regisss/math_qa huggingface dataset:
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 500 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 500 km in = 500 / 50 * 1 = 10 hours answer is a"
Answer: a
Problem: in a renowned city , the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 345,600 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 8 persons are added ( 10 - 2 ) . every second 4 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 4 = 345600 option c"
Answer: c
Problem: two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310
Rationale: "1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ."
Answer: b
Problem: in town x , 64 percent of the population are employed , and 38 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 38 are employed males , hence 26 % are employed females . ( employed females ) / ( total employed people ) = 26 / 64 = 40 % answer : d ."
Answer: d
Problem: there were two candidates in an election . winner candidate received 55 % of votes and won the election by 100 votes . find the number of votes casted to the winning candidate ?
Options: a ) 550 , b ) 744 , c ) 255 , d ) 199 , e ) 231
Rationale: "w = 55 % l = 45 % 55 % - 45 % = 10 % 10 % - - - - - - - - 100 55 % - - - - - - - - ? = > 550 answer : a"
Answer: a
Problem: 5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ?
Options: a ) 25 % , b ) 28 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 %
Answer: a
Problem: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 8 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 10 sec , b ) 8 sec , c ) 9 sec , d ) 7 sec , e ) 12 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 12 + 8 ) = 8 sec answer : b"
Answer: b
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 41 then sum is
Options: a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 4100
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 41 4100 answer : e"
Answer: e
Problem: a leak in the bottom of a tank can empty the full tank in 4 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 2160 , e ) none
Rationale: solution work done by the inlet in 1 hour = ( 1 / 4 - 1 / 12 ) = 1 / 6 . work done by the inlet in 1 min . = ( 1 / 6 × 1 / 60 ) = 0.002778 volume of 0.002778 part = 6 litres . therefore , volume of whole = ( . 002778 × 6 ) ‹ = › 2160 litres . answer d
Answer: d
Problem: a can run 224 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 224 / 32 = 28 / 4 = 7 m / sdistance covered by b in 4 seconds = speed × time = 7 × 4 = 28 metre i . e . , a beat b by 28 metre answer is b"
Answer: b
Problem: in the manufacture of a certain product , 8 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 ) 0.32 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 8 % 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 ) * ( 8 / 100 ) * 100 % = ( 32 / 10000 ) * 100 % = ( 32 / 100 ) % = . 32 % answer b"
Answer: b
Problem: $ 700 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 280 , e ) $ 250
Rationale: a : ( b + c ) = 2 : 3 a ' s share = 700 * 2 / 5 = $ 280 answer is d
Answer: d
Problem: the number of boxes in a warehouse can be divided evenly into 12 equal shipments by boat or 32 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 96 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 12 and 32 = 96 answer c"
Answer: c
Problem: the salary of a worker is first increased by 20 % and afterwards reduced by 20 % . what is the net change in the worker ' s salary ?
Options: a ) 4 % decrease , b ) 8 % decrease , c ) 4 % increase , d ) 8 % increase , e ) no change
Rationale: "let x be the original salary . the final salary is 0.8 ( 1.2 x ) = 0.96 x the answer is a ."
Answer: a
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 37 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 148 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 37 = > 4 / x = 1 / 37 x = 37 ∗ 4 = 148 mins option a"
Answer: a
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 5 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 11 , b ) 14 , c ) 15 , d ) 18 , e ) 30
Rationale: within one standard deviation of the average age means 31 + / - 7 26 - - 31 - - 36 number of dif . ages - 26 27 28 29 30 31 32 33 34 35 36 total = 11 a
Answer: a
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 78 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2600 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 78 1 percent for 1 year = 26 = > 100 percent = 2600 answer : b"
Answer: b
Problem: what is the dividend . divisor 16 , the quotient is 6 and the remainder is 2
Options: a ) 86 , b ) 87 , c ) 88 , d ) 89 , e ) 90
Rationale: "c = d * q + r c = 16 * 6 + 2 c = 86 + 2 c = 88"
Answer: c
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 8 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 1 / 15
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 8 = 280 remaining work is 300 - 280 = 20 remaining fraction of work is = 20 / 300 = 1 / 15 answer e"
Answer: e
Problem: in a college the ratio of the numbers of boys to the girls is 5 : 7 . if there are 140 girls , the total number of students in the college is ?
