regisss/math_qa huggingface dataset:
Problem: a bag contains 5 red , 6 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 39 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , 5 c 213 c 2 = 6 c 213 c 2 = 10 / 78 = 5 / 39 c"
Answer: c
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 61 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: b ) 2
Answer: b
Problem: the maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 50 , b ) 75 , c ) 69 , d ) 79 , e ) 82
Rationale: "number of pens = 100 number of pencils = 50 required number of students = h . c . f . of 100 and 50 = 50 answer is a"
Answer: a
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 95 students ?
Options: a ) 14 years , b ) 1.7 years , c ) 1.9 years , d ) 2.8 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 95 = 2.8 years . answer d"
Answer: d
Problem: rahul travels from a to b a distance of 200 miles in 5 hours . he returns to a in 4 hours . find his average speed ?
Options: a ) 52.2 mph , b ) 61.9 mph , c ) 44.4 mph , d ) 35.7 mph , e ) 65.6 mph
Rationale: speed from a to b = 200 / 5 = 40 mph speed from b to a = 200 / 4 = 50 mph average speed = 2 * 40 * 50 / 90 = 44.4 mph answer is c
Answer: c
Problem: if 5 x * x + 14 * x + k = 0 having two reciprocal roots find the value of k .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: product of reciprocal roots = 1 product of roots of quadratic eqn ax ^ 2 + bx + c = 0 is c / a . hence k / 5 = 1 k = 5 answer : e
Answer: e
Problem: a watch was sold at a loss of 15 % . if it was sold for rs . 400 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1600 , b ) 2998 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "85 % 120 % - - - - - - - - 25 % - - - - 400 100 % - - - - ? = > rs . 1600 answer : a"
Answer: a
Problem: meena wrote all the numbers from 1 to 49,999 inclusive . how many digits did she write in total ?
Options: a ) 154,889 , b ) 196,889 , c ) 238,889 , d ) 250,889 , e ) 264,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 49999 = > 5 * 40,000 = 200,000 the answer is 238,889 the answer is c ."
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 12 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 12 x = 12 answer : e"
Answer: e
Problem: two employees x and y are paid a total of rs . 770 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 . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 770 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 770 â ‡ ’ y [ 12 / 10 + 1 ] = 770 â ‡ ’ 22 y / 10 = 770 â ‡ ’ 22 y = 7700 â ‡ ’ y = 700 / 22 = 700 / 2 = rs . 350 d )"
Answer: d
Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 2 5 5 number of possibilities = 3 * 4 * 4 = 48 . then , just add up the number of 1 digits numbers = 4 , so total is 48 + 4 = 52 . answer : b"
Answer: b
Problem: if 3 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 6 , c ) - 3 , d ) 1 , e ) 6
Rationale: "the phrase “ 3 is one solution of the equation ” means that one value of x is 3 . thus , we first must plug 3 for x into the given equation to determine the value of k . so we have 3 ^ 2 + ( 3 ) ( 3 ) + k = 10 9 + 9 + k = 10 18 + k = 10 k = - 8 next we plug - 8 into the given equation for k and then solve for x . x ^ 2 + 3 x – 8 = 10 x ^ 2 + 3 x – 18 = 0 ( x + 6 ) ( x - 3 ) = 0 x = - 6 or x = 3 thus , - 6 is the other solution . answer b ."
