regisss/math_qa huggingface dataset:
Problem: at a supermarket , john spent 1 / 5 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 11 on candy , how much did john spend at the supermarket ?
Options: a ) $ 20 , b ) $ 30 , c ) $ 50 , d ) $ 90 , e ) $ 110
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 5 of his money on fresh fruits and vegetables , or ( 1 / 5 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 11 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 5 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 11 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 6 t + 10 t + 3 t + 330 = 30 t 19 t + 330 = 30 t 330 = 11 t t = 30 john spent $ 90 at the supermarket . answer : b"
Answer: b
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 12 days . c alone will finish the job in
Options: a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 12 = ( 15 * x ) / ( 15 + x ) 180 + 12 x = 15 x 3 x = 180 x = 60 answer : option c"
Answer: c
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 250 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 250 2.5 h = 250 h = 100 . c is the answer ."
Answer: c
Problem: a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 44 + 17 = 61 now 61 divided by 8 so we get 5 as reaminder answer : a"
Answer: a
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 96 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 42
Rationale: "7 c + 6 p = 96 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 * 6 + 6 * 9 = 42 + 54 = 96 hence e is the answer"
Answer: e
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.30 = 12 republicans are expected to vote for candidate a . thus total of 45 + 12 = 57 registered voters are expected to vote for candidate a , which is 57 % of the total number of registered voters . answer : e ."
Answer: e
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960
Rationale: "the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a ."
Answer: a
Problem: a reduction of 10 % in the price of salt enables a lady to obtain 20 kgs more for rs . 400 , find the original price per kg ?
Options: a ) 2.0 , b ) 2.8 , c ) 2.2 , d ) 2.5 , e ) 3.0
Rationale: "answer : 400 * ( 10 / 100 ) = 40 - - - 20 ? - - - 1 = > rs . 2 400 - - - 360 ? - - - 2 = > rs . 2.22 . answer : c"
Answer: c
Problem: in the rectangular coordinate system point o has coordinates ( 0,0 ) and point b has coordinates ( 5,5 ) and if point a is equidistant from points o and b and the area of the triangle oab is 16 , which of the following are the possible coordinates of point a .
Options: a ) ( - 2,6 )
b ) ( 0,4 )
c ) ( 2 , - 6 )
d ) ( 2,6 )
e ) ( 4,0 )
Rationale: area . pngsince a is equidistant from points o and b , then it must be somewhere on the green line ( perpendicular bisector of ob ) . ( 2 , - 6 ) and ( 2,6 ) are not on that line . if a is at ( 0,5 ) or ( 5,0 ) , then the area is 1 / 2 * 5 * 5 = 25 / 2 . thus a must be at ( 2,6 ) . answer : d .
Answer: d
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b"
Answer: b
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 300 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 300 = 3 ^ 600 * 2 ^ 600 the answer is d ."
Answer: d
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 144 = 432 sq inches . hence , the difference is 16 square inches more ( 432 - 416 ) . the correct answer is c"
Answer: c
Problem: 30 men can do a work in 40 days . when should 16 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 14 days , c ) 55 days , d ) 44 days , e ) 22 days
Rationale: "total work to be done = 30 * 40 = 1200 let 16 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 16 * 40 ) = 1200 40 p = 560 = > p = 14 days answer : b"
Answer: b
Problem: what is the normal price of an article sold at $ 126 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 155 , b ) $ 165 , c ) $ 175 , d ) $ 185 , e ) $ 195
Rationale: "0.8 * 0.9 * cost price = $ 126 cost price = $ 175 the answer is c ."
Answer: c
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 40 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 33 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Problem: there are 280 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 600 , b ) 650 , c ) 700 , d ) 750 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 280 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 280 = 2 / 5 t , or 2 / 5 ( t - m ) = 280 , from here we get that t - m = 700 , that would be total number of female employees and the answer ( c )
Answer: c
Problem: the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of p is :
Options: a ) 3050 , b ) 3000 , c ) 4000 , d ) 4050 , e ) 3100
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 3000 . p ' s monthly income = rs . 3000 . answer : b"
Answer: b
Problem: running at the same constant rate , 16 identical machines can produce a total of 32 shirt per minute . at this rate , how many shirt could 8 such machines produce in 10 minutes ?
