regisss/math_qa huggingface dataset:
Problem: 33 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 22 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 33 : : 18 : x [ please pay attention , we have written 27 : 33 rather than 33 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 33 \ times 18 } { 27 } } x = 22 so 22 days will be required to get work done by 27 men . answer : a"
Answer: a
Problem: john makes $ 65 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 7.69 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 5 / 65 ) * 100 = ( 1 / 13 ) * 100 = 7.69 % . a"
Answer: a
Problem: an error 38 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 26.64 % , e ) 90.44 %
Rationale: "percentage error in calculated area = ( 38 + 38 + ( 38 ã — 38 ) / 100 ) % = 90.44 % answer : e"
Answer: e
Problem: if n is a positive integer , what is the remainder when ( 7 ^ ( 4 n + 3 ) ) ( 3 ^ n ) is divided by 10 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 2 b or j in this problem ."
Answer: b
Problem: in kaya ' s teacher ' s desk there are 6 pink highlighters , 2 yellow highlighters , and 4 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 12 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 6 + 2 + 4 = 12 . answer is b ."
Answer: b
Problem: if a speaks the truth 20 % of the times , b speaks the truth 80 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.82 , b ) 0.84 , c ) 1.5 , d ) 1.2 , e ) 1.4
Rationale: "probability of a speaks truth p ( a ) = 2 / 10 ; false = 8 / 10 probability of b speaks truth p ( b ) = 8 / 10 ; false = 2 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 8 / 10 ) * ( 2 / 10 ) ] = 1 - 16 / 100 = 1 - 0.16 = 0.84 answer : b"
Answer: b
Problem: a man can do a piece of work in 15 days , but with the help of his son , he can do it in 6 days . in what time can the son do it alone ?
Options: a ) 13 , b ) 9 , c ) 15 , d ) 8 , e ) 10
Rationale: "son ' s 1 day ' s work = ( 1 / 6 ) - ( 1 / 15 ) = 3 / 30 = 1 / 10 the son alone can do the work in 10 days answer is e"
Answer: e
Problem: how many of the positive factors of 45 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 45 - 1 , 3 , 9 , 15 and 45 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 1 answer ( a )"
Answer: a
Problem: what is the unit ’ s digit of 7 ^ 5
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 5 = 7 answer d"
Answer: d
Problem: if y is the smallest positive integer such that 8820 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "8820 = 2 ^ 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 5 . the answer is b ."
Answer: b
Problem: if 20 typists can type 60 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 240 , b ) 200 , c ) 270 , d ) 300 , e ) 310
Rationale: "no . of letters typing by 20 typists in 20 minutes = 60 no . of letters typing by 20 typists in 60 minutes = 60 * 3 = 180 no . of letters typing by 30 typists in 60 minutes = 180 / 20 * 30 = 270 answer : c"
Answer: c
Problem: a batsman makes a score of 85 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 37 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 85 = 17 x therefore x = 37 answer : c"
Answer: c
Problem: of the families in city x in 1998 , 20 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 40 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?
Options: a ) 49.66 % , b ) 52.66 % , c ) 28.22 % , d ) 33.33 % , e ) 25.92 %
Rationale: "say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 20 number of families owning computer in 2002 = 20 * 140 / 100 = 28 number of families in 2002 = 108 the percentage = 28 / 108 * 100 = 25.92 % . answer : e"
Answer: e
Problem: three unbiased coins are tossed . what is the probability of getting 3 heads ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { hhh } p ( e ) = n ( e ) / n ( s ) = 1 / 8"
Answer: e
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 240 . their h . c . f . is :
Options: a ) 30 , b ) 20 , c ) 40 , d ) 60 , e ) 70
Rationale: "explanation : let the number be 2 x , 3 x and 4 x lcm of 2 x , 3 x and 4 x = 12 x 12 x = 240 = > x = 240 / 12 = 20 hcf of 2 x , 3 x and 4 x = x = 20 answer : option b"
Answer: b
Problem: if the radius of a circle is increased by 10 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 144 % , d ) 40 % , e ) 21 %
Rationale: "initially a = pi * r 2 now r 2 = 110 / 100 r then area = pi * ( 110 r / 100 ) 2 area = 121 r / 100 that is area increases from 100 to 121 = increase in area = 21 % answer : e"
Answer: e
Problem: 217 x 217 + 183 x 183 = ?