Options: a ) 200 , b ) 240 , c ) 160 , d ) 250 , e ) 310
Rationale: "let the number of boys and girls be 5 x and 7 x then , 7 x = 140 x = 20 total number of students = 12 x = 12 * 20 = 240 answer is b"
Answer: b
Problem: 62467 × 9998 = ?
Options: a ) 624545037 , b ) 627745452 , c ) 624545077 , d ) 624545066 , e ) 625454211
Rationale: "d 624545066 62467 × 9998 = 62467 × ( 10000 - 2 ) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066"
Answer: d
Problem: a boat takes 38 hours for travelling downstream from point a to point b and coming back to point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 240 km , b ) 120 km , c ) 360 km , d ) 180 km , e ) none of these
Rationale: "explanation : velocity of the stream = 4 kmph speed of the boat in still water is 14 kmph speed downstream = ( 14 + 4 ) = 18 kmph speed upstream = ( 14 - 4 ) = 10 kmph let the distance between a and b be x km time taken to travel downstream from a to b + time taken to travel upstream from b to c ( mid of a and b ) = 38 hours ⇒ x / 18 + ( x / 2 ) 10 = 38 ⇒ x / 18 + x / 20 = 38 ⇒ 19 x / 180 = 38 ⇒ x / 180 = 2 ⇒ x = 360 i . e . , the distance between a and b = 360 km . answer : option c"
Answer: c
Problem: a boatman goes 3 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour 7 min , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 3 / 1 = 3 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 3 + 6 ) = 4.5 kmhr time taken in stationary = 5 / 4.5 = 1 hrs 7 min answer : b"
Answer: b
Problem: 30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 32 , c ) 45 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 30 ã — 13.5 = 405 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 405 â  „ 9 = 45 answer c"
Answer: c
Problem: a man two flats for $ 675958 each . on one he gains 14 % while on the other he loses 14 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.96 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 14 / 10 ) ^ 2 = 49 / 25 = 1.96 % answer is a"
Answer: a
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 20 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 18 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 20 = 100 * 5 / 18 = 250 / 9 t = 500 * 9 / 250 = 18 sec answer : option b"
Answer: b
Problem: how many pairs ( r , r + 1 ) have one or more prime factors common , where r is an integer and 2 ≤ r ≤ 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: r and r + 1 are consecutive integers . two consecutive integers are co - prime , which means that they do n ' t share any common factor but 1 . for example 20 and 21 are consecutive integers , thus only common factor they share is 1 . answer : a .
Answer: a
Problem: walking at 4 / 5 of his usual speed a man is 10 mins too late . find his usual time .
Options: a ) 81 mins , b ) 64 mins , c ) 52 mins , d ) 40 mins , e ) none
Rationale: "speed = s , time = t , 4 / 5 s * ( t + 10 ) = st t = 40 answer : d"
Answer: d
Problem: tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 7 weeks have been $ 406 , $ 413 , $ 420 , $ 436 , $ 395 , $ 410 , $ 360 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 9 - week period ?
Options: a ) $ 360 , b ) $ 380 , c ) $ 430 , d ) $ 290 , e ) $ 520
Rationale: official solution : ( b ) first , we need to add up the wages over the past 7 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 + $ 410 + $ 360 = $ 2840 . to average $ 400 over 9 weeks , the salesman would need to earn : $ 400 × 9 = $ 3600 . subtract $ 2840 from $ 3600 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 9 weeks : $ 3600 – $ 2840 = $ 760 . dividing $ 760 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 760 / 2 = $ 380 . the correct answer is choice ( b ) .