Options: a ) 911 , b ) 100 , c ) 101 , d ) 160 , e ) 785
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 32 / 16 = 2 shirt per minute per machine . 8 machines = 16 per minute . 10 minutes worth = 160 shirt . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d ."
Answer: d
Problem: a certain cube floating in a bucket of water has between 70 and 85 percent of its volume below the surface of the water . if between 8 and 20 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 70 % = 240.1 , 85 % = 291.55 so vol above water , between 102.9 and 51.45 - - > too big if side are 4 , vol = 64 70 % = 44.8 , 85 % = 54.4 vol above water between 19.2 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 70 % = 87.5 , . 85 % = 106.25 vol above water between 18.75 - 37.5 ( sides are 4 cubic centimeters ) a"
Answer: a
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 14 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 77 / 2 , b ) 1 / 7 , c ) 78 / 85 , d ) 1 / 5 , e ) 47 / 85
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 14 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 14 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 14 * 2 b * b 3 b - 2 b ^ 2 = 28 b ^ 2 3 b = 30 b ^ 2 b = 3 / 30 = 1 / 10 so , a = 2 b = 1 / 5 the correct answer is d ."
Answer: d
Problem: three numbers are in the ratio of 3 : 4 : 6 and their product is 1944 . the largest of these numbers is
Options: a ) 6 , b ) 12 , c ) 18 , d ) 26 , e ) 28
Rationale: "solution let the numbers be 3 x , 4 x and 6 x . then , 3 x × 4 x × 6 x = 1944 ‹ = › 72 x 3 = 1944 ‹ = › x 3 = 27 ‹ = › x = 3 therefore , largest number = 6 x = 18 . answer c"
Answer: c
Problem: two stations p and q are 200 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 noon , c ) 10.30 am , d ) 12.30 am , e ) 11 am
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 200 = > 20 x + 25 ( x - 1 ) = 200 = > 45 x = 225 = > x = 5 means , they meet after 5 hours after 7 am , ie , they meet at 12 noon answer is b ."
Answer: b
Problem: walking at 1 / 3 th of its usual speed a cab is 20 mnts late . find its usual time to cover the journey ?
Options: a ) 10 m , b ) 15 m , c ) 20 m , d ) 25 m , e ) 12 m
Rationale: "new speed = 1 / 3 th of usual speed new time = 3 of usual time 3 ut - ut = 20 m 2 ut = 20 m ut = 10 m answer is a"
Answer: a
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 17 days more ?
Options: a ) 89 men , b ) 120 men , c ) 90 men , d ) 60 men , e ) 134 men
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 17 x * 17 = 760 * 20 x = 894 760 - - - - - - - 134 answer : e"
Answer: e
Problem: find large number from below question the difference of two numbers is 1015 . on dividing the larger number by the smaller , we get 9 as quotient and the 15 as remainder
Options: a ) 1209 , b ) 1324 , c ) 1245 , d ) 1140 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1015 ) . x + 1015 = 9 x + 15 8 x = 1000 x = 125 large number = 125 + 1015 = 1140 answer : d"
Answer: d
Problem: a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,205 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.35 * 4500 = 6075 cost of type b products next year = 1.1 * 8300 = 9130 total 6075 + 9130 = 15205 option b"
Answer: b
Problem: in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ?
Options: a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10
Rationale: a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8
Answer: a
Problem: mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?
Options: a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000
Rationale: x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c
Answer: c
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 176 in 4 years ?