Answer: b
Problem: a starts business with rs . 35,000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882
Rationale: "explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b ⇒ 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 / 7 b = 2 / 3 ⇒ b = ( 3500 × 12 × 3 ) / ( 2 × 7 ) = 500 × 6 × 3 = 9000 answer : d"
Answer: d
Problem: a person want to give his money of $ 600 to his 3 children a , b , c in the ratio 1 : 2 : 3 . what is the b + c share ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 150 , d ) $ 450 , e ) $ 500
Rationale: "b ' s share = 600 * 2 / 6 = $ 200 c ' s share = 600 * 3 / 6 = $ 300 b + c = $ 500 answer is e"
Answer: e
Problem: if the area of a square with sides of length 7 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 13 , e ) 18
Rationale: "let length of rectangle = l 7 ^ 2 = l * 4 = > l = 49 / 4 = 13 answer d"
Answer: d
Problem: a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 98 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 56
Rationale: "7 c + 6 p = 98 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 2 + 6 * 14 = 14 + 84 = 98 hence b is the answer"
Answer: b
Problem: the tax on a commodity is diminished by 30 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 70 * 115 = 8050 10000 - - - - - - - 1950 100 - - - - - - - ? = 20 % answer : a"
Answer: a
Problem: two trains 137 meters and 163 meters in length are running towards each other on parallel lines , one at the rate of 42 kmph and another at 48 kmpb . in what time will they be clear of each other from the moment they meet
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 16 sec
Rationale: explanation : relative speed of the trains = ( 42 + 48 ) kmph = 90 kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec . time taken by the trains to ‘ pass each other = time taken to cover ( 137 + 163 ) m at 25 m / sec = ( 300 / 25 ) sec = 12 sec answer : option c
Answer: c
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 17 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 17 0 = a + d - 16 a + d = 16 a = d ( as they are twin brothers ) a = d = 8 e is the answer"
Answer: e
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30 % of the original number . what percent of the red candies remain ?
Options: a ) 22.5 % , b ) 31.5 % , c ) 37.5 % , d ) 42.5 % , e ) 46.5 %
Rationale: "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.5 x red + yellow = 0.75 x red = 0.375 x , since red = yellow . the answer is c ."
Answer: c
Problem: mixture a is 10 percent alcohol , and mixture b is 40 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 20 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.6 , b ) 1.7 , c ) 1.8 , d ) 1.9 , e ) 2.0
Rationale: "( 40 - 20 ) / ( 20 - 15 ) = qa / qb 20 / 10 = qa / qb 2 / 1 = qa / qb qa = ( 2 / 5 ) * 4 = 8 / 5 = 1.6 approx answer : a"
Answer: a
Problem: rs . 100 amounts to rs . 320 in 4 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) 246 , b ) 650 , c ) 110 , d ) 240 , e ) 360
Rationale: "( 100 * 4 * 3 ) / 100 = 12 100 + 12 = 112 answer : c"
Answer: c
Problem: a family has two children . find the probability that both the children are girls given that at least one of them is a girl ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 3 / 7
Rationale: let b stand for boy and g for girl . the sample space of the experiment is s = { ( g , g ) , ( g , b ) , ( b , g ) , ( b , b ) } let e and f denote the following events : e : ‘ both the children are girls ’ f : ‘ at least one of the child is a girl ’ then e = { ( g , g ) } and f = { ( g , g ) , ( g , b ) , ( b , g ) } now e n f = { ( g , g ) } thus p ( f ) = 3 / 4 and p ( e n f ) = 1 / 4 therefore p ( e | f ) = p ( e ∩ f ) / p ( f ) = ( 1 / 4 ) / ( 3 / 4 ) = 1 / 3 b )
Answer: b
Problem: two good train each 650 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12.4 sec , b ) 24.3 sec , c ) 62.4 sec , d ) 60.1 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 650 + 650 ) m = 1300 m . required time = ( 1300 x 6 / 125 ) sec = 62.4 sec . answer c"
Answer: c
Problem: 1 , 3,5 , 7,9 , . . 50 find term of sequnce for this ?
Options: a ) 1235 , b ) 1540 , c ) 1650 , d ) 2000 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 e"
Answer: e
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 130 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 130 + p c + m = 130 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 130 / 2 = 65 . answer : b"
Answer: b
Problem: the tax on a commodity is diminished by 10 % and its consumption increased by 20 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 8 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % decrease
Rationale: "100 * 100 = 10000 90 * 120 = 10800 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % increase answer : b"
Answer: b
Problem: 4 , 12 , 48 , 240 , 1440 , ( . . . )
Options: a ) 7620 , b ) 6200 , c ) 10020 , d ) 10080 , e ) 11000
Rationale: "go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 4 x 3 = 12 ; 12 x 4 = 48 . . . . . 1440 x 7 = 10080 answer is d ."