Options: a ) 79698 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 217 ) ^ 2 + ( 183 ) ^ 2 = ( 200 + 17 ) ^ 2 + ( 200 - 17 ) ^ 2 = 2 [ ( 200 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 40000 + 289 ] = 2 x 40289 = 80578 answer is b"
Answer: b
Problem: kim has 6 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 12 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 / 11 , e ) 1 / 25
Rationale: total pairs = 12 c 2 = 66 ; same color pairs = 6 c 1 * 1 c 1 = 6 ; prob = 1 / 11 ans d
Answer: d
Problem: in a kilometer race , a beats b by 40 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 290 sec , b ) 190 sec , c ) 199 sec , d ) 192 sec , e ) 240 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 40 = 250 sec . time taken by a = 250 - 10 = 240 sec . answer : e"
Answer: e
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 100 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: the distance between the nest and the ditch is 100 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 100 = 3000 . d = st 3000 / 1.5 = t , i think we can take 3000 meters as 3 km , then only we get t = 2 . ( 1000 meters = 1 km ) d )
Answer: d
Problem: s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is
Options: a ) 998 , b ) 297 , c ) 999 , d ) 902 , e ) 900
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is first term = 102 ; total terms = 100 ; difference = 3 108 + ( 99 ) 8 = 900 ans e"
Answer: e
Problem: the batting average of a particular batsman is 62 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 225 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 62 * 46 = 2852 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2852 – 2552 = 300 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 300 2 x = 450 x = 225 runs answer d"
Answer: d
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 50 ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: put in simple words , we need to find the highest power of 2 in 100 ^ 50 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 50 = ( 2 ^ 2 * 5 ^ 2 ) ^ 50 = 2 ^ 100 * 5 ^ 100 answer : d
Answer: d
Problem: a towel , when bleached , lost 10 % of its length and 20 % of its breadth . what is the percentage decrease in area ?
Options: a ) 28 % , b ) 30 % , c ) 44 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 10 − 20 + ( 10 × 20 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer : a"
Answer: a
Problem: if 5 ^ 5 × 5 ^ 7 = ( 5 ^ 4 ) ^ x , then what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 5 ^ 5 × 5 ^ 7 = ( 5 ^ 4 ) ^ x 5 ^ ( 5 + 7 ) = 5 ^ ( 12 ) with multiplying numbers with exponents it ' s the same as adding the exponents 5 ^ 12 = ( 5 ^ 4 ) ^ x since base is same , we can equate powers : when raising an exponent to an exponent , it ' s the same as multiplying them , therefore : 12 = 4 x x = 3 ans . b ) 3
Answer: b
Problem: in a group of cows and hens , the number of legs are 16 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 16 4 x + 2 y = 2 x + 2 y + 16 2 x = 16 x = 8 . answer : b"
Answer: b
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 2 cups of tea . last week mo drank a total of 16 cups of tea and hot chocolate together . if during that week mo drank 4 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 16 t - c = 4 - > t = 10 . c = 6 . mo drinks 5 cups of tea a day then number of days that are not rainy = 10 / 2 = 5 so number of rainy days = 7 - 5 = 2 e is the answer ."
Answer: e
Problem: if the price of a tv is first decreased by 20 % and then increased by 30 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 80 % of 100 ) = rs . 130 / 100 * 80 / 100 * 100 = rs . 104 . . ' . increase = 4 % answer : a
Answer: a
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 5 full and other jar 1 / 4 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 5 , c ) 1 / 2 , d ) 7 / 12 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 5 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 5 + 1 / 5 = 2 / 5 full . answer : b ."
Answer: b
Problem: if the average ( arithmetic mean ) of x + 3 , x + 4 , and x + 5 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 3 + x + 4 + x + 5 ) / 3 = 0 = > 3 x + 12 = 0 = > x = - 4 answer a"
Answer: a
Problem: dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 6 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 15 of the job per hour . in 6 hours , dan completes 6 ( 1 / 15 ) = 2 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 3 / 5 / 1 / 10 = 6 hours . the answer is c ."
