regisss/math_qa huggingface dataset:
Problem: there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27
Rationale: total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of total students = 1 / 5 * 1 / 2 * 100 = 10 . . . answer b
Answer: b
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 130 and $ 160 respectively . charles earns $ 30 more than robin who earns $ 130 . therefore , charles ' wage is 30 / 130 * 100 = 23.07 % . correct choice is ( a )"
Answer: a
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 60 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: a ) 1
Answer: a
Problem: how many times are the hands of a clock at right angle in 6 hours ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "in 12 hours , they are at right angles 22 times . in 6 hours , they are at right angles 11 times . answer : option c"
Answer: c
Problem: a and b can do a piece of work in 4 days , b and c in 6 days , c and a in 3 days . how long will c take to do it ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 4 days , e ) 12 days
Rationale: "2 c = 1 / 6 + 1 / 3 – 1 / 4 = 1 / 4 c = 1 / 8 = > 8 days answer : a"
Answer: a
Problem: 45 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 76.36 % , d ) 90.16 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 45 women = 55 men speaking french = 0.6 * 45 = 27 employees speaking french = 0.55 * 100 = 55 therefore women speaking french = 55 - 42 = 13 and women not speaking french = 55 - 13 = 42 % of women not speaking french = 42 / 55 * 100 = 76.36 % answer c"
Answer: c
Problem: a person spent rs . 6,040 from his salary on food and 5,000 on house rent . after that he was left with 80 % of his monthly salary . what is his monthly salary ?
Options: a ) 55,200 , b ) 65,200 , c ) 75,200 , d ) 85,200 , e ) 95,200
Rationale: "total money spent on food and house rent = 6,040 + 5,000 = 11,040 which is 100 - 80 = 20 % of his monthly salary ∴ his salary = 11040 x 100 / 20 = 55200 answer : a"
Answer: a
Problem: if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: 7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b
Answer: b
Problem: the number of singles that a baseball player hit increased 11 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 1 : 3 , b ) 9 : 11 , c ) 1 : 1 , d ) 2 : 1 , e ) 11 : 3
Rationale: "soln : - 1.11 s + 0.99 d = 1.02 [ s + d ] 0.09 s = 0.03 d s / d = 1 / 3 answer : a"
Answer: a
Problem: trail mix consists of chex cereal , m & m ' s , raisins , and assorted nuts . if one serving consists of 4 cups chex cereal , 3 cups m & m ' s , 2 cups rains , and 4 cups assorted nuts , and the ratio of the chex is doubled to to the m & m ' s , what is the ratio of chex to the rest of the dish ?
Options: a ) 10 : 5 , b ) 15 : 9 , c ) 7 : 17 , d ) 19 : 23 , e ) not enough information given for the answer
Rationale: the answer to this question is way too long for such a simple question , but there ' s really not enough information to tell , so the answer is e .
Answer: e
Problem: which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 16 is 6 ?
Options: a ) 168 , b ) 172 , c ) 170 , d ) 174 , e ) 176
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 6 will be { 336 + 6 , 336 x 2 + 6 , 336 x 3 + 6 , . . . } the largest such number less than or equal to 1856 is 336 x 5 + 6 or 1686 to obtain this you need to subtract 170 . c"
Answer: c
Problem: find 96 × × 98
Options: a ) 92 / 8 , b ) 92 / 12 , c ) 92 / 13 , d ) 92 / 10 , e ) 92 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 4 and - 2 compared with 100 . so answer : a"
Answer: a
Problem: a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) 32 yrs , b ) 36 yrs , c ) 40 yrs , d ) 48 yrs , e ) none
Rationale: "explanation : let the mother ' s present age be x years . then , the person ' s present age = ( 2 / 5 ) * x years . ( ( 2 / 5 ) * x ) + 8 = ( 1 / 2 ) ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 . answer : c"
Answer: c
Problem: in a box of 10 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 4 / 9 , b ) 5 / 11 , c ) 7 / 15 , d ) 9 / 22 , e ) 12 / 35
Rationale: "# defective pens = 3 # good pens = 7 probability of the 1 st pen being good = 7 / 10 probability of the 2 nd pen being good = 6 / 9 total probability = 7 / 10 * 6 / 9 = 7 / 15 the answer is c ."