Answer: d
Problem: a salesman gets commission on total sales at 9 % . if the sale is exceeded rs . 10000 he gets an additional commission as bonus of 3 % on the excess of sales over rs . 10000 . if he gets total commission of rs . 1380 , then the bonus he received is :
Options: a ) 22 , b ) 120 , c ) 388 , d ) 377 , e ) 272
Rationale: explanation : commission up to 10000 = \ inline 10000 \ times \ frac { 9 } { 100 } = 900 again after 10000 , commission : bonus 9 : 3 \ inline \ rightarrow 3 x : x \ therefore bonus = \ inline ( 1380 - 900 ) \ times \ frac { 1 } { 4 } = rs . 120 answer : b ) rs . 120
Answer: b
Problem: a work can be finished in 20 days by 10 women . the same work can be finished in fifteen days by 20 men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 2 : 4
Rationale: "work done by 10 women in 1 day = 1 / 20 work done by 1 woman in 1 day = 1 / ( 10 × 20 ) work done by 20 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 × 20 ) ratio of the capacity of a man and woman = 1 / ( 15 × 20 ) : 1 / ( 10 × 20 ) = 1 / 15 : 1 / 10 = 1 / 3 : 1 / 2 = 2 : 3 option c"
Answer: c
Problem: the length of a train and that of a platform are equal . if with a speed of 216 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 1752 , b ) 1799 , c ) 1719 , d ) 1750 , e ) 1800
Rationale: "speed = [ 216 * 5 / 18 ] m / sec = 60 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 60 ã ¨ x = 60 * 60 / 2 = 1800 answer : e"
Answer: e
Problem: if it takes a machine 4 ⁄ 5 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 150 , c ) 80 , d ) 120 , e ) 180
Rationale: 1 item takes 4 / 5 min so it takes 120 min to produce x 4 x / 5 = 120 the x = 150 answer : b
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 120 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 32
Rationale: "we have : l = 20 ft and lb = 120 sq . ft . so , b = 6 ft . length of fencing = ( l + 2 b ) = ( 20 + 12 ) ft = 32 ft . answer : e"
Answer: e
Problem: what is the units digit of 31 ! + 50 ! + 2 ! + 3 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 2 + 6 = 8 the units digit is 8 . the answer is e ."
Answer: e
Problem: what is the smallest positive integer x such that 520 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "given 520 - x is a perfect cube so we will take 512 = 8 * 8 * 8 520 - x = 512 x = 520 - 512 = 8 correct option is c"
Answer: c
Problem: if equation | x / 2 | + | y / 2 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 32 , c ) 100 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 4 | + | y / 4 | = 1 , so these are lines in four quadrants with x and y intercept as 14 , so it is a rhombus with diagonals of 8 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 8 * 8 = 32 . answer b .
Answer: b
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 25 cm .
Options: a ) 700 cm 2 , b ) 600 cm 2 , c ) 500 cm 2 , d ) 400 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 25 x 32 ) cm 2 = 400 cm 2 answer : option d"
Answer: d
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 22 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 22 4 ^ ( 3 k ) > 4 ^ 22 3 k > 22 k = 8 the answer is e ."
Answer: e
Problem: the number 0.8 is how much greater than 1 / 8 ?
Options: a ) ½ , b ) 27 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: let x be the difference then . 8 - 1 / 8 = x 8 / 10 - 1 / 8 = x x = 27 / 40 ans b
Answer: b
Problem: if the radius of a circle is decreased by 50 % , find the percentage decrease
Options: a ) 22 , b ) 099 , c ) 75 , d ) 26 , e ) 18
Rationale: "let original radius = r . new radius = = original area = and new area = decrease in area = = 75 % answer : c"
Answer: c
Problem: guadalupe owns 2 rectangular tracts of land . one is 300 m by 500 m and the other is 250 m by 630 m . the combined area of these 2 tracts is how many square meters ?