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 9 % , e ) 5.5 %
Rationale: "176 = ( 180 * 4 * r ) / 100 r = 5.5 % answer : e"
Answer: e
Problem: a 6 litre sol is 35 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 1.8 , e ) e . 5.4
Rationale: "35 % of 6 = 2.1 50 % of 6 = 3 shortage is 0.9 so we need to have 0.9 / 50 % to get 50 % alcohol content . = 1.8 d"
Answer: d
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ?
Options: a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a
Answer: a
Problem: if 6 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 420 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 6 c 2 for vertical 8 c 2 total parallelogram is 6 c 2 * 8 c 2 = 15 * 28 = 420 answer : c"
Answer: c
Problem: what is the remainder if 7 ^ 8 is divided by 100 ?
Options: a ) 7 , b ) 1 , c ) 9 , d ) 10 , e ) 11
Rationale: "7 ^ 8 can be written as ( 7 ^ 4 ) ^ 2 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 2 by 100 , the reminder is 1 ^ 2 = 1 answer : b"
Answer: b
Problem: 65 % of x = 20 % of 617.50 . find the value of x ?
Options: a ) 100 , b ) 190 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 615.50 then , 65 / 100 * x = 20 / 100 * 6175 / 10 x = 190 answer is b"
Answer: b
Problem: find the smallest number of five digits exactly divisible by 24 , 48,64 and 88 .
Options: a ) 11952 , b ) 11852 , c ) 11752 , d ) 11652 , e ) 11552
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 24,48 , 64,88 i . e 2012 , on dividing 10000 by 2012 , we get 60 as remainder . therefore , required number = 10000 + ( 2012 â € “ 60 ) = 11952 . answer is a ."
Answer: a
Problem: how many numbers from 12 to 82 are exactly divisible by 6 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' d ' 12 / 6 = 2 and 82 / 6 = 13 = = > 13 - 2 = 11 numbers"
Answer: d
Problem: 10 men and 15 women finish a work in 6 days . one man alone finishes that work in 100 days . in how many days will a woman finish the work ?
Options: a ) 125 days , b ) 150 days , c ) 90 days , d ) 225 days , e ) none of these
Rationale: 15 women ' s work of a day = 1 ⁄ 6 - 1 ⁄ 10 ⇒ 1 ⁄ 15 part ∴ for 1 whole part a woman will take = 15 × 15 = 225 days . answer d
Answer: d
Problem: a certain quantity is measured on two different scales , the r - scale and the s - scale , that are related linearly . measurements on the r - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the r - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: question says they are both related linearly so they the relationships can be represented by standard linear definition y = mx + b . let s scale = y . and r scale = x . 30 = 6 m + b eqn 1 60 = 24 m + b eqn 2 eqn 2 - eqn 1 = > 30 = 18 m = > m = 5 / 3 solving for b using either equation gives us b = 20 linear relationship is represented by y = ( 5 / 3 ) x + 20 solve for 100 : 100 = 5 / 3 x + 20 80 = 5 / 3 x x = 48 ans = c
Answer: c
Problem: a fruit seller had some apples . he sells 30 % and still has 420 apples . originally , he had ?
Options: a ) 30 apples , b ) 600 apples , c ) 420 apples , d ) 70 apples , e ) none
Rationale: "answer â ˆ µ 70 % of n = 420 â ˆ ´ n = ( 420 x 100 ) / 70 = 600 correct option : b"
Answer: b
Problem: a family x went for a vacation . unfortunately it rained for 13 days when they were there . but whenever it rained in the mornings , they had clear afternoons and vice versa . in all they enjoyed 11 mornings and 12 afternoons . how many days did they stay there totally ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 13 , e ) 14
Rationale: explanation : clearly 11 mornings and 12 afternoons = 23 half days = > since 13 days raining means 13 half days . = > so 23 - 13 = 10 halfdays ( not effecetd by rain ) = > so 10 halfdays = 5 fulldays hence , total no . of days = 13 + 5 = 18 days answer : b
Answer: b
Problem: what is 92 % of 4 / 5 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.736 , d ) 0.6859 , e ) 0.69
Rationale: "92 % * ( 4 / 5 ) = 0.92 * 0.8 = 0.736 answer : c"
Answer: c
Problem: a textile manufacturing firm employees 125 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 125 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 2800 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 124 / 125 ) â ˆ ’ 150000 ã — ( 124 / 125 ) â ˆ ’ 75000 . = > rs 2 , 72,200 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 72,200 = > rs . 2,800 . answer : d"
Answer: d
Problem: a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b"
Answer: b
Problem: a thief is spotted by a policeman from a distance of 100 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 500 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 100 m / 1000 ) x 1 / 2 hr = 1 / 20 hr . in 1 / 20 hrs , the thief covers a distance of 8 x 1 / 20 km = 2 / 5 km = 400 m answer is c ."