Answer: c
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is :
Options: a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) none of these
Rationale: "explanation : let b ' s present age = x years . then , a ' s present age = ( x + 9 ) years . ( x + 9 ) + 10 = 2 ( x - 10 ) = > x + 19 = 2 x - 20 = > x = 39 . answer : c"
Answer: c
Problem: in the recent , climate conference in new york , out of 700 men , 500 women , 800 children present inside the building premises , 20 % of the men , 40 % of the women and 10 % of the children were indians . find the percentage of people who were not indian ?
Options: a ) 77 % , b ) 73 % , c ) 79 % , d ) 83 % , e ) none
Rationale: solution : number of indians men present there = 700 * 20 / 100 = 140 indian women = 500 * 40 / 100 = 200 indian children = 800 * 10 / 100 = 80 . total member present in climate conference = 700 + 500 + 800 = 2000 total indian = 200 + 140 + 80 = 420 hence , % of indian present there = 420 * 100 / 2000 = 21 % % of people who were not indian = 100 - 42 = 79 % . answer c
Answer: c
Problem: a can do a work in 9 days and b can do the same work in 18 days . if they work together , in how many days will they complete the work ?
Options: a ) 6 days , b ) 7 days , c ) 5 days , d ) 3 days , e ) 2 days
Rationale: one day ' s work of a and b = 1 / 9 + 1 / 8 = ( 2 + 1 ) / 18 = 1 / 6 so , the time taken to complete the work is 6 days . answer : a
Answer: a
Problem: the sum of the numbers is 660 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 180
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 660 11 x / 3 = 660 x = 180 answer : e"
Answer: e
Problem: jim drove 642 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 558 miles , d ) 887 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 642 = 558 miles correct answer c"
Answer: c
Problem: working together , jose and jane can complete an assigned task in 30 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 90 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 30 30 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 30 * 90 = 2700 the answer choices are : 90 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 90 days for jose and 30 days for jane . answer : a"
Answer: a
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 8 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 36 , c ) 28 , d ) 20 , e ) 54
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 8 = 30 m / s speed of each train = v = 30 / 2 = 15 m / s = 15 × 36 / 10 km / hr = 54 km / hr answer : option e"
Answer: e
Problem: the floor of a rectangular room is 17 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 132 m 2 , c ) 148 m 2 , d ) 152 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 21 ã — 16 = 336 m 2 area of the inner rectangle = 17 ã — 12 = 204 m 2 required area = ( 336 â € “ 204 ) = 132 m 2 answer b"
Answer: b
Problem: how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge
Options: a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these
Rationale: "explanation : number of cubes = ( 24 x 24 x 24 ) / ( 2 x 2 x 2 ) = 1728 answer : b"
Answer: b
Problem: a sum fetched total simple interest of 4016.25 at the rate of 14 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 5737.5 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 70 % of p = 4016.25 or , p = 5737.5 answer a"
Answer: a
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 21 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 225 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 21 = 315 m . let the length of the platform be x m . then , ( x + 315 ) / 36 = 15 = > x = 225 m . answer : b"
Answer: b
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 24 % ryegrass and 75 % fescue . if a mixture of x and y contains 36 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 25 % , b ) 40 % , c ) 60 % , d ) 75 % , e ) 90 %
Rationale: 36 % is 12 % - points above 25 % and 4 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 3 . the percent of mixture x is 3 / 4 = 75 % . the answer is d .
Answer: d
Problem: hcf of two numbers is 15 and their lcm is 180 . if their sum is 105 , then the numbers are
Options: a ) 30 and 75 , b ) 35 and 70 , c ) 40 and 65 , d ) 45 and 60 , e ) 55 and 70
Rationale: "explanation : let the numbers be 15 a and 15 b . then , 15 a + 15 b = 105 or a + b = 7 . . ( i ) lcm = 15 ab = 180 ab = 12 . . ( ii ) solving equations ( i ) and ( ii ) , we get a = 4 , b = 3 so , the numbers are 15 × 4 and 15 × 3 , i . e . , 60 and 45 answer : d"
Answer: d
Problem: lloyd normally works 7.5 hours per day and earns $ 5.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 66.00
Rationale: daily working hour * regular rate + overtime * increased rate 7.5 * 5.5 + 3 * 5.5 * 1.5 = 66.00 answer e
Answer: e
Problem: the cyclist going at a constant rate of 20 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 60 miles per hour . the motor - cyclist stops to wait for the cyclist 10 minutes after passing her , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 40
Rationale: "for the 10 minutes the motor - cyclist continues to overtake the cyclist , she is going at 40 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 20 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 40 / 20 * 10 or 20 minutes answer is ( b )"
Answer: b
Problem: how many 4 digit numbers divisible by 4 can be made with digits 1 , 2 , 3 , 4 , 5 if the repetition of digits is not allowed ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: a number is divisible by 4 if the last 2 numbers are divisible by 4 ( divisible by 2 twice ) ending can be 12 24 32 42 52 case : ending with 12 , 24,32 , 42,54 first digit - 3 choices second digit - 2 choices third digit - 1 choice fourth digit - 1 choice 6 possible choices for each ending ( e . g . 3412,3512 , 3212 , 4512 , 5312 , 5412 ) total number of 4 digit numbers divisible by 4 = 6 * 5 = 30 answer : c
Answer: c
Problem: x and y are positive integers . when x is divided by 17 , the remainder is 3 , and when x is divided by 19 , the remainder is 1 . when y is divided by 14 , the remainder is 5 , and when y is divided by 21 , the remainder is 12 . what is the least possible value of y - x ?