Options: a ) 3,360
b ) 307,500
c ) 621,500
d ) 704,000
e ) 2 , 816,000
Rationale: one is 300 m by 500 m and the other is 250 m by 630 m : ( 300 * 500 ) + ( 250 * 630 ) = 150000 + 157500 307500 answer : b
Answer: b
Problem: the difference between the place values of 9 and 4 in the number 927435 is
Options: a ) 899600 , b ) 856200 , c ) 875200 , d ) 896200 , e ) none
Rationale: sol . = ( place value of 9 ) – ( place value of 4 ) = ( 900000 - 400 ) = 899600 answer a
Answer: a
Problem: a certain hobby shop sold model cars for $ 5.00 each and model trains for $ 8.00 each . if a customer purchased both cars and trains from the store for a total of $ 31.00 , what total number of cars and trains did the customer purchase ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: we can take numbers , as price of car 5 , 8 for train and 31 total for ease . now we can determine quickly that total number should range between 31 / 8 < = n < = 31 / 5 , so ans should be between 3 and 7 . now solving the expression 5 a + 8 b = 31 decreasing 31 in multiple of 5 and checking divisibility of that number by 8 . this way we get 3 cars , 2 trains we get $ 31.00 total 3 * 5 + 2 * 8 = 31 hence total number is 3 + 2 = 5 ans c
Answer: c
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 180,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 6 a * 1 + a * 5 ) / 6 = 11 a / 6 = 55000 answer is c . $ 55,000"
Answer: c
Problem: john and david work at a hospital with 10 other workers . for an internal review , 2 of the 10 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 45 , b ) 1 / 35 , c ) 1 / 25 , d ) 1 / 15 , e ) 1 / 10
Rationale: "probability that john and david will both be chosen out of 8 workers = ( 2 / 10 ) * ( 1 / 9 ) = 1 / 45 answer a"
Answer: a
Problem: in a two - digit , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) none
Rationale: let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 . sum of digits = x + ( x + 2 ) = 2 x + 2 . ( 11 x + 2 ) ( 2 x + 2 ) = 144 22 x 2 + 26 x - 140 = 0 11 x 2 + 13 x - 70 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 . hence , required number = 11 x + 2 = 24 . option a
Answer: a
Problem: mrs . evans gave a test to her freshmen economics class , which has 30 students enrolled and 25 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 28 , c ) 26 , d ) 22 , e ) 19
Rationale: total number of enrolled students = 30 number of students who did not take test = 5 hence , number of students who took test = 30 - 5 = 25 number of students who answered q 2 correctly = 22 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : d
Answer: d
Problem: what is the smallest number which when diminished by 12 , is divisible 8 , 12 , 22 and 24 ?
Options: a ) 276 , b ) 295 , c ) 230 , d ) 225 , e ) 245
Rationale: "required number = ( lcm of 8 , 12 , 22 and 24 ) + 12 = 264 + 12 = 276 answer : option a"
Answer: a
Problem: k is a 3 digit number such that the the ratio of the number to the sum of its digits is least . what is the difference between the hundreds and tens digit ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: explanation : this is only possible only when the hundreds digit has the least value and tens and units has the highest value . so we could get the highest possible sum but possible lowest number . so by this logic this number could only be 199 . so the difference is 8 . note : remember a number given as abc i . e abc = ax 100 + bx 10 + c . so 123 = 1 x 100 + 2 x 10 + 3 . answer : b
Answer: b
Problem: ♠ n denotes the number obtained when n is rounded to the nearest tenth . for example ♠ 4.31 = 4.3 ♠ 2.423 - ♠ 3.421 =
Options: a ) 1.05 , b ) 1.04 , c ) - 0.8 , d ) - 1.0 , e ) - 0.1
Rationale: ♠ 2.423 - ♠ 3.421 2.4 - 3.2 = - 0.8 answer : c
Answer: c
Problem: if 1 tic equals 5 tacs and 2 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 20 / 1 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "tic = 5 * tac and 2 * tac = 8 * toc ; 2 * tic = 10 * tac and 10 * tac = 40 * toc - - > 2 * tic = 40 * toc - - > tic / toc = 40 / 2 = 20 / 1 . answer : b ."