Answer: c
Problem: a major airplane manufacturer announced the sale of 150 small airliners at $ 125 million each , 75 medium sized airliners at $ 175 million each , and 60 large airliners at $ 220 million each . what percentage of the company ' s income came from large and medium airliners ?
Options: a ) 29 % , b ) 41 % , c ) 58 % , d ) 69 % , e ) 70 %
Rationale: answer is ( money from mid and large plane ) / ( total money from all the planes ) x 100 = ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 = 58.4 % you could just multiply add divide to get answer . however sometimes its much better to make it easy we should see if we have any common terms 125 * 150 = ( 5 * 5 * 5 ) * ( 2 * 3 * 5 * 5 ) 175 * 75 = ( 5 * 5 * 7 ) * ( 3 * 5 * 5 ) 220 * 60 = ( 2 * 2 * 11 * 5 ) * ( 2 * 2 * 3 * 5 ) 3 * 5 * 5 is common cancel it ans becomes ( 175 + 176 ) / ( 176 + 175 + 250 ) * 100 = ~ = ~ 350 / 600 * 100 = ~ = ~ 7 / 12 * 100 = 60 % > > > 58 % is closest . answer : c
Answer: c
Problem: if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a"
Answer: a
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 4 ?
Options: a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a"
Answer: a
Problem: ( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ?
Options: a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7
Rationale: ( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b
Answer: b
Problem: 85 % of the population of a city is 85000 . the total population of the city is ?
Options: a ) 95000 , b ) 97500 , c ) 100000 , d ) 105000 , e ) 102500
Rationale: "x * ( 85 / 100 ) = 85000 x = 1000 * 100 x = 100000 answer : c"
Answer: c
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25
Rationale: it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 = 25 e
Answer: e
Problem: what is the perimeter of a square with area 9 p ^ 2 / 64 ?
Options: a ) 3 p / 2
b ) 3 p ^ 2 / 4
c ) 3 p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a .
Answer: a
Problem: 14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4
Rationale: x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 â € “ 4 xy ( x - y ) 2 = 625 â € “ 576 = > ( x â € “ y ) = 7 answer : a
Answer: a
Problem: ( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x
Options: a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521
Rationale: "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c"
Answer: c
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2500 , what will be the difference between q and r ' s share ?
Options: a ) 2225 , b ) 2325 , c ) 2425 , d ) 2625 , e ) 2525
Rationale: "4 - - - 2100 5 - - - ? = > 2625 answer : d"
Answer: d
Problem: a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a"
Answer: a
Problem: if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 + x - 20 = 0 , then x =
Options: a ) 1 , b ) - 4 , c ) 4 , d ) - 5 , e ) 5
Rationale: x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 + x - 20 = ( x - 4 ) ( x + 5 ) = 0 then x = 4 or x = - 5 . thus x = - 5 . the answer is d .
