regisss/math_qa huggingface dataset:
Problem: if g is to be chosen at random from the set { 5,8 , 7,1 } and k is to be chosen at random from the set { 14 , 8,3 } , what is the probability that gk will be even ?
Options: a ) 1 , b ) 5 , c ) 8 , d ) 4 , e ) 3
Rationale: method - 1 gk will be even when 1 ) g is even and k is odd , probability of g even is ( 1 / 4 ) and probability of k odd is ( 1 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 1 / 3 ) = ( 1 / 12 ) 2 ) g is odd and k is even , probability of g odd is ( 3 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 2 ) = ( 3 / 4 ) * ( 2 / 3 ) = ( 6 / 12 ) 3 ) g is even and k is even , probability of g even is ( 1 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 2 / 3 ) = ( 2 / 12 ) total favorable probability = ( 1 / 12 ) + ( 6 / 12 ) + ( 2 / 12 ) = ( 12 / 12 ) = 1 answer : option a
Answer: a
Problem: the cost of painting the whole surface area of a cube at the rate of 13 paise per sq . cm is rs . 343.98 . then the volume of the cube is
Options: a ) 8500 cm 3
b ) 9000 cm 3
c ) 9250 cm 3
d ) 9261 cm 3
e ) none
Rationale: solution surface area = ( 34398 / 13 ) ‹ = › 2646 cm 3 ‹ = › 6 a 2 = 2646 ‹ = › a 2 = 441 ‹ = › a = 21 . so , volume = ( 21 x 21 x 21 ) cm 3 = 9261 cm 3 . answer d
Answer: d
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 7.82 km , b ) 6 km , c ) 5.76 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 8 s = 1.2 ds = 9.2 us = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.91 d = 3.91 * 2 = 7.82 answer : a"
Answer: a
Problem: the difference between the place values of two fives in the numerical 86510529 is
Options: a ) 0 , b ) 4905 , c ) 49050 , d ) 490500 , e ) none of them
Rationale: "required difference = ( 500000 - 500 ) = 490500 . answer is d"
Answer: d
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 17 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 = > 45 - [ 28 - { 37 - 15 + * } ] = 56 45 - [ 28 - 37 + 15 - * ] = 56 = > 45 [ 43 - 37 - * ] = 56 45 - [ 6 - * ] = 56 = > 45 - 6 + * = 56 39 + * = 56 = > * = 56 - 39 = 17 answer : c"
Answer: c
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration w of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration w would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Problem: how much percentage 80 is of 480 ?
Options: a ) 16.5 , b ) 14.33 , c ) 12.5 , d ) 15.8 , e ) 16.66
Rationale: 80 * 100 / 480 = 16.66 % answer e
Answer: e
Problem: a present value of a machine is $ 2000 . its value depletiation rate is 20 % per annum then find the machine value before 2 years ?
Options: a ) $ 3125 , b ) $ 2945 , c ) $ 3012 , d ) $ 2545 , e ) $ 3150
Rationale: "p = $ 2000 r = 20 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 2000 * 5 / 4 * 5 / 4 = $ 3125 answer is a"
Answer: a
Problem: if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 25000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: "for first 2000 pages - cost 5 cents / paper for 2001 - 10000 - cost 4.5 cents / paper for 10000 + - 4 cents / paper so cost = ( 5 cents * 2000 ) + ( 4.5 cents * 8000 ) + ( 4 cents * 15000 ) = $ 1060 alternatively , ( 0.05 x 2000 ) + ( 0.045 x 8000 ) + ( 0.04 x 15000 ) = 1,060 answer : b"
Answer: b
Problem: 3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ?
Options: a ) 400 , b ) 800 , c ) 600 , d ) 1200 , e ) 1000
Rationale: first persons investment = x second persons investment = x + 1000 third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3 x = 6000 x = 2000 ratio = 2000 : 3000 : 4000 2 : 3 : 4 4 / 9 * 1800 = 800 answer : b
Answer: b
Problem: bombay express left delhi for bombay at 14.30 hrs , travelling at a speed of 60 kmph and rajdhani express left delhi for bombay on the same day at 16.30 hrs , travelling at a speed of 80 kmph . how far away from delhi will the two trains meet ?