Answer: c
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 20 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.6 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 80 % ( 100 - 20 ) . therefore 0.5 x amount of flower - nectar = 0.80 x amount of honey = 0.80 x 1 kg therefore amount of flower - nectar needed = ( 0.80 / 0.51 ) kg = 1.6 kgs answer : d"
Answer: d
Problem: in a throw of dice what is the probability of ge æ « ing number greater than 2
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: "explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : a"
Answer: a
Problem: find the area of a cuboid of length 8 cm , breadth 10 cm . and height 12 cm .
Options: a ) 900 cm cube , b ) 910 cm cube , c ) 920 cm cube , d ) 930 cm cube , e ) 960 cm cube
Rationale: "area of a cuboid = lxbxh = 8 cm x 10 cm x 12 cm = 960 cm cube answer : e"
Answer: e
Problem: if a car went the first third of the distance at 60 kmh , the second third at 24 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 38 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 60 , 24 and 48 ) so : 240 = 60 * t 1 = 4 hrs 240 = 24 * t 2 = 10 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 19 hrs d = rt ( 240 * 3 ) = r * 19 r = 38 answer : a"
Answer: a
Problem: a reduction of 10 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 13 , b ) 15 , c ) 25 , d ) 17 , e ) 19
Rationale: "900 * ( 10 / 100 ) = 90 - - - - 6 ? - - - - 1 = > rs . 15 answer : b"
Answer: b
Problem: the triplicate ratio of 3 : 5 is ?
Options: a ) 27 : 125 , b ) 1 : 62 , c ) 1 : 34 , d ) 3 : 64 , e ) 5 : 64
Rationale: "3 ^ 3 : 5 ^ 3 = 27 : 125 answer : a"
Answer: a
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 . 200 when the rate to profit rises from 5 to 7 percent . find the capital of a ?
Options: a ) 3377 , b ) 2899 , c ) 2500 , d ) 2778 , e ) 10000
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 a capital = 15000 * 2 / 3 = 10000 answer : e"
Answer: e
Problem: find out the square of a number which when doubled exceeds its quarter by 7 ?
Options: a ) 16 , b ) 11 , c ) 31 , d ) 29 , e ) 19
Rationale: "a 16 explanation : let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 4 ) + 7 = > 8 p = p + 28 = > p = 4 p ^ 2 = 4 ^ 2 = 16 ."
Answer: a
Problem: a sports equipment store sold ping pong rackets for a total of $ 490 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 490 x = 50 pairs were sold . answer : a"
Answer: a
Problem: a little girl went to the farm to buy fruits . she bought a bag of apples and grabbed a bag of oranges which was 5 times as heavy as the apples . she brought home a total of 12 pounds of fruits . how many pounds was the oranges ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12
Rationale: pounds of apples = x pounds of oranges = 5 x x + 5 x = 12 6 x = 12 x = 12 / 6 = 2 oranges = 5 x = 5 * 2 = 10 answer : d
Answer: d
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 75 %
Rationale: "explanation : number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % answer is b"
Answer: b
Problem: if 7 < x < 9 < y < 15 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 7 , b ) 4 , c ) 5 , d ) 6 , e ) 3
Rationale: "let x = 7.1 and y = 14.1 greatest possible difference = 14.1 - 7.1 = 7 answer a"
Answer: a
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 2 . if p is less than – 2 , what is the value of p ?
Options: a ) – 18 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: distance between - 2 and 2 = 4 since number p is twice as many units from - 2 as - 2 is from 2 , therefore p can be - 10 since , p is less than - 2 , the value of p = - 10 answer b
Answer: b
Problem: when 100 is divided by positive integer x , the remainder is 3 . what is the remainder when 197 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: if 100 / x leaves a reminder 3 then ( 100 - 3 ) i . e . 97 is divisible by x so ( 100 + 97 ) / x leaves a reminder rem ( 100 / x ) + rem ( 97 / x ) = > 3 + 0 = 3 answer : b
Answer: b
Problem: if 4 ^ k + 4 ^ k = ( 4 ^ 9 ) ^ ( 4 ^ 9 ) - 4 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 4 ^ 11 - 1 , c ) 242 , d ) 3 ^ 10 , e ) 3 ^ 11 - 1
Rationale: 4 ^ k + 4 ^ k = ( 4 ^ 9 ) ^ 4 ^ 9 - 4 ^ k 4 * ( 4 ^ k ) = 4 ^ ( 16 * 4 ^ 9 ) = 4 ^ ( 4 ^ 2 * 4 ^ 9 ) = 4 ( 4 ^ 11 ) 4 ^ k + 1 = 4 ^ ( 4 ^ 11 ) so k + 1 = 4 ^ 11 so k = 4 ^ 11 - 1 answer is b
Answer: b
Problem: if n is a positive integer and n ^ 2 is divisible by 212 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 36 , is n divisible by 48 ? no . so , n is not always divisible by 48 . d"
Answer: d
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 5.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.055 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 55 f - - > s = 4 f - - > f / s = 1 / 4 - - > f / ( s + f ) = 1 / ( 1 + 4 ) = 1 / 5 = 0.2 . answer : b ."
