Cheukting/mathqa huggingface dataset:
Question (geometry): the perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 35
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : d"
Answer: d
Question (gain): what will be the fraction of 50 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 50 * 1 / 100 = 1 / 2 answer : option e"
Answer: e
Question (general): if 0.45 : x : : 4 : 2 , then x is equal to
Options: a ) 0.225 , b ) 0.228 , c ) 0.254 , d ) 0.256 , e ) none
Rationale: "sol . ( x × 4 ) = ( 0.45 × 2 ) ⇒ x = 0.9 / 4 = 0.225 . answer a"
Answer: a
Question (other): a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Question (general): if 0.75 : x : : 5 : 12 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.8 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 12 ) x = 9 / 5 = 1.80 answer : c"
Answer: c
Question (general): the average age of 32 students in a group is 14 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 36 , c ) 47 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 33 ã — 15 â € “ 32 ã — 14 ) years = 47 years . answer c"
Answer: c
Question (general): two employees x and y are paid a total of rs . 650 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 . 200.45 , b ) s . 250.45 , c ) s . 295.45 , d ) s . 300.45 , e ) s . 310.45
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 650 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 650 ⇒ y [ 12 / 10 + 1 ] = 650 ⇒ 22 y / 10 = 650 ⇒ 22 y = 6500 ⇒ y = 6500 / 22 = rs . 295.45 c )"
Answer: c
Question (general): the average speed of a car is 1 3 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 320 km , c ) 360 km , d ) 550 km , e ) 600 km
Rationale: sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 × 2 = 50 km the speed of a car in an hour = 8 / 5 * 50 = 80 km so , the distance covered by car in 4 h is 80 × 4 = 320 km ans . ( b )
Answer: b
Question (other): a certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 340 , b ) 380 , c ) 472 , d ) 528 , e ) 630
Rationale: "1 c 8 * 2 c 12 = 8 * 66 = 528 the answer is ( d )"
Answer: d
Question (general): which number need to add to 859622 to get a number exactly divisible by 456 ?
Options: a ) 456456 , b ) 576834 , c ) 562783 , d ) 634567 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Question (gain): in a factory , there are 40 % technicians and 60 % non - technicians . if the 60 % of the technicians and 40 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: total = 100 t = 40 nt = 60 40 * ( 60 / 100 ) = 24 60 * ( 40 / 100 ) = 24 24 + 24 = 48 = > 100 - 48 = 52 % answer : c
Answer: c
Question (physics): a can do a work in 8 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 400,200 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 8 : 4 ratio of their wages a : b = 2 : 1 a ' s share = ( 2 / 5 ) 1000 = 400 b ' s share = ( 1 / 5 ) 1000 = 200 correct option is c"
Answer: c
Question (gain): harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1235 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . a )"
Answer: a
Question (geometry): if the area of a square with sides of length 11 centimeters is equal to the area of a rectangle with a width of 11 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 11 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 11 ^ 2 = l * 11 = > l = 121 / 11 = 11 answer c"
Answer: c
Question (physics): tanks p and b are each in the shape of a right circular cylinder . the interior of tank p has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank p is what percent of the capacity of tank b ?
Options: a ) 75 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: b . for p , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi p / b = 160 pi / 200 pi = 0.8
Answer: b
Question (general): x and y are both integers . if x / y = 59.40 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 450 , b ) 616 , c ) 672 , d ) 900 , e ) 1024
Rationale: remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : a
Answer: a
Question (gain): last month , john rejected 0.5 % of the products that he inspected and jane rejected 1.00 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 4 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 1.00 ( 1 - x ) = 0.75 0.2 x = 1.00 - 0.75 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 6 ."
Answer: d
Question (gain): what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ?
Options: a ) 30 liters , b ) 50 liters , c ) 60 liters , d ) 70 liters , e ) 80 liters
Rationale: "acid in 20 liters = 80 % of 20 = 16 liters suppose x liters of water be added . then 16 liters of acid in 20 + x liters of diluted solution 20 % of 20 + x = 16 20 + x = 80 x = 60 liters answer is c"
Answer: c
Question (gain): if the compound interest on a certain sum of money for 5 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 1500 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 5 yrs = ( 3000 x 10 x 5 ) / 100 = 1500 / - answer : a ."