Options: a ) 15 , b ) 13 , c ) 11 , d ) 14 , e ) 18
Rationale: when x is divided by 17 , the remainder is 3 : so , the possible values of x are : 3 , 20 , 37,54 , etc . when x is divided by 19 , the remainder is 1 : so , the possible values of x are : 1,20 . . . stop . since both lists include 20 , the smallest possible value of x is 20 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 21 , the remainder is 12 : so , the possible values of y are : 12 , 33 , . . . stop . since both lists include 33 , the smallest possible value of y is 33 since the smallest possible values of x and y are 20 and 33 respectively , the smallest possible value of y - x is 13 . so , b is the correct answer to the original question .
Answer: b
Problem: how many hours are there in 1200 minutes ?
Options: a ) 10 , b ) 20 , c ) 85 , d ) 86 , e ) 88
Rationale: we know that there are 60 minutes in 1 hour . divide the number of minutes by the number of minutes in 1 hour . we get , divide 1200 by 601200 ÷ 60 = 20 so there are 20 hours in 1200 minutes . answer is b
Answer: b
Problem: how many terminating zeroes t does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Problem: brindavan express leave chennai central station every day at 07.50 am and goes to bangalore city railway station . this train is very popular among the travelers . on 25 th july 2012 number of passengers traveling by i class and ii class was in the ratio 1 : 4 . the fare for this travel is in the ratio 3 : 1 . the total fare collected was rs . 224000 / . ( rs . two lakhs 20 4 1000 only ) . what was the fare collected from i class passengers on that day ?
Options: a ) rs . 32000 , b ) rs . 96000 , c ) rs . 128000 , d ) rs . 500000 , e ) none of these
Rationale: solution : let the number of passenger traveling by first class be x . then , number of passenger traveling by second class will be 4 x . but the fare is in the ratio 3 : 1 in other words , if 3 y fare is collected per i class passenger , y would be collected per ii class passenger . fares of i class passengers : fares of ii class passengers = x * 3 y : 4 x * y = 3 : 4 the above ratio can be interpreted as follows . if total fare is 3 + 4 = 7 , then i class passengers should pay rs . 3 similarly , we can calculate the fare of i class passengers when total was 224000 total fare i class fare 7 3 224000 ? = 224000 * ( 3 / 7 ) = rs . 96000 . answer : option b
Answer: b
Problem: worker a takes 5 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 15 / 4 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 5 one day work of b = 1 / 15 so one day work of a and b together = 1 / 5 + 1 / 15 = 4 / 15 so total days required = 15 / 4 answer : a"
Answer: a
Problem: there are 14 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 240
Rationale: "the total number of stations = 16 from 16 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 16 p ₂ ways . 16 p ₂ = 16 * 15 = 240 . answer : e"
Answer: e
Problem: in a theater , the first row has 12 seats and each row has 2 more seats than previous row . if the last row has 48 seats , what is the total number of seats in the theater ?
Options: a ) 550 , b ) 570 , c ) 590 , d ) 610 , e ) 630
Rationale: "the number of seats in the theater is 12 + ( 12 + 2 ) + . . . + ( 12 + 36 ) = 19 ( 12 ) + 2 ( 1 + 2 + . . . + 18 ) = 19 ( 12 ) + 2 ( 18 ) ( 19 ) / 2 = 19 ( 12 + 18 ) = 19 ( 30 ) = 570 the answer is b ."