Answer: b
Problem: a furniture manufacturer has two machines , but only one can be used at a time . machine q is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine q can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: machine q finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of q = 5 shifts / day rate of b = 4 shifts / day rate of ( q + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
Answer: d
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 9 / 5 , d ) 9 / 8 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 4 lets say x machines are used to attain the desired rate , thus x / 36 + x / 4 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 9 x ) / 36 = 1 / 2 10 x / 36 = 1 / 2 x = 9 / 5 . qa = 9 / 5 ( answer c )"
Answer: c
Problem: mike earns $ 15 per hour and phil earns $ 10 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 33.3 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 15 is 10 let it be x % less , then = 15 ( 1 - x / 100 ) = 10 1 - x / 100 = 10 / 15 x = 100 / 3 x = 33.3 % ans a"
Answer: a
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 79 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 93 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 79 ( subtracting twice of incorrect from correct ) 3 x = 279 x = 93 answer : c"
Answer: c
Problem: the edges of three metal cubes are 2 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 4.0 , b ) 4.2 , c ) 4.4 , d ) 4.6 , e ) 4.8
Rationale: "the total volume is 2 ^ 3 + 3 ^ 3 + 4 ^ 3 = 99 the edge of the new cube is the cube root of 99 which is about 4.6 cm . the answer is d ."
Answer: d
Problem: rahim bought 50 books for rs . 1000 from one shop and 40 books for rs . 800 from another . what is the average price he paid per book ?
Options: a ) 28 , b ) 20 , c ) 27 , d ) 29 , e ) 21
Rationale: "average price per book = ( 1000 + 800 ) / ( 50 + 40 ) = 1800 / 90 = rs . 20 answer : b"
Answer: b
Problem: in a hostel there were 100 students . to accommodate 40 more students the average is decreased by rupees 10 . but total expenditure decreased by rs . 400 . find the total expenditure of the hostel now ?
Options: a ) 1400 , b ) 2500 , c ) 3000 , d ) 1500 , e ) 2100
Rationale: "100 x - 400 = 140 ( x – 10 ) x = 25 100 * 25 - 400 = 2100 answer : e"
Answer: e
Problem: the radius of a cone is 8 m , height 6 m . find the slant height ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "cone slant height ( l ) = √ r ( power 2 ) + h ( power 2 ) = √ 64 + 36 = 10 m . answer is b ."
Answer: b
Problem: a store ’ s selling price of $ 2500 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ?
Options: a ) $ 2678 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - a
Answer: a
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 10 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 910 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? d"
Answer: d
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 9 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 19
Rationale: "within one standard deviation of the average age means 31 + / - 7 24 - - 31 - - 38 number of dif . ages - 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 total = 19 e"
Answer: e
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 8 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 332
Rationale: "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 8 = 32 minutes . total time = 300 + 32 = 332 minutes . answer : e ."
Answer: e
Problem: what is the leastvalue of x . so that 45 x 09 is divisible by 3 ?
Options: a ) 0 , b ) 5 , c ) 2 , d ) 6 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 5 + x + 0 + 9 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . a"
Answer: a
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 6 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 36 km
Rationale: distance = relative speed * time = ( 6 + 3 ) * 4 = 36 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : e
Answer: e
Problem: the price of a book is increased from $ 300 to $ 360 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "explanation : change in the price = rs 360 – rs 300 = rs 60 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 60 300 ) * 100 = 20 % b"
Answer: b
Problem: the simple interest on rs . 26 for 6 months at the rate of 7 paise per rupeeper month is
Options: a ) 1.2 , b ) 10.92 , c ) 12.98 , d ) 12.38 , e ) none
Rationale: "sol . s . i . = rs . [ 26 * 7 / 100 * 6 ] = rs . 10.92 answer b"
Answer: b
Problem: ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ?