Answer: a
Question (gain): the percentage profit earned by selling an article for rs . 1620 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1812.5 , c ) 2000 , d ) 5600 , e ) 3400
Rationale: "c . p . be rs . x . then , ( 1620 - x ) / x * 100 = ( x - 1280 ) / x * 100 1620 - x = x - 1280 2 x = 2900 = > x = 1450 required s . p . = 125 % of rs . 1450 = 125 / 100 * 1450 = rs . 1812.5 . answer b"
Answer: b
Question (gain): a trader bought a car at 25 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 105 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 75 s = 75 * ( 140 / 100 ) = 105 100 - 105 = 5 % answer : c"
Answer: c
Question (physics): a 750 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 300 , b ) 875 , c ) 360 , d ) 770 , e ) 380
Rationale: "speed = 750 / 18 = 125 / 3 m / sec . let the length of the platform be x meters . then , ( x + 750 ) / 39 = 125 / 3 = > x = 1625 m . l = 1625 - 750 = 875 answer : option b"
Answer: b
Question (general): john bought a total of 20 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 20 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 9 , e ) 12
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 20 - x ) 0.60 / 20 = 0.65 solving for x , we get x = 5 - - > mangoes 5 , oranges 15 now , number of oranges to be returned be y 0.80 * 5 + ( 15 - y ) * 0.60 / 20 - y = 0.72 solving for y , y = 12 ans : e"
Answer: e
Question (general): a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 10 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 855 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 10 ) = ( 8550 / 10 ) = 855 answer : option d"
Answer: d
Question (general): when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "let possible value of x is 76 least possible value of x / 18 is 76 / 18 = > 4 quotient with remainder 4 thus answer is ( d ) 4"
Answer: d
Question (general): 26 : 62 : : 32 : ?
Options: a ) 49 , b ) 25 , c ) 36 , d ) 64 , e ) 23
Rationale: "ans 23 reverse of 32 answer : e"
Answer: e
Question (gain): a reduction of 50 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.75 , b ) 8.75 , c ) 7.75 , d ) 3.75 , e ) 1.75
Rationale: "explanation : 40 * ( 50 / 100 ) = 20 - - - 64 ? - - - 12 = > rs . 3.75 answer : d"
Answer: d
Question (general): marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 54.2 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 65 ; projected revenue = 120 . actual / projected * 100 = 65 / 120 * 100 = 54.2 % . answer : a ."
Answer: a
Question (physics): mr . shah decided to walk down the escalator of a tube station . he found â that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stairs he would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins â to descend to the time he steps off the last step at the bottom , find out the height of the stair way in steps ?
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: ( s 1 * t 2 ~ s 2 * t 1 ) / ( t 2 ~ t 1 ) = ( 26 * 18 ~ 34 * 30 ) / ( 18 ~ 30 ) = 46 answer : c
Answer: c
Question (general): the average age of 18 students of a class is 18 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 18 th student is
Options: a ) 101 , b ) 66 , c ) 110 , d ) 160 , e ) 12
Rationale: "explanation : age of the 18 th student = [ 18 * 18 - ( 14 * 5 + 16 * 9 ) ] = ( 324 - 214 ) = 110 years . answer : c"
Answer: c
Question (gain): what is 15 percent of rs . 34 ?
Options: a ) rs . 3.40 , b ) rs . 3.75 , c ) rs . 4.50 , d ) rs . 5.10 , e ) none
Rationale: "sol . 15 % of rs . 34 = rs . ( 15 / 100 x 34 ) = rs . 5.10 answer d"
Answer: d
Question (general): on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "d = ( d - r ) / q = ( 123 - 4 ) / 7 = 119 / 7 = 17 c"
Answer: c
Question (gain): a reduction of 10 % in the price of tea enables a dealer to purchase 25 kg more tea for rs . 22500 . what is the reduced price per kg of tea ?
Options: a ) rs . 70 , b ) rs . 80 , c ) rs . 90 , d ) rs . 100 , e ) none
Rationale: solution : 1 st method : let the original price of tea be rs . x / kg . after reduction the price becomes = x - 10 % of x = 9 x / 10 per kg . now , ( 22500 / ( 9 x / 10 ) ) - 22500 / x = 25 or , 22500 [ 10 / 9 x - 1 / x ] = 25 or , 25 * 9 x = 22500 ; or , x = ( 22500 / 2589 ) = rs . 100 . hence , new price = 90 per kg . thought process method : let the original price be rs . 100 per kg , he get tea = 22500 / 100 = 225 kg . after reduction the price becomes = 90 per kg , he get tea = 22500 / 90 = 250 kg . so , reduction price is rs . 90 per kg as it enables him to buy 25 kg of more tea . answer : option c
Answer: c
Question (physics): at 12 : 30 , the hour hand and the minute hand of a clock form an angle of
Options: a ) 120 ° , b ) 135 ° , c ) 125 ° , d ) 150 ° , e ) 180 °
Rationale: "answer : 180 degree answer : e"
Answer: e
Question (general): 896.7 – 573.07 – 95.007 = ?
Options: a ) 228.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 896.7 - ( 573.07 + 95.007 ) = 896.7 - 668.077 = 228.623 . answer a"
Answer: a
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2200 , what will be c ' s share of the earnings ?