Answer: b
Problem: one hour after yolanda started walking from x to y , a distance of 65 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 7 miles per hour , how many miles had bob walked when they met ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 65 miles , so 7 t + 5 ( t + 1 ) = 65 , which may be solved for t as follows 7 t + 5 ( t + 1 ) = 65 7 t + 5 t + 5 = 65 12 t = 60 t = 5 ( hours ) therefore , bob had walked 7 t = 7 ( 5 ) = 35 miles when they met . the best answer is e ."
Answer: e
Problem: if 30 % of 100 is greater than 50 % of a number by 10 , then the number is ?
Options: a ) 40 , b ) 30 , c ) 60 , d ) 80 , e ) 50
Rationale: "let the number be x 30 % of 100 - 50 % of x = 10 50 / 100 x = ( 30 / 100 * 100 ) - 10 x / 2 = 20 x = 40 answer is a"
Answer: a
Problem: there were 35 students in a hostel . due to the admission of 7 new students , he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 125 , b ) 321 , c ) 561 , d ) 852 , e ) 420
Rationale: "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 ; 7 x = 84 ; x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . ans : e"
Answer: e
Problem: at a speed of 40 miles per hour , a certain car uses 1 gallon of gasoline every 40 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 5 / 12 , c ) 7 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 40 miles / hour ) * ( 1 gallon / 40 miles ) = 5 gallons portion used = ( 5 ) / 12 = 5 / 12 ans b"
Answer: b
Problem: niharika covers a distance in 30 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 30 % .
Options: a ) 84.71 kmph . , b ) 85.74 kmph . , c ) 83.71 kmph . , d ) 85.71 kmph . , e ) 84.71 kmph .
Rationale: given speed = 60 kmph . it means niharika covered 60 km in 60 min ( 1 hour ) . so , in 30 min he will cover 30 km . 30 % time reduced = 30 - 30 % of 30 = 21 min . thus , niharika needs to cover 30 km in 21 min ( 0.35 hour ) . speed * time = distance . speed * 0.35 = 30 speed = 85.71 kmph . answer : option d
Answer: d
Problem: rahul ' s housing colony have one tap , working alone at its maximum constant rate , can fill a certain tank in 230 seconds . a second tap , working alone at its maximum constant rate , can fill the same tank in 234 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the tank is closest to
Options: a ) 116 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 230 secs tap 2 : 234 secs considering the average of these 2 taps : 232 secs . so 1 tap can fill the tank in 232 secs , so 2 taps can fill the tank in 232 / 2 = 116 secs . closest answer is a .
Answer: a
Problem: a certain junior class has 1,000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 10,000 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 600 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 600 * 1000 ) = 1 / 10,000 b"
Answer: b
Problem: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 2 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) none of the above , e ) 5
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 2 , which yields remainder of 0 upon division by 2 . answer : d"
Answer: d
Problem: a can do a work in 20 days , b in 30 days . a alone start the work after 10 days he left work . in how many days b can finish the work ?
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 10 days , e ) 15 days
Rationale: "10 days work of a = 10 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 b can finish 1 / 2 work = 30 * 1 / 2 = 15 days answer is e"
Answer: e
Problem: there are 24 students in chad â € ™ s class . he brought 27 cookies to pass out for his birthday . how many cookies will each student get ? will there be any cookies left over ?
Options: a ) 1 - 9 , b ) 1 - 7 , c ) 2 - 8 , d ) 1 - 3 , e ) 3 - 10
Rationale: 27 / 24 = 1 r 3 chad will give each student 1 cookie and there will be 3 cookies left over correct answer d
Answer: d
Problem: a shopkeeper sells 450 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 45 , e ) 21
Rationale: sp per metre = 18000 / 450 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
Answer: d
Problem: a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 55 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 37 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a"
Answer: a
Problem: a man goes from a to b at a speed of 35 kmph and comes back to a at a speed of 28 kmph . find his average speed for the entire journey ?