Answer: b
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 5 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 30 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 5 = x 5 x + 30 = 6 x x = 30 km answer : option d"
Answer: d
Problem: the sum of two consecutive even integers is 26 . what are the two numbers ?
Options: a ) 12 - 14 , b ) 13 - 13 , c ) 10 - 16 , d ) 9 - 17 , e ) 8 - 18
Rationale: "let 2 n be the first even integer and let 2 n + 2 be the second integer 2 n + 2 n + 2 = 26 4 n + 2 = 26 4 n + 2 - 2 = 26 - 2 4 n = 24 n = 6 so the first even integer is 2 n = 2 × 6 = 12 and the second is 12 + 2 = 14 correct answer is a ) 12 - 14"
Answer: a
Problem: total 75 cows 25 cow gives each 2 liter milk 25 cow gives each 3 / 4 liter milk 25 cow gives each 1 / 4 liter milk this is split into 3 son per each 25 cows & 25 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 25 , e ) 18
Rationale: "25 cow 2 liter each = 50 liter 25 cow 3 / 4 liter each = 3 / 4 = 0.75 * 25 = 18.75 25 cow 1 / 4 liter each = 1 / 4 = 0.25 * 25 = 6.25 add 50 + 18.75 + 6.25 = 75 milk split into 3 son each 25 liter then 75 / 3 = 25 answer : d"
Answer: d
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 968 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 968 = > x = 11 answer : e"
Answer: e
Problem: two trains 210 m and 260 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 16.92 sec , b ) 14.8 sec , c ) 10.68 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 210 + 260 = 470 m . required time = 470 * 9 / 250 = 16.92 = 16.92 sec . answer : a"
Answer: a
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 900 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 15000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 900 = > 30 x / 100 - 24 x / 100 = 900 = > 6 x / 100 = 900 = > x = 15000 . answer : c"
Answer: c
Problem: a batsman scored 125 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 600 / 11 , d ) 55 % , e ) 60 %
Rationale: "explanation : number of runs made by running , = > 125 − ( 5 × 4 + 5 × 6 ) . = > 125 - 50 = > 75 hence , the required percentage is : - = > 75 / 125 * 100 = > 60 % answer : e"
Answer: e
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 15 wins and 5 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 2
Rationale: "15 wins , 3 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 5 games so it can lose another 2 at most . answer ( e )"
Answer: e
Problem: on selling 13 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 90
Rationale: "( c . p . of 13 balls ) - ( s . p . of 13 balls ) = ( c . p . of 5 balls ) c . p . of 8 balls = s . p . of 13 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 8 = rs . 90 . answer : option e"
Answer: e
Problem: 3 friends neha , sabi and mahi divide $ 1100 amongs them in such a way that if $ 5 , $ 8 and $ 4 are removed from the sums that neha , sabi and mahi received respectively , then the share of the sums that they got will be in the ratio of 2 : 8 : 6 . how much did mahi receive ?
Options: a ) $ 122 , b ) $ 152 , c ) $ 202 , d ) $ 107 , e ) $ 102
Rationale: explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 5 : y - 8 : z - 4 is 2 a : 8 a : 6 a when $ 5 , $ 8 and $ 4 are removed , we are removing a total of $ 17 from $ 1100 . therefore , 2 a + 8 a + 6 a = 1100 - 17 = 1093 i . e . , 16 a = 1093 or a = 68 . we know that z - 6 = 16 a = 6 * 16 = 96 therefore , z = 96 + 6 = $ 102 the correct choice is ( e )
Answer: e
Problem: the maximum number of girls among them 2923 bags and 3239 eyeliners can be distributed in such a way that each student gets the same number of bags and eyeliners .