Options: a ) 120 km , b ) 360 km , c ) 480 km , d ) 500 km , e ) none
Rationale: sol . suppose they meet x hours after 14.30 hrs . then , 60 x = 80 ( x - 2 ) or x = 8 . ∴ required distance = ( 60 x 8 ) km = 480 km . answer c
Answer: c
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 600 , what is the reduced price for kg ?
Options: a ) 30 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 600 * ( 25 / 100 ) = 150 - - - - 5 ? - - - - 1 = > rs . 30"
Answer: a
Problem: the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ?
Options: a ) 97 , b ) 151 , c ) 209 , d ) 211 , e ) 219
Rationale: what is the largest possible sum of these three numbers that we can form ? maximize the first digit : 76 + 73 + 71 = 220 = even , so not a prime . let ' s try next largest sum , switch digits in 76 and we ' ll get : 67 + 73 + 71 = 211 = prime . answer : d .
Answer: d
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 46 )
Options: a ) 351 , b ) 360 , c ) 363 , d ) 369 , e ) 378
Rationale: "there are 41 digits in 10 ^ 4 when we subtract 46 from it , there will be 40 digits left . 10 ^ 4 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 46 = 9999999 . . . . ( 40 times ) + 1 - 46 = 9999999 . . . . ( 40 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 54 the sum of the digits will be ( 38 * 9 ) + 5 + 4 = 351 answer : - a"
Answer: a
Problem: a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 5 : 6 : 9 . what is the a + c share ?
Options: a ) $ 1890 , b ) $ 2002 , c ) $ 3500 , d ) $ 1500 , e ) $ 5640
Rationale: "a ' s share = 2700 * 5 / 20 = $ 675 c ' s share = 2700 * 9 / 20 = $ 1215 a + d = $ 1890 answer is a"
Answer: a
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 81 th number in this set ?
Options: a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 645
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 81 th number = 8 * ( 81 - 1 ) + 5 = 645 answer = e"
Answer: e
Problem: how many multiples of 5 are there between 0 and 358 ?
Options: a ) 54 , b ) 75 , c ) 76 , d ) 71 , e ) 58
Rationale: "5 * 1 = 5 5 * 71 = 355 total number of multiples = ( 71 + 1 ) = 72 answer d"
Answer: d
Problem: a bowl was filled with 10 ounces of water , and 0.012 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 6 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 012 * 50 = . 012 * 100 / 2 = 1.2 / 2 = . 6 percent of the original amount of water evaporated during this period = ( . 6 / 10 ) * 100 % = 6 % answer d"
Answer: d
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 9 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 4 / 189 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 1 / 3 * 1 / 9 = 12 / 567 = 4 / 189 answer : c"
Answer: c
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 9 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 27 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 9 = > m = 27 answer c"
Answer: c
Problem: company z has 61 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 13 , d ) 9 , e ) 12
Rationale: say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 61 . now , plug options for x . only c and e give an integer value for y . but only for c x > y as needed . answer : c .
Answer: c
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 17 ] * [ 4 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 105 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 17 ] * [ 4 ] = ( 2 * 17 + 1 ) ( 4 / 2 + 1 ) = [ 105 ] . ans - c"
Answer: c
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 155 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: 10 * 155 = 1550 3 * 100 + 5 * 150 = 1050 1550 – 1050 = 500 c
Answer: c
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 7 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 79
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 7 = 75 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 â € “ 316 = 4 a = e + 4 = 75 + 4 = 79 e"
Answer: e
Problem: if there are 4 peanuts in a box and mary puts 4 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "4 + 4 = 8 correct answer is a ) 8"
Answer: a
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 50 kilometers , maxwell ' s walking speed is 3 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 33.3 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 3 = 9 kms / hr time taken = 50 / 9 = 5.55 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 5.55 = 33.3 kms . . . answer - d"
Answer: d
Problem: the average marks of 30 students in a class is 60 . but a student mark is wrongly noted as 90 instead of 15 then find the correct average marks ?
