Cheukting/mathqa huggingface dataset:
Question (physics): a train running at the speed of 30 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 75 m , b ) 180 m , c ) 324 m , d ) can not be determined , e ) none of these
Rationale: "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a"
Answer: a
Question (probability): three unbiased coins are tossed , what is the probability of ge ƫ ng at least 2 tails ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : total cases are = 2 * 2 * 2 = 8 , which are as follows [ ttt , hhh , tth , tht , htt , thh , hth , hht ] favoured cases are = [ tth , tht , htt , ttt ] = 4 so required probability = 4 / 8 = 1 / 2 answer : c"
Answer: c
Question (general): in the next cricket world cup t - 20 , team t has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team t score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team t can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 5 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 5 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 5 = 4 / 5 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 4 / 5 = 4 / 10 = 2 / 5 - - - > p ( of burning out in a six mnth period ) = 1 - 2 / 5 = 3 / 5 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 4 / 5 * 3 / 5 = 1 / 2 ans c"
Answer: c
Question (geometry): the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 4 , b ) 5.656 , c ) 5 , d ) 6 , e ) 7
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b"
Answer: b
Question (general): when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 18 = 26 - x or , 4 x = 44 or , x = 11 . c answer ."
Answer: c
Question (other): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (probability): 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
Question (general): 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
Question (other): 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
Question (other): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (geometry): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (physics): 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
Question (general): 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