Options: a ) 80 , b ) 79 , c ) 78 , d ) 81 , e ) 82
Rationale: max no of girls = hcf of 2923 and 3239 = 79 answer : b
Answer: b
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers w are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes w in this range . answer : a ."
Answer: a
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 95 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 ) 190 π
b ) 210 π
c ) 240 π
d ) 320 π
e ) 380 π
Rationale: area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 95 π ) = 380 π the answer is e .
Answer: e
Problem: i have a huge bed - sheet of 1 meter long . i want to cuts this role into pieces of 20 centimeter long cloth . how long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
Options: a ) 150 min , b ) 245 min , c ) 185 min , d ) 300 min , e ) 205 min
Rationale: b it will take 49 cuts not 50 . so 49 * 5 = > 245 minutes
Answer: b
Problem: 30 men can do a work in 40 days . when should 14 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 16 days , c ) 55 days , d ) 44 days , e ) 22 days
Rationale: "total work to be done = 30 * 40 = 1200 let 14 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 14 * 40 ) = 1200 40 p = 640 = > p = 16 days answer : b"
Answer: b
Problem: if the cost price of 50 articles is equal to the selling price of 32 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 56.25 , c ) 78 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 32 articles . let cost price of one article = rs . 1 selling price of 32 articles = rs . 50 but cost price of 32 articles = rs . 32 therefore , the trader made profit . \ percentage of profit = 18 / 32 * 100 = 56.25 % answer : b"
Answer: b
Problem: on dividing 23 by a number , the quotient is 7 and the remainder is 2 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "d = ( d - r ) / q = ( 23 - 2 ) / 7 = 21 / 7 = 3 c"
Answer: c
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.3 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.03 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.3 for x = 0.6 = 3 ( 0.3 * 0.3 ) - 6 * 0.3 * ( 0.3 ) + 0.3 = - 3 * 0.3 * 0.3 + 0.3 = - 0.27 + 0.3 = 0.03 correct option : c"
Answer: c
Problem: the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 86
Rationale: "there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 250 - 168 = 281 range is therefore 128 - 42 = 86 answer e"
Answer: e
Problem: a , b and c enter into a partnership and theirs shares are in the ratio 1 / 2 : 1 / 3 : 1 / 4 . after two months , a withdraws half of his capital and after 10 months , a profit of rs . 378 is divided among them . what is b ’ s share ?
Options: a ) rs . 129 , b ) rs . 144 , c ) rs . 156 , d ) rs . 168 , e ) rs . 178
Rationale: ratio of initial investments = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 . let their initial investments be 6 x , 2 x and 3 x respectively . a : b : c = ( 6 x * 2 + 3 x * 10 ) : ( 4 x * 12 ) : ( 3 x * 12 ) = 42 : 48 : 36 = 7 : 8 : 6 . therefore , b ’ s share = rs . 378 * 8 / 21 = rs . 144 . answer : b
Answer: b
Problem: on a scale that measures the intensity of a certain phenomenon , a reading of d + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d . on that scale , the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3 ?
Options: a ) 5 , b ) 50 , c ) 10 ^ 5 , d ) 5 ^ 10 , e ) 8 ^ 10 - 3 ^ 10
Rationale: to solve this problem we need to examine the information in the first sentence . we are told that “ a reading of d + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d . ” let ’ s practice this idea with some real numbers . let ’ s say d is 2 . this means that d + 1 = 3 . with the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2 . furthermore , we can say that a reading of 4 is actually 10 x 10 = 10 ^ 2 times as great as the intensity of a reading of 2 . increasing one more unit , we can say that a reading of 5 is 10 x 10 x 10 = 10 ^ 3 times as great as the intensity of a reading of 2 . we have found a pattern , which can be applied to the problem presented in the stem : 3 is “ one ” unit away from 2 , and thus a reading of 3 is 10 ^ 1 times as great as the intensity of a reading of 2 . 4 is “ two ” units away from 2 , and thus a reading of 4 is 10 ^ 2 times as great as the intensity of a reading of 2 . 5 is “ three ” units away from 2 , and thus a reading of 5 is 10 ^ 3 times as great as the intensity of a measure of 2 . we can use this pattern to easily answer the question . here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3 . because 8 is 5 units greater than 3 , a reading of 8 is 10 ^ 5 times as great as the intensity corresponding to a reading of 3 . answer c .