Options: a ) 55.65 , b ) 57.5 , c ) 62.5 , d ) 45.25 , e ) 50
Rationale: correct avg marks = 60 + ( 15 - 90 ) / 30 avg = 60 - 2.5 = 57.5 answer is b
Answer: b
Problem: there are two inlets and one outlet to a cistern . one of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 9 : 00 am with the cistern completely empty , and at 10 : 00 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ?
Options: a ) 2 hours , b ) 2.5 hours , c ) 3 hours , d ) 3.5 hours , e ) 4 hours
Rationale: the combined inflow rate of the two inlets is 1 / 2 + 1 / 4 = 3 / 4 cistern / hour . thus , working together , it takes 4 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 9 : 00 am to 10 : 00 am , so in 1 hours , the inlet pipes will fill ( time ) * ( rate ) = 1 * 3 / 4 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 4 - x = 1 / 4 - - > x = 1 / 2 cistern / hour , which means that it takes 2 hours the outlet working alone to empty the cistern . answer : a
Answer: a
Problem: if log 0.318 = 0.3364 and log 0.317 = 0.33320 then log 0.319 = ?
Options: a ) 0.33365 , b ) 0.3368 , c ) 0.3396 , d ) 0.3369 , e ) 0.3469
Rationale: log 0.318 / log 0.317 = log ( 0.318 - 0.317 ) = log 0.001 = 0.3364 / 0.33320 = 1.0096 now , log 0.318 * log 0.001 = log ( 0.318 + 0.001 ) = log 0.319 = 0.3364 * 1.0096 = 0.3396 so option c answer : c
Answer: c
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 50 ( 50,000 / 1,000 = 50 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 50 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 6 = 64 , i . e . the population has to double 6 times . since it takes the population 2 minutes to double once it takes 6 * 2 minutes = 12 minutes to double nine times . thus , solution b = 12 is correct ."
Answer: b
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 900 m long ?
Options: a ) 200 sec , b ) 210 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 10 t = 210 sec answer : b"
Answer: b
Problem: we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 368 . how many math books did we buy ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: m + h = 80 h = 80 - m 4 m + 5 h = 368 4 m + 5 * ( 80 - m ) = 368 m = 32 the answer is b .
Answer: b
Problem: how many seconds will a 420 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 30 km / hr ?
Options: a ) 25 , b ) 63 , c ) 40 , d ) 45 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 420 / 6.66 ) sec = 63 sec . answer : b"
Answer: b
Problem: if x + y = 25 and x 2 y 3 + y 2 x 3 = 25 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: xy = 1 as x + y = 25 x 2 y 3 + y 2 x 3 = 25 x 2 y 2 ( y + x ) = 25 substituting x + y x 2 y 2 = 1 xy = 1 answer : a
Answer: a
Problem: there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 2288 , then what was the price of the article initially ?
Options: a ) rs . 2008 , b ) rs . 2022 , c ) rs . 2000 , d ) rs . 2029 , e ) rs . 2021
Rationale: let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 2288 for 114.4 - - - > 100 ; 2288 - - - > ? required price = ( 2288 * 100 ) / 114.4 = 20 * 100 = rs . 2000 . answer : c
Answer: c
Problem: if p ( a ) = 2 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 4 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 2 / 5 . 2 / 5 p ( a n b ) = 4 / 25 . b"
Answer: b
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 64 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 ) - 18 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 64 x < = 7 x > = - 9 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 9 × - 6 = 54 minimum possible value of xy is - 9 × 8 = - 72 - 72 + 54 = - 18 answer : b"
Answer: b
Problem: if the difference between compound interest ( interest compounded yearly ) and simple interest on a sum for 2 years at 10 % p . a . is rs . 150 then sum is
Options: a ) rs . 12000 , b ) rs . 15000 , c ) rs . 13000 , d ) rs . 10000 , e ) rs . 14000
Rationale: compund interest = p [ 1 + r / 100 ] ^ t - p ci = p [ 21 / 100 ] simple interest = ptr / 100 si = p [ 20 / 100 ] difference p [ 21 / 100 ] - p [ 20 / 100 ] = 150 p = 15000 answer : b