Options: a ) $ 2100 , b ) $ 2222 , c ) $ 2320 , d ) $ 2083.33 , e ) $ 2183.33
Rationale: there is a property to solve such questions withcommon selling priceandcommon % gain and loss . such cases always result in a loss and . . . total % loss = ( common gain % or loss % / 10 ) ^ 2 hence here loss % = ( 20 / 10 ) ^ 2 = 4 % which means he recovered only 96 % of his investment which amount to a total revenue = 25000 + 25000 = 50000 i . e . 96 % of cost = 40000 therefore , 4 % of cost ( loss ) = $ 2083.33 answer : d
Answer: d
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 3 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 3 m = 20 books total = 30 books m ' = 30 = 1 / 2 * 60 ratio : 1 / 2 ans : a"
Answer: a
Problem: an engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose . after 50 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 22 , b ) 30 , c ) 15 , d ) 18 , e ) 20
Rationale: "30 workers working already let x be the total men required to finish the task in next 100 days 2 km done hence remaining is 8 km also , work has to be completed in next 100 days ( 150 - 50 = 100 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 50 ) / ( 2 * 100 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : b"
Answer: b
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 7 , c ) 9 , d ) 7.5 , e ) 6
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 it takes a total of nine hours to cover the 280 mile distance . answer : b"
Answer: b
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 8 years will be
Options: a ) 4 : 3 , b ) 12 : 11 , c ) 7 : 4 , d ) 6 : 5 , e ) 6 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 8 ) : ( 12 + 8 ) = 24 : 20 = 6 : 5 answer : d"
Answer: d
Problem: a certain junior class has 1000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 1 / 1000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 1000 first then we can only pick 1 other pair from the 800 so total will be 60 / 600 * 1000 simplify and you get 1 / 10000 answer is b"
Answer: b
Problem: what is the difference between the place values of two 1 ' s in the numeral 135.21
Options: a ) 99.999 , b ) 100.2 , c ) 134 , d ) 99.99 , e ) 99.9
Rationale: required difference = 100 - 0.01 = 99.99 answer is d
Answer: d
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 36 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 12 : 2 = > for 12 soap , salt = 2 = > for 2 soap , salt = ( 2 / 12 ) * 2 = 1 / 3 so , water : soap : salt = 3 : 2 : 1 / 3 = 36 : 24 : 4 after open container , water : soap : salt = 18 : 24 : 4 so , water : salt = 18 : 4 = 36 : 8 e"
Answer: e
Problem: if x + ( 1 / x ) = 5 , what is the value of e = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) e = 21 , b ) e = 22 , c ) e = 23 , d ) 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Problem: find the smallest number of five digits exactly divisible by 16 , 24,36 and 54 .
Options: a ) 10368 , b ) 10638 , c ) 10836 , d ) 10846 , e ) none of them
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 16,24 , 36,54 i . e 432 , on dividing 10000 by 432 , we get 64 as remainder . therefore , required number = 10000 + ( 432 – 64 ) = 10368 . answer is a ."
Answer: a
Problem: 8 is 4 % of a , and 4 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 32 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 5
Rationale: "explanation : given , = > 4 a / 100 = 8 . = > a = 8 × ( 100 / 4 ) = 200 . - - - - - - - - - ( i ) and , = > ( 8 / 100 ) × b = 4 . = > b = 50 . - - - - - - - - - ( ii ) now , c = b / a ( from ( i ) and ( ii ) ) = > 50 / 200 . = > 1 / 4 . answer : b"
Answer: b
Problem: the volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 2 : 5
b ) 2 : 9
c ) 2 : 2
d ) 2 : 9
e ) 2 : 1
Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 10 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 2 / 5 i . e . h 1 : h 2 = 2 : 5 answer : a
Answer: a
Problem: the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ?
Options: a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg
Rationale: let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a
Answer: a
Problem: sum of two numbers is 50 . two times of the difference of first and seceond is 20 . then the numbers will be ?