Answer: c
Problem: if 6 x ^ 2 + x - 12 = ( hx + b ) ( cx + d ) , then | h | + | b | + | c | + | d | = for a complete solution and more practice problems , see this blog : http : / / magoosh . com / gmat / 2012 / algebra - on . . . to - factor /
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: 6 x ^ 2 + x - 12 = 6 x ^ 2 + 9 x - 8 x - 12 = > 3 x ( 2 x + 3 ) - 4 ( 2 x + 3 ) = > ( 2 x + 3 ) ( 3 x - 4 ) = ( hx + b ) ( cx + d ) hence h = 2 , b = c = 3 , d = - 4 so , 2 + 3 + 3 + | - 4 | = 2 + 3 + 3 + 4 = 12 answer b .
Answer: b
Problem: 4 men and 6 women finish a job in 8 days , while 3 men and 7 women finish it in 10 days . in how many days will 10 women working together finish it ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 70 days
Rationale: explanation : let 1 man ' s 1 day work = x and 1 woman ' s 1 days work = y . then , 4 x + 6 y = 1 / 8 and 3 x + 7 y = 1 / 10 solving , we get y = 1 / 400 [ means work done by a woman in 1 day ] 10 women 1 day work = 10 / 400 = 1 / 40 10 women will finish the work in 40 days option b
Answer: b
Problem: how many trailing zeros will be there after the rightmost non - zero digit in the value of 25 ! ( factorial 25 ) ?
Options: a ) 25 , b ) 8 , c ) 6 , d ) 5 , e ) 2
Rationale: explanatory answer 25 ! means factorial 25 whose value = 25 * 24 * 23 * 22 * . . . . * 1 when a number that has 5 as its factor is multiplied by an even number , it results in a trailing zero . ( product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied ) in 25 ! , the following numbers have 5 as their factor : 5 , 10 , 15 , 20 , and 25 . 25 is the square of 5 and hence it has two 5 s in it . in toto , it is equivalent of having six 5 s . there are at least 6 even numbers in 25 ! hence , the number 25 ! will have 6 trailing zeroes in it . choice c
Answer: c
Problem: alice leaves her home and walks toward bob ' s house . one hour later , bob leaves his home and walks toward alice ' s house . the distance between their homes is 41 kilometers , alice ' s walking speed is 5 km / h , and bob ' s walking speed is 4 km / h . how many kilometers will alice walk before she meets bob ?
Options: a ) 22 , b ) 25 , c ) 27 , d ) 38 , e ) 30
Rationale: alice walks 5 km in the first hour so there are 36 km remaining . when bob starts walking , they complete a total of 9 km per hour . they will meet four hours after bob starts walking . since alice walks for 5 hours , she walks 25 km . the answer is b .
Answer: b
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 17 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 17 a – d = 3 a + d = 17 2 d = 14 d = 7 answer : d"
Answer: d
Problem: a man can row 7 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 ) 6.24 km , b ) 6 km , c ) 6.79 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 7 s = 1.2 ds = 8.2 us = 5.8 x / 8.2 + x / 5.8 = 1 x = 3.40 d = 3.40 * 2 = 6.79 answer : c"
Answer: c
Problem: how many prime numbers between 1 and 100 are factors of 67830 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 2
Rationale: "factor of 67830 = 2 * 3 * 5 * 7 * 17 * 19 - - - 6 prime numbers c"
Answer: c
Problem: the speed of a car is 20 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 25 kmph , b ) 85 kmph , c ) 34 kmph , d ) 23 kmph , e ) 45 kmph
Rationale: "s = ( 20 + 30 ) / 2 = 25 kmph answer : a"
Answer: a
Problem: how many shots of 1 cm radius can be prepared from a sphere of 4 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 64 , e ) 99
Rationale: "4 / 3 ï € * 4 * 4 * 4 = 4 / 3 ï € * 1 * 1 * 1 * x x = 64 answer : d"
Answer: d
Problem: in a class , 7 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 3 = 12 a )"
Answer: a
Problem: p has $ 42 more than what q and r together would have had if both b and c had 1 / 8 of what p has . how much does p have ?