Answer: b
Problem: a leak in the bottom of a tank can empty the full tank in 7 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 ) 6048 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 7 - 1 / 12 ) = 5 / 84 work done by the inlet in 1 min . = ( 5 / 84 × 1 / 60 ) = 0.000992 volume of 0.000992 part = 6 litres . therefore , volume of whole = ( ( 1 / 0.000992 ) × 6 ) ‹ = › 6048 litres . answer d"
Answer: d
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 500 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 340 , b ) 346 , c ) 352 , d ) 365 , e ) 370
Rationale: number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d
Answer: d
Problem: kim has 5 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 10 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "total pairs = 10 c 2 = 45 ; same color pairs = 5 c 1 * 1 c 1 = 5 ; prob = 1 / 9 or 2 / 10 * 1 / 9 * 5 = 1 / 9 ans c"
Answer: c
Problem: the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.24 , b ) 36.14 , c ) 36.24 , d ) 36.44 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 45 - 23 ) = 1822 . â ˆ ´ correct mean = 1822 / 50 = 36.44 . answer d"
Answer: d
Problem: a man can do a piece of work in 5 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 7 1 / 2 days , b ) 6 1 / 2 days , c ) 5 1 / 2 days , d ) 4 1 / 2 days , e ) 3 1 / 2 days
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as , son ' s one day work = ( 1 / 3 − 1 / 5 ) = ( 5 − 3 / 15 ) = 2 / 15 so son will do whole work in 15 / 2 days which is = 7 1 / 2 days option a"
Answer: a
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 15 heads and 43 legs . how many cats does the ship host ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "sa ' s + co + ca + cats = 15 . sa ' s + 1 + 1 + cats = 15 or sa ' s + cats = 13 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 43 sa ' s * 2 + cats * 4 = 40 or sa ' s + cats * 2 = 20 or 13 - cats + cat * 2 = 20 then cats = 7 d"
Answer: d
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 20 % per first year and 25 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5460 , d ) 7500 , e ) 1671
Rationale: "5000 * 120 / 100 * 125 / 100 = > 7500 answer : d"
Answer: d
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 26 sec , b ) 76 sec , c ) 48 sec , d ) 27 sec , e ) 22 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.9 = 2 km = 2000 m . required time = 2000 * 3 / 125 = 48 sec . answer : c"
Answer: c
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of c ?
Options: a ) 3377 , b ) 2899 , c ) 3750 , d ) 2778 , e ) 1991
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 c ' s capital = 22500 * 1 / 6 = 3750 answer : c"
Answer: c
Problem: define a * by the equation a * = π - x . then ( ( − π ) * ) * =
Options: a ) − 2 π , b ) - 1 , c ) − π , d ) 2 π , e ) 4 π
Rationale: for a * f ( f ( − π ) ) = f ( π − ( − π ) ) = f ( π + π ) = f ( 2 π ) = π − 2 π = − π = c
Answer: c
Problem: the average age of a group of n people is 15 years old . one more person aged 35 joins the group and the new average is 17 years old . what is the value of n ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: 15 n + 35 = 17 ( n + 1 ) 2 n = 18 n = 9 the answer is b .
Answer: b
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 4 , 11 and 12 units ?
Options: a ) 1.6 units
b ) 6 units
c ) 3 units
d ) 5 units
e ) 12 units
Rationale: sides are 4 , 11 and 12 . . . thus it is right angle triangle since 12 ^ 2 = 4 ^ 2 + 11 ^ 2 therefore , area = 1 / 2 * 11 * 4 = 22 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 12 + 11 + 4 / 2 = 13,5 thus , 22 = 13,5 * r and hence r = in - radius = 1.6 option a
Answer: a
Problem: what is x if x + 2 y = 10 and y = 4 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 10 - 2 y x = 10 - 8 . x = 2 answer : e"
Answer: e
Problem: we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 396 . how many math books did we buy ?
Options: a ) 47 , b ) 54 , c ) 56 , d ) 61 , e ) 64
Rationale: "m + h = 90 h = 90 - m 4 m + 5 h = 396 4 m + 5 * ( 90 - m ) = 396 m = 54 the answer is b ."
