therefore the quotient will be less than 5 . which is only in the answer a ."
Answer: a