Options: a ) 38.9 kmph , b ) 38.8 kmph , c ) 38.1 kmph , d ) 37.1 kmph , e ) 37.8 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 35 ) + ( d / 28 ] = ( 2 d ) / [ 11 d / 140 ) = > 38.1 kmph . answer : c"
Answer: c
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 23.56 , b ) 33.0 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 20 ) = 84 cm parameter of the square = 84 cm i . e . 4 a = 84 a = 21 diameter of the semicircle = 21 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) 21 = 1 / 2 ( 22 / 7 ) ( 21 ) = 66 / 2 = 33 cm answer : b"
Answer: b
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 5 of the mice are brown . if there are 12 white mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 18 , e ) 16
Rationale: "let total number of mice = m number of brown mice = 2 / 5 m number of white mice = 3 / 5 m = 12 = > m = 20 answer a"
Answer: a
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length and width of this rectangle .
Options: a ) w = 15 and l = 20
b ) w = 25 and l = 30
c ) w = 35 and l = 40
d ) w = 45 and l = 50
e ) w = 55 and l = 60
Rationale: l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer a
Answer: a
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.6 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 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.6 ( x ) + 0.5 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.5 x = 0.25 / 0.1 x = 1 / 4 therefore the answer is a : 1 / 4 ."
Answer: a
Problem: the total number of digits used in numbering the pages of a book having 346 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 930 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 247 ) = ( 9 + 180 + 741 ) = 930 . answer : d"
Answer: d
Problem: a light has a rating of 110 watts , it is replaced with a new light that has 30 % higher wattage . how many watts does the new light have ?
Options: a ) 143 , b ) 145 , c ) 156 , d ) 134 , e ) 100
Rationale: "final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a"
Answer: a
Problem: a train 150 m long crosses a platform 100 m long in 10 sec ; find the speed of the train ?
Options: a ) 100 , b ) 70 , c ) 95 , d ) 90 , e ) 85
Rationale: "d = 150 + 100 = 250 t = 10 s = 250 / 10 * 18 / 5 = 90 kmph . answer : d"
Answer: d
Problem: calculate the time it will take for a train that is 240 meter long to pass a bridge of 130 meter length , if the speed of the train is 50 km / hour ?
Options: a ) 21.64 seconds , b ) 22.64 seconds , c ) 23.64 seconds , d ) 26.64 seconds , e ) 35.64 seconds
Rationale: "speed = 35 km / hr = 50 * ( 5 / 18 ) m / sec = 13.89 m / sec total distance = 240 + 130 = 370 meter time = distance / speed = 370 * ( 1 / 13.89 ) = 26.64 seconds answer : d"
Answer: d
Problem: there are 200 doctors and nurses at a hospital . if the ratio of doctors to nurses is 4 to 6 , how many nurses are at the hospital ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "the number of nurses at the hospital is ( 6 / 10 ) * 200 = 120 . the answer is b ."
Answer: b
Problem: milk contains 5 % water . what content of pure milk should be added to 10 liters of milk to reduce this to 2 % ?
Options: a ) 10 liters , b ) 15 liters , c ) 20 liters , d ) 18 liters , e ) 22 liters
Rationale: "quantity of water in 10 liters = 5 % of 10 liters = 0.5 liters let x liters of pure milk be added . then , 0.5 / ( 10 + x ) = 2 / 100 2 x = 30 x = 15 liters answer is b"
Answer: b
Problem: the current in a river is 4 mph . a boat can travel 18 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 85.5 miles , c ) 96 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 18 - 4 = 14 mph downstream speed = 18 + 4 = 22 mph d / 14 + d / 22 = 10 hours solving for d we get d = 85.5 answer : b"
Answer: b
Problem: a batsman scored 90 runs which included 2 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 57 % , d ) 60 % , e ) 80 %
Rationale: "explanation : number of runs made by running = 90 - ( 2 x 4 + 5 x 6 ) = 90 - ( 38 = 52 now , we need to calculate 38 is what percent of 90 . = > 52 / 90 * 100 = 57 % option c"
Answer: c
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 2835 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "2835 = 3 * 3 * 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 ( that is : 3 , 6 , and 9 = 3 * 3 ) . the answer is c ."