Answer: b
Problem: what is the smallest positive perfect square that is divisible by 12 , 15 , and 18 ?
Options: a ) 900 , b ) 1,600 , c ) 2,500 , d ) 3,600 , e ) 4,900
Rationale: "take the lcm of 12 , 15,18 that will come 180 . the smallest positive perfect square given in the option that can be divided with 180 is 900 . so the ans is ( a )"
Answer: a
Problem: find the probability that a leap year selected at random will have 53 mondays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 mondays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 mondays we should have either { mon , tuesday } or { sun , mon } case . the probability of that is 2 / 7 . answer : e .
Answer: e
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 81 km / hr . what is the length of the platform ?
Options: a ) 240 , b ) 288 , c ) 277 , d ) 360 , e ) 422
Rationale: "speed = 81 * 5 / 18 = 22.5 m / sec . length of the train = 22.5 * 20 = 450 m . let the length of the platform be x m . then , ( x + 450 ) / 36 = 22.5 = > x = 360 m . answer : d"
Answer: d
Problem: solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 32 % chemical a , what percent of the mixture is solution x ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.32 ( x + y ) x = 4 y x / ( x + y ) = 4 / 5 = 80 % . the answer is b .
Answer: b
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 50 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 15 % , d ) 50 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.5 * 10 = 15 percentage by which wage earned by charles is more than that earned by robin = ( 15 - 13 ) / 13 * 100 % = 2 / 13 * 100 % = 15 % answer c"
Answer: c
Problem: 8 x 5.4 - 0.6 x 10 / 1.2 = ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 31 , e ) 21
Rationale: "given expression = ( 43.2 - 6 ) / 1.2 = 37.2 / 1.2 = 31 answer is d ."
Answer: d
Problem: veena ranks 65 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 96 , b ) 108 , c ) 110 , d ) 90 , e ) 93
Rationale: "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 65 + 1 = 96 answer : a"
Answer: a
Problem: there were 36000 hardback copies of a certain novel sold before the paperback version was issued . from the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold . if a total of 440000 copies of the novel were sold in all , how many paperback copies were sold ?
Options: a ) 45,000 , b ) 360,000 , c ) 364,500 , d ) 363,600 , e ) 396,900
Rationale: say x was the # of hardback copies sold from the time the first paperback copy was sold . then the total # of paperback copies sold was 9 x ; hence the total # of copies sold was ( hardback ) + ( paperback ) = ( 36 + x ) + ( 9 x ) = 440 - - > x = 40.4 . so , the total # of paperback copies sold was 9 x = 9 * 40.4 = 363.6 or 363,600 . answer : d .
Answer: d
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 1,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: "important point to notice - 2.5 % decrease from the original price 2.5 % of 22,000 = 550 total reduction in 6 years = 550 * 6 = 3300 final price = 22,000 + 1500 - 3300 = 20,200 c is the answer"
Answer: c
Problem: in a covering a certain distance , the speeds of a and b are in the ratio of 3 : 4 . a takes 30 minutes more than b to reach the destination . the time taken by a to reach the destination is ?
Options: a ) 8 hrs , b ) 9 hrs , c ) 2 hrs , d ) 2 hrs , e ) 9 hrs
Rationale: ratio of speeds = 3 : 4 ratio of times taken = 4 : 3 suppose a takes 4 x hrs and b takes 3 x hrs to reach the destination . then , 4 x - 3 x = 30 / 60 = > x = 1 / 2 time taken by a = 4 x hrs = 4 * 1 / 2 = 2 hrs . answer : c
Answer: c
Problem: in a group of ducks and cows , the total number of legs are 24 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 19
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 24 = > 2 x = 24 = > x = 12 b"
Answer: b
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 2500 . then his monthly salary is
Options: a ) rs . 12500 , b ) rs . 1000 , c ) rs . 8000 , d ) rs . 6000 , e ) rs . 15000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 2500 â ‡ ” 20 / 100 x = 2500 â ‡ ” x = 2500 ã — 5 = 12500 . answer a"
Answer: a
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 20 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 232 km , e ) 200 km
Rationale: "0.5 x / 20 + 0.5 x / 20 = 10 - - > x / 20 + x / 20 = 20 - - > 2 x = 20 x 20 - - > x = ( 20 x 20 ) / 2 = 200 km . answer : e ."