Options: a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60
Rationale: "p = ( 2 / 8 ) * p + 42 ( 6 / 8 ) * p = 42 p = 56 the answer is d ."
Answer: d
Problem: one hour after yolanda started walking from x to y , a distance of 24 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 12
Rationale: "when b started walking y already has covered 3 miles out of 24 , hence the distance at that time between them was 24 - 3 = 21 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 21 / 7 = 3 hours . in 6 hours b walked 3 * 4 = 12 miles . answer : e ."
Answer: e
Problem: the cost of an article is decreased by 10 % . if the original cost is $ 100 , find the decrease cost .
Options: a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 90
Rationale: "original cost = $ 100 decrease in it = 10 % of $ 100 = 10 / 100 ã — 100 = 1000 / 100 = $ 10 therefore , decrease cost = $ 100 - $ 10 = $ 90 answer : e"
Answer: e
Problem: how long will a boy take to run round a square field of side 35 metres . if he runs at the rate of 9 km / hr ?
Options: a ) 56 sec , b ) 1 minute , c ) 45 sec , d ) 58 sec , e ) 50 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 35 * 4 = 140 m time taken = 140 * 2 / 5 = 56 sec . answer is a"
Answer: a
Problem: a can do a piece of work in 20 days , b can do a piece of work in 12 days , both are working together for 3 days after a left the job , then how many days b requires to complete the remaining work ?
Options: a ) 6 days , b ) 5 days , c ) 3 days , d ) 7 days , e ) 12 days
Rationale: first take lcm of ( 20,12 ) = 60 ; total work = 60 ; a ' s one day work = 60 / 20 = 3 ; b ' s one day work = 60 / 12 = 5 ; one day work of both a + b = 3 + 5 = 8 ; total work completed in 3 days = 8 * 3 = 24 ; remaining work is = 60 - 24 = 36 ; remaining work completed by b in = 36 / 12 = 3 days . answer = c
Answer: c
Problem: the average ( arithmetic mean ) of the integers from 200 to 800 , inclusive , is how much greater than the average of the integers from 50 to 300 , inclusive ?
Options: a ) 450 , b ) 375 , c ) 400 , d ) 425 , e ) 300
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 200 to 800 , inclusive = ( 200 + 800 ) / 2 = 500 average of numbers between 50 to 300 , inclusive = ( 50 + 300 ) / 2 = 175 difference = 500 - 175 = 425 answer is d"
Answer: d
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum r of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : r = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Problem: bipin is 6 times old as alok . bipin ' s age will be twice of chandan ' s age after 10 years . if chandan ' s 7 th birthday was celebrated 3 years ago , what is alok ' s present age ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: let the present ages of bipin , alok , chandan are b , a , c respectively given conditions are 1 ) b = 6 a 2 ) ( b + 10 ) = 2 * ( c + 10 ) 3 ) chandans present age = c = 10 years therefore b = 30 so a = 5 answer : d
Answer: d
Problem: a big container is 30 % full with water . if 36 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 80 liters
Rationale: "a big container is 30 % full with water and after 36 liters of water is added , the container becomes 75 % full . hence these 36 liters account for 45 % of the container , which means that the capacity of it is 36 / 0.45 = 80 liters . or : if the capacity of the container is x liters then : 0.3 x + 36 = 0.75 x - - > x = 80 liters . answer : e ."
Answer: e
Problem: find the cost of fencing around a circular field of diameter 42 m at the rate of rs . 5 a meter ?
Options: a ) 655.9 , b ) 659.75 , c ) 650.57 , d ) 655.9 , e ) 600.3
Rationale: "2 * 22 / 7 * 14 = 131.95 131.95 * 5 = rs . 659.75 answer : b"
Answer: b
Problem: length of a rectangular plot is 60 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 60 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 60 ) + x ] = 200 2 x + 60 = 100 2 x = 40 x = 20 . hence , length = x + 60 = 80 m e"
Answer: e
Problem: exactly 36 % of the numbers in set a are even multiples of 3 . if 40 % of the even integers in set a are not multiples of 3 , what percent of the numbers in set a are not even integers ?