Answer: d
Problem: the rate at which a sum becomes 4 times of itself in 15 years at s . i . , will be :
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) none
Rationale: sol . let sum = x . then , s . i . = 3 x ∴ rate = [ 100 * s . i . / p * t ] = [ 100 * 3 x / x * 15 ] % = 20 % . answer c
Answer: c
Problem: 20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 330 , d ) 390 , e ) 445
Rationale: "there are 20 business exec and in each handshake 2 business execs are involved . hence 20 c 2 = 190 also , each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake . total = 190 + 140 = 330 ans : c"
Answer: c
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 9 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 11 / 20 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: x * 6 / 100 * 1 + ( 20000 - x ) * 9 / 100 * 1 = 1440 6 x - 8 x = 144000 - 180000 = > - 2 x = - 18000 = > x = 9000 so 11000 / 20000 = 11 / 20 answer - a
Answer: a
Problem: in a school of 850 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 163 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 850 * 18 / 100 = 153 answer : c"
Answer: c
Problem: 109 × 109 + 91 × 91 = ?
Options: a ) 20162 , b ) 18322 , c ) 13032 , d ) 18662 , e ) none of these
Rationale: "explanation : ( a + b ) 2 + ( a − b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1092 + 912 = ( 100 + 9 ) 2 + ( 100 − 9 ) 2 = 2 ( 1002 + 92 ) = 2 ( 10000 + 81 ) = 20162 . answer : option a"
Answer: a
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price q per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Problem: if x = 3 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.02 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de answer : b"
Answer: b
Problem: last year , for every 100 million vehicles that travelled on a certain highway , 98 vehicles were involved in accidents . if 3 billion vehicles travelled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 100000000 )
Options: a ) 288 , b ) 320 , c ) 2,940 , d ) 3,200 , e ) 28,800
Rationale: to solve we will set up a proportion . we know that “ 100 million vehicles is to 98 accidents as 3 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 98 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 98 x = 30 * 98 = 2,940 correct answer is c .
Answer: c
Problem: in what time will a train 125 m long cross an electric pole , it its speed be 130 km / hr ?
Options: a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 130 * 5 / 18 = 36 m / sec time taken = 125 / 36 = 3.5 sec . answer : a"
Answer: a
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 80 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 80 - { both correctly } + 5 { both correctly } = 70 . answer : c ."
Answer: c
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 71
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 71 answer : e"
Answer: e
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 9.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 30 = 10 * 2 = 20 time difference = 9.1 ans : d"
Answer: d
Problem: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 77 , c ) 42 , d ) 88 , e ) 12
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 96 = 42 . answer : c"
Answer: c
Problem: the length of a side of a hexagon is 8 inches . what is the perimeter ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 38
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 8 ) = 48 inches answer c"
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 11 . if n / j = 724.04 , what is value of j ?
Options: a ) 140 , b ) 150 , c ) 260 , d ) 275 , e ) 280
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 724.04 here 724 is the quotient . given that remainder = 11 so , 724.04 = 724 + 11 / j so , j = 275"
Answer: d
Problem: a can complete the job in 2 hours and b can complete the same job in 4 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 6
Answer: a
Problem: if a ' s income is 25 % less than b ' s . by what % b ' s income is greater than a ?
Options: a ) 11 , b ) 12 , c ) 33 , d ) 15 , e ) 36
Rationale: if b ' s income is rs 100 , a ' s income = rs 75 % b ' s income is greater than a = 100 * 25 / 75 = 33.33 % answer : c
Answer: c
Problem: x starts a business with rs . 56000 . y joins in the business after 4 months with rs . 44000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 21 : 11 , b ) 11 : 21 , c ) 22 : 23 , d ) 25 : 23 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 56000 * 12 : 44000 * 8 = 56 * 12 : 44 * 8 = 7 * 3 : 11 = 21 : 11 . answer : option a"
Answer: a
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 965 , d ) d ) 1060 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"
Answer: c
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is theprobability that the extracted ball would turn onto be white , if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ?
Options: a ) 3 / 5 , b ) 5 / 8 , c ) 6 / 7 , d ) 7 / 8 , e ) 6 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 36 meter head start . if cristina runs at a pace of 6 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 36 for cristina = c = 6 * t @ t = 12 , n = 72 c = 72 right answer ans : e"
Answer: e
Problem: 587 * 999 = ?