Answer: e
Problem: the probability of a student possessing a ball point pen in exam is 3 / 5 & possessing an ink pen is 2 / 3 . find his probability of possessing at least one of them
Options: a ) 10 / 15 , b ) 11 / 15 , c ) 12 / 15 , d ) 13 / 15 , e ) 14 / 15
Rationale: the probability of a student possessing a ball point pen in exam is 3 / 5 . the probability of a student not possessing a ball point pen in exam is 2 / 5 & possessing an ink pen is 2 / 3 . & not possessing an ink pen is 1 / 3 . his probability of possessing none of them = 2 / 5 * 1 / 3 = 2 / 15 his probability of possessing one of them = 1 - 2 / 15 = 13 / 15 answer : d
Answer: d
Problem: if 200 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 48 , e ) 49
Rationale: "we have to basically count the number of 5 s withing 200 200 / 5 = 40 200 / 5 ^ 2 = 8 200 / 5 ^ 3 = 1 we know for sure that there will be at least 49 even numbers ( multiples of 2 ) within 200 so there are 49 10 s in 200 ! answer : e"
Answer: e
Problem: if you write down all the numbers from 1 to 50 , then how many times do you write 3 ?
Options: a ) a ) 11 , b ) b ) 15 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : explanation : clearly , from 1 to 50 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 , 33 , 43 , and ten numbers with 3 as the ten ' s digit - 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 . so , required number = 5 + 10 = 15 . answer : b"
Answer: b
Problem: evaluate 248 + 64 − − √ − − − − − − − − − √
Options: a ) 14 , b ) 26 , c ) 16 , d ) 36 , e ) 46
Rationale: explanation : = 248 + 64 − − √ − − − − − − − − − √ = 248 + 8 − − − − − − √ = 256 − − − √ = 16 answer : c
Answer: c
Problem: two employees x and y are paid a total of rs . 638 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 . 299 , 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 = 638 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 638 ⇒ y [ 12 / 10 + 1 ] = 638 ⇒ 22 y / 10 = 638 ⇒ 22 y = 6380 ⇒ y = 6380 / 22 = 580 / 2 = rs . 290 c"
Answer: c
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 920 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 14 , b ) 12 , c ) 10 , d ) 16 , e ) 18
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 1000 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 920 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 920 so , 3 y < 408 = = > y < 136 so , y can take any value which is less than 136 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . d"
Answer: d
Problem: a circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside . find the area of path .
Options: a ) 1694 m 2
b ) 1700 m 2
c ) 1598 m 2
d ) 1500 m 2
e ) none of thes
Rationale: radius of a circular grass lawn ( without path ) = 35 m ∴ area = π r 2 = π ( 35 ) 2 radius of a circular grass lawn ( with path ) = 35 + 7 = 42 m ∴ area = π r 2 = π ( 42 ) 2 ∴ area of path = π ( 42 ) 2 – π ( 35 ) 2 = π ( 422 – 352 ) = π ( 42 + 35 ) ( 42 – 35 ) answer a
Answer: a
Problem: sonika deposited rs . 6000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9660 , b ) 6560 , c ) 7560 , d ) 9560 , e ) 8560
Rationale: "( 6000 * 3 * 2 ) / 100 = 360 9200 - - - - - - - - 9560 answer : d"
Answer: d
Problem: excluding stoppages , the speed of a train is 42 kmph and including stoppages it is 27 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 19.42 , b ) b ) 20.42 , c ) c ) 21.42 , d ) d ) 22.42 , e ) e ) 23.42
Rationale: "explanation : t = 15 / 42 * 60 = 21.42 answer : option c"
Answer: c
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 80 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 800 gm ) of tea and 1 / 2 kg ( 800 gm ) of coffee ( equal quantities ) = 80 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 80 = > x = 80 thus proved . . . option c ."