Options: a ) 10 , 40 , b ) 20 , 30 , c ) 35 , 15 , d ) 30 , 20 , e ) 15 , 35
Rationale: explanation : x + y = 50 2 x ã ¢ â ‚ ¬ â € œ 2 y = 20 x = 30 y = 20 answer : d
Answer: d
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 25 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 67.5 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 25 % , price = 81 - 20.25 = 60.75 which is 60.75 / 90 * 100 of the sale price on day 1 = ~ 67.5 % answer b"
Answer: b
Problem: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 220 - 320 = = = > a + b - b - c = - 100 = = = > a - c = - 100 answer : b"
Answer: b
Problem: if a and b are the roots of the equation x 2 - 7 x + 7 = 0 , then the value of a 2 + b 2 is :
Options: a ) 35 , b ) 24 , c ) 17 , d ) 6 , e ) 5
Rationale: sol . ( b ) the sum of roots = a + b = 7 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 49 - 14 = 35 answer a
Answer: a
Problem: each machine of type a has 4 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 1 chrome parts . if a certain group of type a and type b machines has a total of 30 steel parts and 33 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 19
Rationale: "look at the below representation of the problem : steel chrome total a 4 2 30 > > no . of type a machines = 30 / 6 = 5 b 2 1 33 > > no . of type b machines = 33 / 3 = 11 so the answer is 16 i . e d . hope its clear ."
Answer: d
Problem: a circular well with a diameter of 2 meters , is dug to a depth of 14 meters . what is the volume of the earth dug out .
Options: a ) 40 m 3
b ) 42 m 3
c ) 44 m 3
d ) 46 m 3
e ) none of these
Rationale: explanation : volume = π r 2 hvolume = ( 22 / 7 ∗ 1 ∗ 1 ∗ 14 ) m 3 = 44 m 3 option c
Answer: c
Problem: there are 750 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 750 - x x / 2 + 750 - x / 4 = 1 / 3 * ( 750 ) = 250 x = 250 x / 2 = 125 is supposed to be the answer answer : c"
Answer: c
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 16 !
Options: a ) 8 , b ) 10 , c ) 6 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 - - - - count 3 ' s = 6 so answer is 6"
Answer: c
Problem: if 25 % of x is 5 less than 10 % of 500 , then x is ?
Options: a ) 188 , b ) 180 , c ) 156 , d ) 840 , e ) 121
Rationale: "25 % of x = x / 4 ; 10 % of 500 = 10 / 100 * 500 = 50 given that , x / 4 = 50 - 5 = > x / 4 = 45 = > x = 180 . answer : b"
Answer: b
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 675 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 45 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 675 / 7 + 8 = 45 sec answer is c"
Answer: c
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 16 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 10 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 16 x < = 3 x > = - 5 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 5 × - 6 = 30 minimum possible value of xy is - 5 × 8 = - 40 - 40 + 30 = - 10 answer : b"
Answer: b
Problem: what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ?
Options: a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8
Rationale: explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a
Answer: a
Problem: a and b can finish a work in 12 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 30 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 12 – 1 / 20 = 2 / 60 = 1 / 30 = > 30 days answer : b"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 200 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 ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec
Rationale: speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e
Answer: e
Problem: a certain tax rate is $ 82 per $ 100.00 . what is the rate , expressed as a percent ?
Options: a ) 82 % , b ) 8.2 % , c ) 0.82 % , d ) 0.082 % , e ) 0.0082 %
Rationale: "here in question it is asking $ . 82 is what percent of $ 100 . suppose $ . 82 is x % of 100 means 100 * ( x / 100 ) = 82 hence x = 82 % so answer is a"
Answer: a
Problem: how many integers from 101 to 600 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 5 = 5 6 is not possible here because it would result in a number greater than 6 ( i . e 606 , 616 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 5 * 10 = 50 answer is a ."
Answer: a
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 30 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 20 , e ) 28
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 30 , it is 14 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 30 is already 14 more than 16 and hence we only have 29 - 14 = 15 extra to distribute between r and s . since s must be greater than r , r can be 16 + 12 = 28 and s can be 16 + 13 = 29 . so r is 28 . answer ( e )"
Answer: e
Problem: x , a , z , and b are single digit positive integers . x = 1 / 6 a . z = 1 / 6 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 35 , b ) 30 , c ) 43 , d ) 60 , e ) 65
Rationale: "a = 6 x , b = 6 z therefore ( 6 x . 10 + 6 z ) - ( 10 x + z ) = ( 6 - 1 ) ( 10 x + z ) = 5 . ( 10 x + z ) number should be divisible by 5 c"
Answer: c
Problem: rs . 200 amounts to rs . 800 in 8 years at simple interest . if the interest is increased by 5 % , it would amount to how much ?