Options: a ) 586411 , b ) 586413 , c ) 486411 , d ) 486413 , e ) none of these
Rationale: "explanation : trick : 587 * ( 1000 - 1 ) = 587000 - 587 = 586413 option b"
Answer: b
Problem: it takes 35 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "35 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 6 / 7 * 1 / 12 = 1 / 14 of the job each hour . the answer is a ."
Answer: a
Problem: a sum was put at si at certain rate for 2 years . had it been put at 3 % higher rate , it would have fetched rs . 300 more . find the sum
Options: a ) rs 4000 , b ) rs 5000 , c ) rs 6000 , d ) rs 7000 , e ) rs 8000
Rationale: let p be the sum . and x be the interest rate . ( 2 * ( x + 3 ) * p / 100 ) - ( 2 * x * p / 100 ) = 300 therefore 6 p / 100 = 300 p = rs 5000 answer : b
Answer: b
Problem: 9 people decided to split the restaurant bill evenly . if the bill was $ 314.16 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 314.16 , b ) $ 314.17 , c ) $ 314.18 , d ) $ 314.19 , e ) $ 314.20
Rationale: this is equivalent to finding the first number that is divisible by 9 that occurs after 31416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 31416 = 15 and 18 is divisible by 9 . hence , we need to add 3 to this number for it to be divisible by 9 correct option : d
Answer: d
Problem: 1395 x 1395 = ?
Options: a ) a ) 1951609 , b ) b ) 1946025 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1395 x 1395 = ( 1395 ) 2 = ( 1400 - 5 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 2 x 1400 x 5 ) = 1960000 + 25 - 14000 = 1960025 - 14000 = 1946025 . answer : b"
Answer: b
Problem: x ÷ 4 × 5 + 10 – 12 = 48 , then x =
Options: a ) 60 , b ) 40 , c ) 100 , d ) 28 , e ) 50
Rationale: follow reverse process 48 + 12 = 60 – 10 = 50 ÷ 5 = 10 × × 4 = 40 option b
Answer: b
Problem: - 84 x 29 + 365 = ?
Options: a ) 2071 , b ) 2436 , c ) 2801 , d ) - 2801 , e ) - 2071
Rationale: "e given exp . = - 84 x ( 30 - 1 ) + 365 = - ( 84 x 30 ) + 84 + 365 = - 2520 + 449 = - 2071"
Answer: e
Problem: 5 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 267 , e ) 6400
Rationale: "( 5 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 20 x = 320 x = 6400 answer : e"
Answer: e
Problem: what is the area of square field whose side of length 25 m ?
Options: a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 625 sq m
Rationale: "25 * 25 = 625 sq m answer : e"
Answer: e
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 3 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 12 : 15 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 3 - - > e : l = 5 : 3 = 20 : 12 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 12 : 15 . answer : a ."
Answer: a
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 168 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 168 km time taken = distance / speed = 168 / 28 = 6 hours answer : option d"
Answer: d
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 10 x + 5 = 0 ?
Options: a ) 6 , b ) 42 , c ) 24 , d ) 18 , e ) 95
Rationale: a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 10 / 1 = - 10 ab = 5 / 1 = 5 hence a / b + b / a = [ ( - 10 ) 2 - 2 ( 5 ) ] / 5 = 90 / 5 = 18 . d )
Answer: d
Problem: jim is able to sell a hand - carved statue for $ 750 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 555.56 , d ) $ 574.90 , e ) $ 588.20
Rationale: "750 = 1.35 * x x = 750 / 1.35 = 555.5555556 . . . which rounds to $ 555.56 , which is ( c ) ."