Answer: b
Problem: the average age of a family of 6 members is 22 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 22 = 132 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 132 - 42 = 90 therefore , avg age at the birth of youngest member = 90 / 6 = 15 . answer : a"
Answer: a
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 77.12 , e ) 81.6
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.1 + 8.5 ) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d"
Answer: d
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 20 % and its breadth is decreased by 5 % ?
Options: a ) 14 percent increase
b ) 5 percent increase
c ) 24 percent increase
d ) 13 percent increase
e ) 11 percent increase
Rationale: let l and b be 100 each 100 * 100 = 10000 l increase by 20 % = 120 b decrease by 5 % = 95 120 * 95 = 11400 14 percent increase answer : a
Answer: a
Problem: how many differently shaped triangles exist in which no two sides are of the same length , each side is of integral unit length and the perimeter of the triangle is less than 14 units ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: explanation : let the lengths of the sides be a , b and c . given , triagle ' s perimeter < 14 = > a + b + c < 14 - - - - - - - - - - ( i ) from triangle inequality theorem , c < a + b = > 2 c < a + b + c . - - - - - - - - - - ( ii ) from ( i ) and ( ii ) , 2 c < a + b + c < 14 . = > c < 7 - - - - - - - - - - ( iii ) = > by similarity , we can say that length of any side must be less than 7 . keeping these in mind , we can find the following possibilities : - ( 2 , 3,4 ) ( 2 , 4,5 ) ( 2 , 5,6 ) ( 3 , 4,5 ) ( 3 , 4,6 ) = > total 5 possibilities . answer : c
Answer: c
Problem: a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is ?
Options: a ) 870 m 3 , b ) 277 m 3 , c ) 270 m 3 , d ) 220 m 3 , e ) 170 m 3
Rationale: "volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 42 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 answer : c"
Answer: c
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c"
Answer: c
Problem: one - third less than 15 % of 180 is equal to :
Options: a ) 18 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 15 % of 180 = 27 1 / 3 of 27 = 9 so , 1 / 3 less than 27 is equal to 27 - 9 = 18 answer : a"
Answer: a
Problem: evaluate 2.5 / . 0005
Options: a ) 5000 , b ) 500 , c ) 50000 , d ) 50 , e ) 0.5
Rationale: "explanation : 2.5 * 10000 / 5 = 25000 / 5 = 5000 option a"
Answer: a
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 63000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 35000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 63000 = 35000 d"
Answer: d
Problem: a wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 70.6 % , b ) 74.5 % , c ) 78.4 % , d ) 82.1 % , e ) 86.9 %
Rationale: "there are a total of 5 * 5 * 5 = 125 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 3 * 3 * 3 = 27 cubes . the number of cubes with at least one side painted red is 125 - 27 = 98 cubes the probability that a cube has at least one side painted red is 98 / 125 which is 78.4 % the answer is c ."
Answer: c
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 40 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 140 / 100 = 84 in june total income = 84 + 40 = 124 % of mrs lee ' s income = 84 / 124 = 67.74 ( b )"
Answer: b
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 86 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 24
Rationale: "3 j + 2 s = 69 2 j + 3 s = 86 - - - - - - - - - - - - - - - - 5 j + 5 s = 155 - - - - ( divide by 5 ) - - - > j + s = 31 3 j + 2 s = j + 2 ( j + s ) = j + 62 = 69 - - - > j = 7 3 * 7 + 2 s = 69 21 + 2 s = 69 2 s = 48 s = 24 answer : e"
Answer: e
Problem: if the cost price of 17 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 32 % loss , d ) 40 % loss , e ) 50 % loss
Rationale: "explanation : 17 cp = 25 sp cost price cp = 25 selling price sp = 17 formula = ( sp - cp ) / cp * 100 = ( 17 - 25 ) / 25 * 100 = 32 % loss answer : option c"
Answer: c
Problem: tough and tricky questions : word problems . if bill ' s salary increased by 16 percent , he would earn $ 812 per month . if instead , his salary were to increase by only 10 percent , how much money r would he earn per month ?
Options: a ) $ 700 , b ) $ 754 , c ) $ 770 , d ) $ 782 , e ) $ 893
Rationale: official solution : ( c ) if bill ’ s salary increased by 16 % he would earn $ 812 . algebraically , this can be written as : $ 812 = 1.16 s , where s is his current salary . then s = $ 812 / 1.16 = $ 700 . now that we know his current salary is $ 700 , we can calculate what his salary would be if it were increased by 10 % . we know that 10 % of $ 700 is $ 70 , so his salary would be : r = $ 700 + $ 70 = $ 770 . the correct answer is choice ( c ) .