Answer: c
Problem: working alone , mary can pave a driveway in 6 hours and hillary can pave the same driveway in 6 hours . when they work together , mary thrives on teamwork so her rate increases by 25 % , but hillary becomes distracted and her rate decreases by 20 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 6 per hour hillary = 1 / 6 per hour rate when working together : mary = 1 / 6 + ( 1 / 4 * 1 / 6 ) = 1 / 5 per hour hillary = 1 / 6 - ( 1 / 5 * 1 / 6 ) = 2 / 15 per hour together they work 1 / 5 + 2 / 15 = 1 / 3 per hour so they will need 3 hours to complete the driveway . the correct answer is a ."
Answer: a
Problem: two boys starts from the same place walking at the rate of 4.5 kmph and 5.5 kmph respectively in the same direction . what time will they take to be 9.5 km apart ?
Options: a ) 9.5 , b ) 5.5 , c ) 8.5 , d ) 9.6 , e ) 9.7
Rationale: explanation : relative speed = 5.5 - 4.5 = 1 kmph ( because they walk in the same direction ) distance = 9.5 km time = distance / speed = 9.5 / 1 = 9.5 hr answer : a
Answer: a
Problem: a train is moving at 4 / 5 of its usual speed . the train is 45 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 45 minutes represents 1 / 4 of the usual time . the usual time is 4 * 45 minutes = 3 hours . the answer is e .
Answer: e
Problem: in a class of 52 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: total = english + german - both + neither - - > 52 = english + 22 - 12 + 0 - - > english = 42 - - > only english = english - both = 42 - 12 = 30 answer : a .
Answer: a
Problem: if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 4 , what is the ratio of apples to cucumbers ?
Options: a ) 1 : 3 , b ) 2 : 5 , c ) 3 : 5 , d ) 5 : 8 , e ) 4 : 7
Rationale: the ratio of bananas to cucumbers is 1 to 4 which equals 2 to 8 . the ratio of apples to bananas to cucumbers is 5 to 2 to 8 . the ratio of apples to cucumbers is 5 to 8 . the answer is d .
Answer: d
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability l that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability l is 2 / 3 . d
Answer: d
Problem: the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidates who passed the examination is ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 120 , e ) 130
Rationale: let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c
Answer: c
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 90 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 360 π , b ) 400 π , c ) 450 π , d ) 500 π , e ) 600 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 90 π ) = 360 π the answer is a ."
Answer: a
Problem: the average of first six prime numbers which are between 40 and 80 is
Options: a ) 35.4 , b ) 50.7 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 40 and 80 = 41 , 43 , 47 , 53 , 59 , 61 average = ( 41 + 43 + 47 + 53 + 59 + 61 ) / 6 = 50.7 answer : b"
Answer: b
Problem: boy sells a book for rs . 720 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 880 , c ) 550 , d ) 590 , e ) 600
Rationale: "cost price = 720 / 90 x 100 = 800 to gain 10 % = 800 x 10 / 100 = 80 sp = cp + gain = 800 + 80 = 880 answer : b"
Answer: b
Problem: renu can do a piece of work in 5 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 5 suma â € ™ s one day â € ™ s work = 1 / 4 - 1 / 5 = 1 / 20 suma can do it alone in 20 days . answer : e"
Answer: e
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 30 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 5 , the remainder is 1 i . e . , n = 5 x + 1 values of n can be one of { 1 , 6 , 11 , 16 , 21 , 26 , 31 . . . . . . . . . . . . . 46 , 51 , 56,61 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 , 61 . . . . . . . . } combining both the sets we get n = { 19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 30 or 30 x in case of n = 26 p = 4 c is the answer ."
Answer: c
Problem: the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is :
Options: a ) 1 : 2 , b ) 5 : 9 , c ) 2 : 1 , d ) 11 : 24 , e ) none
Rationale: answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1
Answer: c
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number p and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number of students p that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Problem: what is the remainder when 30 ^ 72 ^ 87 is divided by 11 .