Answer: c
Problem: in a fuel station the service costs $ 4.25 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 309.85 $
Rationale: "service cost of 3 van and 2 truck = 4.25 * ( 3 + 2 ) = 21.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 21.25 = 309.85 answer is e"
Answer: e
Problem: a cistern is normally filled in 10 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 60 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 10 - 1 / x = 1 / 12 , solving 1 / x = 1 / 60 so in 60 hours full cistern will be empty . answer : c"
Answer: c
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 795 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 199 , c ) 193 , d ) 212 , e ) 213
Rationale: total movies submitted are 795 . as per question we need to take 1 / 4 of 795 to be considered for top 10 movies = 198.75 approximate the value we 199 . imo option b is the correct answer . . .
Answer: b
Problem: a man can swim in still water at 9 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 3 , d ) 1.5 , e ) 1.2
Rationale: "m = 9 s = x ds = 9 + x us = 9 - x 9 + x = ( 9 - x ) 2 9 + x = 18 - 2 x 3 x = 9 x = 3 answer : c"
Answer: c
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 6 ) , how many units is p from the y - axis ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 10.5 , e ) 12
Rationale: "the x - axis is 6 units from the point p . thus the y - axis is 12 units from the point p . the answer is e ."
Answer: e
Problem: a can do a piece of work in 24 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 9 , b ) 77 , c ) 66 , d ) 55 , e ) 12
Rationale: "8 / 24 + 6 / x = 1 x = 9 days answer : a"
Answer: a
Problem: milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this to 2 % ?
Options: a ) 5 litres , b ) 7 litres , c ) 15 litres , d ) can not be determined , e ) none of these
Rationale: "here required quantity of pure milk = 10 × ( 5 − 2 ) / 2 = 10 × 3 / 2 = 15 litres . answer c"
Answer: c
Problem: 40 percent of the members of a study group are women , and 20 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.2 , b ) 0.08 , c ) 0.16 , d ) 0.14 , e ) 0.15
Rationale: "say there are 100 people in that group , then there would be 0.4 * 0.20 * 100 = 8 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 8 / 100 . answer : b"
Answer: b
Problem: two goods trains each 750 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 ) 72 , b ) 45 , c ) 48 , d ) 51 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : option a"
Answer: a
Problem: the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . the present worth is :
Options: a ) rs . 608 , b ) rs . 6076 , c ) rs . 600 , d ) rs . 602 , e ) rs . 601
Rationale: "t . d . = b . g . x 100 = rs . 24 x 100 = rs . 120 . rate x time 10 x 2 p . w . = 100 x t . d . = rs . 100 x 120 = rs . 600 . rate x time 10 x 2 answer : c"
Answer: c
Problem: a rectangular plot measuring 90 metres by 60 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 60 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 60 ) = 300 m . ∴ number of poles = [ 300 / 5 ] = 60 m answer c"
Answer: c
Problem: a 1200 m long train crosses a tree in 80 sec , how much time will i take to pass a platform 1000 m long ?
Options: a ) 288 , b ) 146.66 , c ) 188 , d ) 180 , e ) 12
Rationale: "l = s * t s = 1200 / 80 s = 15 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 15 t = 146.66 sec answer : b"
Answer: b
Problem: simplify : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 .
Options: a ) - 1 , b ) – 2 , c ) 1 , d ) 2 , e ) 0
Rationale: "solution : ( 7 + 2 ) – ( 5 + 3 + 1 ) - 1 = 9 - 5 - 3 + 1 - 1 = 9 - 8 + 1 - 1 = 2 - 1 = 1 answer : ( c )"
Answer: c
Problem: how many shots of 1 cm radius can be prepared from a sphere of 7 cm radius ?
Options: a ) 343 , b ) 388 , c ) 327 , d ) 88 , e ) 99
Rationale: "4 / 3 ï € * 7 * 7 * 7 = 4 / 3 ï € * 1 * 1 * 1 * x x = 343 answer : a"
Answer: a
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 10 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 18 % , c ) 15 % , d ) 22 % , e ) 11.11 %
Rationale: "0.1 m = 0.90 e = > e / m = 1 / 9 * 100 = 11.11 % = e . m - # of motorists e - # of motorists exceeding speed"
Answer: e