Answer: c
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 25 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 80 , b ) 28 , c ) 90 , d ) 26 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 25 = rs . 80 . answer : a"
Answer: a
Problem: an aeroplane covers a certain distance of 480 kmph in 4 hours . to cover the same distance in 4 1 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 443 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 480 kmph distance travelled in 4 hours = 480 * 4 = 1920 km speed of aeroplane to acver 1920 km in 13 / 3 = 1920 * 3 / 13 = 443 km answer c ."
Answer: c
Problem: tough and tricky questions : decimals . the value of x is derived by summing a , b , and c and then rounding the result to the tenths place . the value of y is derived by first rounding a , b , and c to the tenths place and then summing the resulting values . if a = 5.45 , b = 2.95 , and c = 3.74 , what is y – x ?
Options: a ) - 0.1 , b ) 0 , c ) 0.05 , d ) 0.2 , e ) 0.3
Rationale: to find x , we first sum a , b , and c , then round to the tenths place . 5.45 + 2.95 + 3.74 = 12.14 , which rounds to 12.2 . to find y , we first round a , b , and c to the tenths place and them sum them . so 5.4 + 2.9 + 3.7 = 12.0 . we are looking for y - x , which gives us 12.2 - 12.0 = 0.2 , or answer choice d .
Answer: d
Problem: a train covers a distance of 20 km in 30 min . if it takes 18 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 125 m , c ) 120 m , d ) 217 m , e ) 200 m
Rationale: "speed = ( 20 / 30 * 60 ) km / hr = ( 40 * 5 / 18 ) m / sec = 100 / 9 m / sec . length of the train = 100 / 9 * 18 = 200 m . answer : e"
Answer: e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 794 m , b ) 704 m , c ) 454 m , d ) 186 m , e ) 176 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b"
Answer: b
Problem: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 16 cm height . what is the diameter of each sphere ?
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c ."
Answer: c
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 35 years . the ratio of their ages after 8 years will be
Options: a ) 28 : 23 , b ) 6 : 11 , c ) 5 : 4 , d ) 3 : 5 , e ) 7 : 11
Rationale: let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 35 x = 5 mini ’ s age = 20 years and minakshi ’ s age = 15 years ratio of their ages after 8 years = ( 20 + 8 ) : ( 15 + 8 ) = 28 : 23 answer : a
Answer: a
Problem: one fourth of a solution that was 15 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 19 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.15 + 25 * x = 100 * 0.16 - - > x = 0.19 . answer : d ."
Answer: d
Problem: [ 1 / ( 1 . 2.3 ) ] + [ 1 / ( 2 . 3.4 ) ] + [ 1 / ( 3 . 4.5 ) ] + [ 1 / ( 4 . 5.6 ) ] is equal to
Options: a ) 7 / 30 , b ) 11 / 30 , c ) 13 / 30 , d ) 17 / 30 , e ) none
Rationale: answer given exp . = [ ( 4 x 5 x 6 ) + ( 5 x 6 ) + ( 2 x 6 ) + ( 2 x 3 ) ] / [ ( 2 x 3 x 4 x 5 x 6 ) ] = 168 / ( 24 x 30 ) = 7 / 30 correct option : a
Answer: a
Problem: a ’ s speed is 21 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 2 / 21 , b ) 2 / 19 , c ) 1 / 11 , d ) 1 / 7 , e ) 1 / 5
Rationale: let d be the full distance . let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 21 v / 19 ) = xd / v ( 19 / 21 ) * d / v = x * d / v x = 19 / 21 b should have a head start of 2 / 21 of the full distance . the answer is a .
Answer: a
Problem: 2.01 ã — 0.001 = ?
Options: a ) 0.201 , b ) 0.000201 , c ) 2.01 , d ) 0.0201 , e ) 0.00201
Rationale: "2.01 ã — 0.001 = ? or , ? = 0.00201 answer e"
Answer: e
Problem: if there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40 % of the total . what fraction of the total is women who own cars ?