Options: a ) 76 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 24 %
Rationale: everything is correct except the red part with a typo : it should be n = 0.6 a - - > even numbers are 60 % of a - - > 40 % of a are not even integers . answer : d .
Answer: d
Problem: the number of timeshare condos available at sunset beach is 3 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 320 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 80 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 3 / 5 x = 320 hence , x = 200 . so , number of timeshare condos available at playa del mar = 200 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 3 / 5 x = 2 / 5 x = 2 / 5 ( 200 ) = 80 the correct answer is a ."
Answer: a
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm
Options: a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c"
Answer: c
Problem: if the operation @ is defined for all a and b by the equation a @ b = ( a ^ 2 * b ) * 3 , then 2 @ ( 3 @ - 1 ) =
Options: a ) - 324 , b ) 223 , c ) 324 , d ) - 223 , e ) - 410
Rationale: "work within the parenthesis first so solve ( 3 @ - 1 ) first ( 3 @ - 1 ) = ( ( 3 ^ 2 ) * - 1 ) * 3 = ( 9 * - 1 ) * 3 = - 9 * 3 = - 27 now take - 3 plug back into equation and solve the rest 2 @ ( - 27 ) = ( ( 2 ^ 2 ) * - 3 ) * 3 = ( 4 * - 27 ) * 3 = - 324 so - 324 is the answer . . . . this question is merely testing order of operations remember pemdas option a"
Answer: a
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 7 inches wide on each side , the total area would have been ( m + 264 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 14 ) ( y + 14 ) = m and so ( 2 ) xy + 14 x + 14 y + 196 = m + 264 let ' s subtract equation ( 1 ) from equation ( 2 ) . 12 x + 12 y + 192 = 264 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Problem: a picnic attracts 240 persons . there are 60 more men than women , and 60 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 130 , e ) 85
Rationale: "adult + children = 240 let , children = y then , adult = y + 60 i . e . y + ( y + 60 ) = 240 i . e . y = 90 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 60 i . e . x + ( x + 60 ) = 2 x + 60 = 110 i . e . x = 25 i . e . men , m = 25 + 60 = 85 answer : option e"
Answer: e
Problem: the price for a loaf of bread in april was $ 1.17 , in may the price was $ 1.30 , and in june the price was $ 1.05 . if 2 / 3 as much bread was sold in april as in may , and twice as much was sold in june as in april , what was the average price for a loaf of bread sold during the 3 - month period ?
Options: a ) $ 1.13 , b ) $ 1.14 , c ) $ 1.15 , d ) $ 1.16 , e ) $ 1.17
Rationale: let x be the number of loaves sold in may . then 2 x / 3 loaves were sold in april and 4 x / 3 loaves were sold in june . the average price was ( 2 x / 3 ) ( 117 ) + 130 x + ( 4 x / 3 ) ( 105 ) / ( 2 x / 3 + x + 4 x / 3 ) = ( 78 + 130 + 140 ) / ( 3 ) = 348 / 3 = $ 1.16 the answer is d .
Answer: d
Problem: a person travels equal distances with speeds of 9 km / hr , 10 km / hr and 11 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 8 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 9 + x / 10 + x / 11 = 47 / 60 29 x / 96 = 47 / 60 = > x = 2.59 total distance = 3 * 2.59 = 7.78 km . answer : c"
Answer: c
Problem: if the sides of a triangle are 26 cm , 22 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 26 cm , 22 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 22 * 10 = 110 cm 2 answer : option b"
Answer: b
Problem: the average mark of the students of a class in a particular exam is 72 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 15
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 72 x - ( 5 * 40 ) = 92 ( x - 5 ) 260 = 20 x = > x = 13 answer : b"
Answer: b
Problem: suresh borrowed some money at the rate of 12 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ?
Options: a ) s . 8500 , b ) s . 6000 , c ) s . 6800 , d ) s . 9000 , e ) s . 7000
Rationale: using the formula s . i = p * t * r / 100 ( x * 12 * 3 / 100 ) + ( x * 9 * 5 / 100 ) + ( x * 13 * 3 / 100 ) = 8160 x = 6800 i . e money borrowed is rs . 6800 answer : c
Answer: c