Options: a ) 520 , b ) 440 , c ) 260 , d ) 280 , e ) 120
Rationale: "( 200 * 5 * 8 ) / 100 = 80 200 + 80 = 280 answer : d"
Answer: d
Problem: the product of three consecutive numbers is 336 . then the sum of the smallest two numbers is ?
Options: a ) 13 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 336 336 = 6 * 7 * 8 . so , the three numbers are 6 , 7 and 8 . and sum of smallest of these two = 6 + 7 = 13 . answer : option a"
Answer: a
Problem: a , b , c are positive numbers such that they are in increasing geometric progression then how many such numbers are there in ( loga + logb + logc ) / 6 = log 6
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given that a , b , c are in gp so b / a = c / b = > b ^ 2 = ac ( loga + logb + logc ) / 6 = log 6 = > log ( abc ) = 6 * log 6 = > log ( ac * b ) = log ( 6 ^ 6 ) = > log ( b ^ 3 ) = log ( 6 ^ 6 ) = > b ^ 3 = 6 ^ 6 = > b ^ 3 = ( 6 ^ 2 ) ^ 3 = > b = 6 ^ 2 = 36 it means a = 2 , c = 18 or a = 3 c = 12 or a = 4 c = 9 or a = 6 c = 6 . hence there are four such numbers answer : d
Answer: d
Problem: calculate the l . c . m of 2 / 5 , 4 / 7 , 3 / 7 , 6 / 13 is :
Options: a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11
Rationale: "required l . c . m = l . c . m . of 2 , 4 , 3 , 6 / h . c . f . of 5 , 7 , 7 , 13 = 12 / 1 = 12 answer is d"
Answer: d
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 18 of the area of the field . what is the length of the field ?
Options: a ) 23 , b ) 32 , c ) 34 , d ) 43 , e ) 48
Rationale: "explanation : a / 18 = 8 * 8 = > a = 8 * 8 * 18 x * 2 x = 8 * 8 * 18 x = 24 = > 2 x = 48 answer : option e"
Answer: e
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 290 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 169 , d ) 196 , e ) 212
Rationale: "lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 8 = 2 * s also , together they weight 290 pounds j + s = 290 solvong the 2 equation , we get j = 196 pounds ! d"
Answer: d
Problem: how many integers from 0 to 59 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 58 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 58 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 57 or , n - 1 = 19 or , n = 20 e"
Answer: e
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 2,500 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 160,000 . 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 ) 45,000 , b ) 40,000 , c ) 50,000 , d ) 55,000 , e ) 60,000
Rationale: "let the rate be x , then population of the bacteria after each hour can be given as 2500 , 2500 x , 2500 ( x ^ 2 ) , 2500 ( x ^ 3 ) now population at 4 pm = 160,000 thus we have 2500 ( x ^ 3 ) = 160,000 = 64 thus x = 4 therefore population at 3 pm = 2500 ( 16 ) = 40,000 answer : b"
Answer: b
Problem: on a trip covering 850 km , a bicyclist travels the first 400 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 16.0 , b ) 16.5 , c ) 17.0 , d ) 17.5 , e ) 18.0
Rationale: "time 1 = 400 / 20 = 20 hours time 2 = 450 / 15 = 30 hours total time = 50 hours average speed = 850 / 50 = 17 km / hr the answer is c ."