Options: a ) 3 ⁄ 20 , b ) 11 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 5 , e ) 2 ⁄ 15
Rationale: "consider a group of 200 men and 100 women , a total of 300 people . 40 % of them , which is 120 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 60 . it means that there are 100 - 60 = 40 women who own a car , and this represents 40 / 300 = 2 / 15 of the total . answer e"
Answer: e
Problem: the total population of city a and city b is 5000 more than the total population of city b and city c . how much lesser is the population in city c as compared to city a ?
Options: a ) 8500 , b ) 3500 , c ) 4500 , d ) 5000 , e ) 1500
Rationale: ( a + b ) - ( b + c ) = 5000 a - c = 5000 answer : d
Answer: d
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 sq . cm , what is the length of the rectangle ?
Options: a ) 15 cm , b ) 18 cm , c ) 21 cm , d ) 24 cm , e ) 27 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 294 3 w ^ 2 / 2 = 294 w ^ 2 = 196 w = 14 l = 3 ( 14 ) / 2 = 21 the answer is c ."
Answer: c
Problem: the length of the bridge , which a train 250 metres long and travelling at 72 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 350 m , e ) 240 m
Rationale: "speed = [ 72 x 5 / 18 ] m / sec = 20 m / sec time = 30 sec let the length of bridge be x metres . then , ( 250 + x ) / 30 = 20 = > 250 + x = 600 = > x = 350 m . answer : d"
Answer: d
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 14 % solution of acid . as a result , a 23 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.14 ( x ) = 0.23 0.36 x = 0.27 x = 3 / 4 the answer is d ."
Answer: d
Problem: if 7 spiders make 7 webs in 7 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 7 webs 7 : 1 1 x 7 x x = 7 x 1 x 7 = > x = 7 answer is 7
Answer: a
Problem: if p ' s height is 40 % less than that of q , how much percent q ' s height is more than that of p ?
Options: a ) 75.56 % , b ) 66.66 % , c ) 70.05 % , d ) 80 % , e ) 85 %
Rationale: excess of q ' s height over p = ( 40 / ( 100 - 40 ) ) * 100 = = > 66.66 % answer b
Answer: b
Problem: a can finish a piece of work in 12 days . b can do it in 20 days . they work together for 9 days and then a goes away . in how many days will b finish the work ?
Options: a ) 6 days , b ) 4 days , c ) 5 days , d ) 3 days , e ) 7 days
Rationale: "9 / 12 + ( 9 + x ) / 20 = 1 = > x = 5 days answer : c"
Answer: c
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 120 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 120 ( p ) ( p - 1 ) = 240 = 16 * 15 p = 16 the answer is b ."
Answer: b
Problem: a parking garage rents parking spaces for $ 10 per week or $ 35 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 100 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: 10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 35 = 420 $ 520 - 420 = 100 ans b
Answer: b
Problem: the cost of the paint is rs . 40 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 30 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 10800 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 30 ^ 2 = 5400 sq . ft quantity of paint required = ( 5400 / 20 ) = 270 kg cost of painting = 40 x 270 = rs . 10800 answer : d"
Answer: d
Problem: a rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it . one parallel to the length and the other parallel to breadth . the cost of graveling the roads at 75 paise per sq meter is
Options: a ) 378
b ) 278
c ) 258
d ) 287
e ) 271
Rationale: explanation : area of cross roads = 55 * 4 + 35 * 4 - 4 * 4 = 344 sq m cost of graveling = 344 * ( 75 / 100 ) = rs . 258 answer : c ) rs . 258
Answer: c
Problem: the sum of four consecutive even numbers is 52 , find the third number ?
Options: a ) 14 , b ) 10 , c ) 12 , d ) 16 , e ) 20
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 let the third number be n + 6 n + n + 2 + n + 4 + n + 6 = 52 combine like terms : 4 n + 12 = 52 4 n + 12 = 52 4 n = 52 - 12 4 n = 40 n = 10 n + 2 = 12 n + 4 = 14 n + 6 = 16 the third number is 14 answer : a"
Answer: a
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 60 envelopes
Options: a ) 1 minute , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 60 envelopes they will take 60 / 60 mins . i . e . , 1 mins . answer : a"
Answer: a
Problem: if 5395 / 4.15 = 1300 , then 539.5 / 41.5 is equal to ?
Options: a ) 17 , b ) 13 , c ) 15 , d ) 14 , e ) 16
Rationale: "answer given expression 539.5 / 41.5 = 5395 / 415 = 5395 / ( 415 x 100 ) = 1300 / 100 = 13 correct option : b"
Answer: b
Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 80 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ?