Options: a ) 5 , b ) 7 , c ) 1 , d ) 3 , e ) 4
Rationale: "let us take n = 72 ^ 87 eq is . . 30 ^ n / 11 = 8 ^ n / 11 here cyclicity of 8 is 10 then n / 10 = 72 ^ 87 / 10 = 2 ^ 87 / 10 here cyclicity of 2 is then 87 % 4 = 3 ( 3 rd cycle of 2 ) . . . . i . e 2 ^ 3 % 10 = 8 ( 8 th cycle of 8 ) therefore final ans is 8 ^ 8 % 11 = 5 answer : a"
Answer: a
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people v who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , v = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Problem: in a recent election , geoff received 1 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 56 , d ) 51 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3000 = 3060 now what ' s the problem wants ? ? a x % . . . . . . . . 3060 is what % of total votes 6000 . . . . . . . . translating : 3060 = x / 100 * 6000 - - - x = 51 % . . . . . . . . . . d"
Answer: d
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability e that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability e = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Problem: if 40 % of a certain number is 160 , then what is 20 % of that number ?
Options: a ) 75 , b ) 100 , c ) 120 , d ) 30 , e ) 80
Rationale: "explanation : 40 % = 40 * 4 = 160 20 % = 20 * 4 = 80 answer : option e"
Answer: e
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 . 3.15 lacs . how many workers were they ?
Options: a ) 300 , b ) 230 , c ) 500 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 315000 - 300000 ) = 15000 n = 15000 / 50 = 300 a"
Answer: a
Problem: 1 ^ 2 – 2 ^ 2 + 3 ^ 2 – 4 ^ 2 + 5 ^ 2 – 6 ^ 2 + 7 ^ 2 – 8 ^ 2 + 9 ^ 2 – 10 ^ 2 = ?
Options: a ) - 21 , b ) - 53 , c ) - 35 , d ) - 55 , e ) - 58
Rationale: 1 - 4 + 9 - 16 + 25 - 36 + 49 - 64 + 81 - 100 = - 55 answer : d
Answer: d
Problem: there are 7 players in a bowling team with an average weight of 112 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 115 kg . , b ) 110 kg . , c ) 106 kg . , d ) 105 kg . , e ) 100 kg .
Rationale: "the new average will be = ( 112 * 7 + 110 + 60 ) / 9 = 106 kgs c is the answer"
Answer: c
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 25 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 3.12 kg , d ) 10 kg , e ) none of these
Rationale: the weight of non - water in 25 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 25 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.12 answer : c .
Answer: c
Problem: anna left for city a from city b at 5.20 a . m . she traveled at the speed of 80 km / hr for 2 hrs 15 min . after that the speed was reduced to 60 km / hr . if the distance between two cities is 350 kms , at what time did anna reach city a ?
Options: a ) 10.21 , b ) 10.27 , c ) 10.25 , d ) 10.23 , e ) 60.25
Rationale: distance covered in 2 hrs 15 min i . e . , 2 1 / 4 hrs = 80 * 9 / 4 = 180 hrs . time taken to cover remaining distance = ( 350 - 180 ) / 60 = 17 / 6 hrs = 2 5 / 6 = 2 hrs 50 min total time taken = ( 2 hrs 15 min + 2 hrs 50 min ) = 5 hrs 5 min . so , anna reached city a at 10.25 a . m . answer : e
Answer: e
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 155 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 155 male associates implies 55 female associates which means the remaining 35 females must be managers e . 35"
Answer: e
Problem: pencils , pens and exercise books in a shop are in the ratio of 10 : 2 : 3 . if there are 120 pencils , the number of exercise books in the shop is :
Options: a ) 26 , b ) 36 , c ) 46 , d ) 56 , e ) 66
Rationale: "explanation : let pencils = 10 x , pens = 2 x & exercise books = 3 x . now , 10 x = 120 hence x = 12 . number of exercise books = 3 x = 36 . answer : b"
Answer: b
Problem: in a group of ducks and cows , the total number of legs are 26 more than thrice the number of heads . find the total number of cows .
Options: a ) a ) 14 , b ) b ) 13 , c ) c ) 16 , d ) d ) 8 , e ) e ) 6
Rationale: "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 26 more than twice the number of heads = > 2 ( d + 2 c ) = 26 + 2 ( c + d ) = > d + 2 c = 13 + c + d = > 2 c = 13 + c = > c = 13 i . e . , total number of cows = 13 answer : b"
Answer: b