Options: a ) $ 488.9 , b ) $ 480.9 , c ) $ 588.9 , d ) $ 680.9 , e ) $ 788.9
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2200 = $ 488.9 hence : a"
Answer: a
Question (physics): two pipes a and b can fill a tank in 36 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hrs , b ) 22 hrs , c ) 23 hrs , d ) 24 hrs , e ) 21 hrs
Rationale: "1 / ( 1 / 36 + 1 / 45 ) = 180 / 9 = 20 hrs answer : a"
Answer: a
Question (general): a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 18 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 18 the total number of traditionalists is 6 p / 18 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Question (general): a man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 5.33 kmph , b ) 6.00 kmph , c ) 5.00 kmph , d ) 6.00 kmph , e ) 4.00 kmph
Rationale: "m = 6.5 s = 1.5 ds = 8 us = 4 as = ( 2 * 8 * 4 ) / 12 = 5.33 answer : a"
Answer: a
Question (gain): in order to obtain an income of rs . 1250 from 10 % stock at rs . 210 , one must make an investment of
Options: a ) 5363 , b ) 26250 , c ) 28678 , d ) 29002 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 210 . to obtain rs . 1250 , investment = = rs . 26250 . answer : b"
Answer: b
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 400 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 8,250 , c ) rs . 15,600 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 400 x 20.625 ) = rs . 8,250 . answer b"
Answer: b
Question (general): given that 268 x 74 = 19632 , find the value of 2.68 x . 74 .
Options: a ) 1.9632 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9632 answer a"
Answer: a
Question (other): a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: xc 1 * ( x - 1 ) c 1 = 56 x ^ 2 - x - 56 = 0 ( x - 8 ) ( x + 7 ) = 0 x = 8 , - 7 - 7 ca n ' t possible . hence 8 should be the answer b
Answer: b
Question (general): a businessman earns $ 26800 in december , thus decreasing his average annual ( january to december ) earnings by $ 1200 . his average annual earnings would be source : cmat preparation
Options: a ) $ 29000 , b ) $ 33500 , c ) $ 40000 , d ) $ 41000 , e ) $ 42300
Rationale: ( x - 26,800 ) / 11 - x / 12 = 1,200 x = 480,000 x / 12 = 40,000 answer : c .
Answer: c
Question (gain): a can complete a certain job in 16 days . b is 60 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: let , total work unit = 160 units a can finish in 16 days = 160 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 60 / 100 ) * 10 = 16 unit work days in which b will complete the work alone = 160 / 16 = 10 days answer : option e
Answer: e
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 7 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 88.2 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 7 % of 400 = 28 therefore , total number of rotten fruits = 90 + 28 = 118 therefore number of fruits in good condition = 1000 - 118 = 882 therefore percentage of fruits in good condition = ( 882 / 1000 × 100 ) % = ( 88200 / 1000 ) % = 88.2 % answer : b"
Answer: b
Question (gain): sandy had $ 231 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 270 , b ) $ 290 , c ) $ 310 , d ) $ 330 , e ) $ 350
Rationale: "let the money sandy took for shopping be x . 0.7 x = 231 x = 330 the answer is d ."
Answer: d
Question (physics): 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 12 pumps work to empty the tank in 1 day ?
Options: a ) 4 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 12 pumps then 48 / 12 = 4 hrs . answer : a"
Answer: a
Question (general): 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 70 / kg . how much did a kg of coffee cost in june ?
Options: a ) 70 , 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 ( 700 gm ) of tea and 1 / 2 kg ( 700 gm ) of coffee ( equal quantities ) = 70 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 70 = > x = 70 thus proved . . . option a ."
Answer: a
Question (general): a sum of rs . 66000 is divided into 3 parts such that the simple interests accrued on them for 6 , two and 11 years respectively may be equal . find the amount deposited for 11 years .
Options: a ) 6500 , b ) 2000 , c ) 4500 , d ) 3000 , e ) 6000
Rationale: let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e
Answer: e
Question (other): what is the number of integers from 1 to 100 ( inclusive ) that are divisible by neither 5 nor by 6 ?
Options: a ) 35 , b ) 47 , c ) 58 , d ) 26 , e ) 34
Rationale: "in 100 consecutive numbers , number of multiples of 5 = 100 / 5 = 20 ( ignore decimals ) in 100 consecutive numbers , number of multiples of 6 = 100 / 6 = 16 number of multiples of 5 * 6 i . e . 30 = 100 / 30 = 3 number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - ( 29 + 16 - 3 ) { using the concept of sets here ) = 58 answer is c"
Answer: c
Question (general): in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what percent z of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c
Answer: c
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 16 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7 , d ) 7.8 , e ) 9
Rationale: "answer is c . x / x + 36 = 1 / 5 x = 9 16 - 9 = 7"
Answer: c
Question (general): the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?
Options: a ) 15.5 , b ) 15.4 , c ) 15.25 , d ) 10.4 , e ) 15.6
Rationale: total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d
Answer: d