Options: a ) 8 % , b ) 12 % , c ) 16 % , d ) 20 % , e ) 24 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.8 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.8 x = 1.2 x the number of students in advanced trigonometry is 0.3 x the percentage in advanced trigonometry is 0.3 x / 2.5 x = 12 % the answer is b ."
Answer: b
Problem: pipe a can fill a tank in 15 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 24
Rationale: "let the pipe b be closed after x minutes . 30 / 15 - x / 24 = 1 = > x / 24 = 30 / 15 - 1 = 1 = > x = 1 * 24 = 24 . answer : e"
Answer: e
Problem: a train starts full of passengers at the first station it drops 1 / 3 of the passengers and takes 280 more at the second station it drops one half the new total and takes 12 more . on arriving at the third station it is found to have 242 passengers . find the no of passengers in the beginning ?
Options: a ) 292 , b ) 270 , c ) 192 , d ) 144 , e ) 168
Rationale: let no of passengers in the beginning be x after first station no passengers = ( x - x / 3 ) + 280 = 2 x / 3 + 280 after second station no passengers = 1 / 2 ( 2 x / 3 + 280 ) + 12 1 / 2 ( 2 x / 3 + 280 ) + 12 = 242 2 x / 3 + 280 = 2 * 230 = 460 - 280 = 180 2 x / 3 = 180 x = 270 . so the answer is option b ) 270 .
Answer: b
Problem: a farming field can be ploughed by 6 tractors in 4 days . when 6 tractors work together , each of them ploughs 120 hectares a day . if two of the tractors were moved to another field , then the remaining 4 tractors could plough the same field in 5 days . how many hectares a day would one tractor plough then ?
Options: a ) 144 , b ) 255 , c ) 148 , d ) 265 , e ) 320
Rationale: if each of 66 tractors ploughed 120120 hectares a day and they finished the work in 44 days , then the whole field is : 120 ⋅ 6 ⋅ 4 = 720 ⋅ 4 = 2880120 ⋅ 6 ⋅ 4 = 720 ⋅ 4 = 2880 hectares . let ' s suppose that each of the four tractors ploughed xx hectares a day . therefore in 5 days they ploughed 5 ⋅ 4 ⋅ x = 20 ⋅ x 5 ⋅ 4 ⋅ x = 20 ⋅ x hectares , which equals the area of the whole field , 2880 hectares . so , we get 20 x = 288020 x = 2880 x = 288020 = 144 x = 288020 = 144 . hence , each of the four tractors would plough 144 hectares a day . correct answer is a ) 144
Answer: a
Problem: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 3.2 ) + e ( – 1.7 ) + o ( – 3.3 ) + e ( 4.7 ) is :
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "o ( 3.2 ) + e ( – 1.7 ) + o ( – 3.3 ) + e ( 4.7 ) = 5 + 0 + ( - 5 ) + 4 = 4 the answer is b ."
Answer: b
Problem: a mixture of 125 gallons of wine and water contains 20 % of water . how much water must be added to the mixture in order to increase the percentage of water to 25 % of the new mixture ?
Options: a ) 10 gallons , b ) 8.5 gallons , c ) 8 gallons , d ) 8.33 gallons , e ) 9.33 gallons
Rationale: in 125 gallons of the solution there are 0.2 ∗ 125 = 25 gallons of water . we want to add w gallons of water to 125 gallons of solution so that 25 + w gallons of water to be 25 % of new solution : 25 + w = 0.25 ( 125 + w ) - - > w = 253 ≈ 8.33 . answer : d
Answer: d
Problem: barbata invests $ 3000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 1500
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 3000 + 0.05 * 3000 + x + 0.08 x = 3000 + x + 0.06 ( 3000 + x ) 0.05 * 3000 + 0.08 x = 0.06 x + 0.06 * 3000 0.02 x = 3000 ( 0.06 - 0.05 ) x = 3000 * 0.01 / 0.02 = 1500 ans : ` ` e ' '"
Answer: e
Problem: the price of a jacket is reduced by 15 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 60 , b ) 65 , c ) 69 , d ) 68.25 , e ) 67.5
Rationale: 1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 15 % , therefore bringing down the price to $ 85 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 59.5 4 ) now 59.5 has to be added byx % in order to equal the original price . 59.5 + ( x % ) 59.5 = 100 . solving this eq for x , we get x = 68.25 ans is d
Answer: d
Problem: village p ’ s population is 800 greater than village q ' s population . if village q ’ s population were reduced by 700 people , then village p ’ s population would be 7 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 910 , b ) 920 , c ) 930 , d ) 940 , e ) 950
Rationale: "p = q + 800 . p = 7 ( q - 700 ) . 7 ( q - 700 ) = q + 800 . 6 q = 5700 . q = 950 . the answer is e ."