Answer: c
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 15 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.02 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 15 % are damaged - - > available tomatoes to sell = 85 85 * x - 80 = 0.08 * 80 85 x - 80 = 6.4 85 x = 86.64 x = 86.64 / 85 = 87 / 85 ( approx ) = 1.023 x is slightly under 1.023 = 1.02 answer : d"
Answer: d
Problem: the greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 4 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1642 - 6 ) and ( 1856 - 4 ) = h . c . f . of 1636 and 1852 = 4 . answer : d"
Answer: d
Problem: marcella has 27 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 27 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 27 pairs of shoes minus the 5 ' destroyed ' pairs yields 22 pairs that still fulfill the requirements . answer : a"
Answer: a
Problem: how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and none of the digits is repeated ?
Options: a ) 5 , b ) 4 , c ) 20 , d ) 25 , e ) 30
Rationale: since each desired number is divisible by 5 , so we must have 5 at the unit place . so , there is 1 way of doing it . the tens place can now be filled by any of the remaining 5 digits ( 2 , 3 , 6 , 7 , 9 ) . so , there are 5 ways of filling the tens place . the hundreds place can now be filled by any of the remaining 4 digits . so , there are 4 ways of filling it . required number of numbers = ( 1 x 5 x 4 ) = 20 . answer c
Answer: c
Problem: a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio .
Options: a ) 35 : 44 , b ) 34 : 44 , c ) 22 : 44 , d ) 20 : 40 , e ) 50 : 45
Rationale: in case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer is a .
Answer: a
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,055 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1055 / 1000 ) - 1 = 0.055 = 5.5 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.055 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.055 - 0.01 x = - 0.005 x = - 0.005 / - 0.01 = 5 / 10 = 50 % so x = 50 % of the 1000 which is 500 answer : a"
Answer: a
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 288 . what is their h . c . f . ?
Options: a ) 18 , b ) 24 , c ) 36 , d ) 42 , e ) 48
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 288 x = 24 hcf of 2 x , 3 x and 4 x = x = 24 the answer is b ."
Answer: b
Problem: a merchant sells an item at a 10 % discount , but still makes a gross profit of 20 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: original sp = x cost = c current selling price = . 9 x ( 10 % discount ) . 9 x = 1.2 c ( 20 % profit ) x = 1.2 / . 9 * c x = 4 / 3 c original selling price is 1.3 c which is 30 % profit answer a
Answer: a
Problem: what decimal fraction is 70 ml of a litre ?
Options: a ) . 7 , b ) . 07 , c ) . 05 , d ) 0.07 , e ) none of these
Rationale: "answer required fraction = 70 / 1000 = 7 / 100 = . 07 correct option : b"
Answer: b
Problem: the average age of applicants for a new job is 20 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 20 - 8 = 12 maximum age = average + 1 standard deviation = 20 + 8 = 28 maximum number of different ages of the applicants = 28 - 12 + 1 = 17 answer c"
Answer: c
Problem: p , q and r have $ 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2800 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930
Rationale: a 2800 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 .
Answer: a
Problem: in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 2 ) lies inside the circle and the point ( 4 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
Options: a ) 6 , b ) 5.5 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 4 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 4 , - 3 ) - - - > lesser than 6 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,2 ) - - - - > greater than 5 units . thus the radius is > 5 but < 6 and as it is an integer , the only possible value of radius = 5 . 5 units . b is the correct answer ."
Answer: b
Problem: unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5 . choose exact number of cubes that can completely fill the box .
Options: a ) 750
b ) 850
c ) 950
d ) 1050
e ) none of the above
Rationale: let the dimensions of the box be , length = 5 * a , breadth = 5 * ( a + 1 ) , height = 5 * ( a + 2 ) hence , volume = 5 * 5 * 5 * a * ( a + 1 ) * ( a + 2 ) among any 3 consecutive positive integers , we will either have ( a number that is divisible by both 23 ) or ( a number divisible by 2 and another number divisible by 3 ) . volume = multiple of ( 125 * 2 * 3 ) 750 = 125 * 2 * 3 answer : a
Answer: a
Problem: p and q started a business investing rs 85000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 17 : 5 , b ) 17 : 3 , c ) 17 : 6 , d ) 17 : 7 , e ) 17 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 15000 = 85 : 15 = 17 : 3 option b"
Answer: b