Answer: c
Problem: in a class of 120 students , 25 did not opt for math . 10 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 63 , b ) 95 , c ) 77 , d ) 87 , e ) 48
Rationale: "120 students total 25 did not opt for math 10 did not opt for science 2 did not opt for either total of 95 students in math and 8 did not opt for sci but did for math 95 - 8 = 87 87 students of the class opted for both math and science answer : d . 87"
Answer: d
Problem: the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e"
Answer: e
Problem: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 4.25 = ( 20 * ( $ 4.25 ) ) / 100 - - > ( $ 85 ) / 100 - - > $ 0.85 therefore , chef wages per hour = $ 4.25 + $ 0.85 = = > $ 5.10 difference of wages between manager and chef = $ 8.50 - $ 5.10 = = > $ 3.40 answer : c"
Answer: c
Problem: 101 ã — 101 + 99 ã — 99 = ?
Options: a ) 10002 , b ) 20004 , c ) 20002 , d ) 20102 , e ) 20202
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1012 + 992 = ( 100 + 1 ) 2 + ( 100 â ˆ ’ 1 ) 2 = 2 ( 1002 + 12 ) = 2 ( 10000 + 1 ) = 20002 . answer : option c"
Answer: c
Problem: in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a female or younger than 70 years old ?
Options: a ) 231 / 260 , b ) 117 / 130 , c ) 51 / 65 , d ) 23 / 32 , e ) 11 / 16
Rationale: "the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 the number of people who are either female or younger than 70 is 1800 + 510 = 2310 . p ( a person is younger than 70 or male ) = 2310 / 2600 = 231 / 260 the answer is a ."
Answer: a
Problem: jaclyn buys $ 40 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 950 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 40000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 950 answer : a"
Answer: a
Problem: 60 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 / 7 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "60 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 60 ) * 100 = 60 square feet answer : option d"
Answer: d
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 500 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 500 bc , b ) 500 b / c , c ) 1000 bc , d ) 1000 b / c , e ) 1000 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 500 clips / box = 1000 bc paper clips the answer is c ."
Answer: c
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 8 hours of the journey .
Options: a ) 296 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 8 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 = sum of 8 terms in ap whose first term is 30 and last term is 44 = 8 / 2 [ 30 + 44 ] = 296 km . answer : a"
Answer: a
Problem: a , b and c start a business with each investing rs 20000 . after 5 months a withdraws rs 5000 , b withdraws rs 4000 and c invests rs 6000 more . at the end of the year , a total profit of rs 69900 was recorded . find the share of a .
Options: a ) 20000 , b ) 21500 , c ) 20500 , d ) 22000 , e ) 21000
Rationale: a : b : c = ( 20000 × 5 + 15000 × 7 ) : ( 20000 × 5 + 16000 × 7 ) : ( 20000 × 5 + 26000 × 7 ) = ( 20 × 5 + 15 × 7 ) : ( 20 × 5 + 16 × 7 ) : ( 20 × 5 + 26 × 7 ) = 205 : 212 : 282 a ' s share = 69900 × 205 / ( 205 + 212 + 282 ) = 69900 × 205 / 699 = 20500 answer is c .
Answer: c
Problem: the c . p of 15 books is equal to the s . p of 20 books . find his gain % or loss % ?
Options: a ) 25 % loss , b ) 16 2 / 8 % loss , c ) 16 3 / 3 % loss , d ) 36 2 / 3 % loss , e ) 56 2 / 3 % loss
Rationale: "15 cp = 20 sp 20 - - - 5 cp loss 100 - - - ? = > 25 % loss answer : a"
Answer: a
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6647 , how much amount did raghu invest ?
Options: a ) 2300 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6647 = x = 6647 / 2.89 = 2300 therefore , amount invested by raghu is rs . 2300 . answer : a"
Answer: a
Problem: sonika bought a v . c . r . at the list price of 18,800 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,304 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,800 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,800 = 8 ⁄ 100 × 18800 = 1504 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,800 + 1504 = 20,304 . answer a"
Answer: a
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 42 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 48 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.42 m = = > revenue = price x quantity = 0.48 ( m + w ) = = > profit = 0.48 ( m + w ) - 0.42 m = 0.2 * ( 0.42 m ) [ 20 % of cost ] = = > 0.48 m + 0.48 w - 0.42 m = 0.084 m = = > 0.024 m = 0.48 w = = > m / w = 0.48 / 0.024 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Problem: 4524 - ? = 2456
Options: a ) 2058 , b ) 2069 , c ) 2072 , d ) 2089 , e ) none of these
Rationale: "explanation : none of these answer : option e"
Answer: e
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 600 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 300 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 600 pounds . we sum the two variables to obtain : f + s = 600 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 600 3 f = 900 f = 300 answer is c"
Answer: c
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm .
Options: a ) 335 cm 2 , b ) 228 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 725 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : b"
Answer: b
Problem: in measuring the sides of a rectangle , one side is taken 8 % in excess , and the other 7 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.44 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c ."
Answer: c
Problem: what is the 9 th digit to the right of the decimal point in the decimal equivalent of 48 / 11 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 2
Rationale: "48 / 11 = 4.3636 . . . . 36 is non - terminating repeating decimal . the 9 th digit to the right of decimal point will be 3 . answer a"
Answer: a
Problem: a is two years older than b who is twice as old as c . the total of the ages of a , b and c is 27 . how old is b ?
Options: a ) 25 , b ) 20 , c ) 15 , d ) 10 , e ) 5
Rationale: "let age of c = x . then , age of b = 2 x age of a = 2 + 2 x total age of a , b and c = 27 ⇒ ( 2 + 2 x ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 255 = 5 b ' s age = 2 x = 2 × 5 = 10 answer is d ."
Answer: d
Problem: find the value of x : x ² + 6 x + 9 .
Options: a ) 9 , b ) - 1 , c ) - 3 , d ) 3 , e ) - 9
Rationale: that quadratic is factored as follows : x ² + 6 x + 9 = ( x + 3 ) ( x + 3 ) . lesson 17 . now , it is easy to see that that both factors will be 0 when x = - 3 . the solution is : x = - 3 c
Answer: c
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 6 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 120 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 6 ) * 360 = 60 gallons . remaning paint = 300 gallons paint used in the second week = ( 1 / 5 ) * 300 = 60 gallons total paint used = 120 gallons . option b"
Answer: b
Problem: the e train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the e train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says e it took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Problem: dana borrows 5000 pounds annually for her college education . if dana gives her parents 4 % of that amount back each month , how much will she still owe her parents after 4 years of college ?
Options: a ) 9800 , b ) 10000 , c ) 10200 , d ) 10400 , e ) 10600
Rationale: dana borrows 5000 and returns 4 % per month . so returns 200 per month . and 2400 per year . so dana owes 5000 - 2400 = 2600 per year . after 4 years she will owe 10400 . ans ( c )
Answer: c
Problem: a student scored an average of 75 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 95 , e ) 26
Rationale: "given m + p + c = 75 * 3 = 225 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 225 = 95 answer : d"
Answer: d
Problem: a positive number x is multiplied by 8 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 8 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "sq rt ( 8 x / 3 ) = x = > 8 x / 3 = x ^ 2 = > x = 8 / 3 ans - c"
Answer: c
Problem: a and b working together could mow a field in 28 days and with the help of c they could have mowed it in 21 days . how long would c take by himself ?
Options: a ) 68 days , b ) 84 days , c ) 90 days , d ) 72 days , e ) 50 days
Rationale: required answer = 28 * 21 / 28 - 21 = 84 days answer is b
Answer: b
Problem: two employees x and y are paid a total of rs . 590 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 . 268 , b ) s . 288 , c ) s . 298 , d ) s . 300 , e ) s . 388
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 590 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 590 ⇒ y [ 12 / 10 + 1 ] = 590 ⇒ 22 y / 10 = 590 ⇒ 22 y = 5900 ⇒ y = 5900 / 22 = 500 / 2 = rs . 268 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 . 36000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 36000 = 20000 a"
Answer: a
Problem: if 10 % of x = 20 % of y , then x : y is equal to ?
Options: a ) 2 : 6 , b ) 2 : 1 , c ) 7 : 1 , d ) 2 : 8 , e ) 2 : 2
Rationale: 10 % of x = 20 % of y 10 x / 100 = 20 y / 100 = > x / 10 = y / 5 x / y = 10 / 5 = 2 / 1 x : y = 2 : 1 . answer : b
Answer: b