Answer: e
Problem: half of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 56 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 17
Rationale: "there are total 56 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 28 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 56 = 35 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 28 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 56 = 28 + 35 - b + ( 28 - b - 1 ) b = 17 answer ( e )"
Answer: e
Problem: for integers x and y , if ( x + 2 ) ( y + 3 ) is even then 4 xy must be divisible by :
Options: a ) 4 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: just looking at the question , ( x + 2 ) ( y + 3 ) could be even * even , odd * even , or even * odd in order for the whole expression to be even . however , just looking at 4 xy , since x * y will always be an integer , it will always be divisible by 4 . 4 divided by 4 is 1 , hence preserving x * y . answer : a . 4
Answer: a
Problem: two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 1 to 1 . find the larger integer .
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 3 , then 3 x = y , where x is the smaller integer . if adding 10 to the smaller integer makes the ratio 1 to 1 , then x + 10 = y . substituting y = 3 x into the second equation yields x + 10 = 3 x . so , x = 5 ( smaller integer ) and , y = 3 x = 15 ( larger integer ) so e is the correct answer . another option is to test the answer choices . a ) the larger number is 6 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 2 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 2 ) , we get 12 . so , the new ratio is 12 to 6 which is the same as 2 to 1 . no good . we want a resulting ratio of 1 to 1 eliminate a b ) the larger number is 9 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 3 ) , we get 13 so , the new ratio is 13 to 9 . no good . we want a resulting ratio of 1 to 1 eliminate b c ) the larger number is 10 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3.33 ( which is not an integer ) since both numbers are integers , the larger number can not be 10 . eliminate c d ) the larger number is 12 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 4 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 4 ) , we get 14 so , the new ratio is 14 to 12 which is 7 to 6 . no good . we want a resulting ratio of 1 to 1 eliminate d e ) the larger number is 15 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 5 if 10 is added to the smaller number , the ratio becomes 1 to 1 if we add 10 to the smaller number ( 5 ) , we get 15 so , the new ratio is 15 to 15 . this is the same as the ratio of 1 to 1 therefore e is the only correct choice ."
Answer: e
Problem: how many integers are divisible by 9 between 10 ! and 10 ! + 100 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "e - 7 10 ! is divisible by 9 there are 11 numbers between 10 ! and 10 ! + 100 that are divisible by 9 . hence 10"
Answer: e
Problem: if x and y are multiples of 2 then which are all the multiples of 2 1 ) x * y 2 ) x ^ y 3 ) x + y 4 ) x - y 5 ) x / y
Options: a ) 13 , b ) 12 , 45 , c ) 1 , 25 , d ) 12 , 34 , e ) all of these
Rationale: x * y , x ^ y , x + y , x - y are even numbers answer : d
Answer: d
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 490 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 350 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 490 number of girls in the school = 5 * 490 / 7 = 350 answer is b"
Answer: b
Problem: the average height of 15 girls out of a class of 30 is 152 cm . and that of the remaining girls is 156 cm . the average height of the whole class is :
Options: a ) 150 cms , b ) 151 cms , c ) 152 cms , d ) 154 cms , e ) 156 cms
Rationale: "explanation : average height of the whole class = ( 15 × 152 + 15 × 156 / 30 ) = 154 cms answer d"
Answer: d
Problem: a cylinder of height h is 6 / 7 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 6 / 7 new cylinder 3 / 5 so 3 / 5 / 6 / 7 = 3 / 5 * 7 / 6 = 0.70 or 70 % . answer d"
Answer: d
Problem: a sum was put a simple interest at a certain rate for 1 years . had it been put at 6 % higher rate , it would have fetched rs . 30 more . the sum is :
Options: a ) s . 500 , b ) s . 600 , c ) s . 700 , d ) s . 800 , e ) s . 900
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 6 ) ã — 1 / 100 â ˆ ’ x ã — r ã — 1 / 100 = 30 â ‡ ’ x ã — 6 ã — 1 / 100 = 30 â ‡ ’ x ã — 1 / 100 = 5 â ‡ ’ x = 500 answer : option a"
Answer: a