regisss/math_qa huggingface dataset:
Problem: by how much does the larger root of the equation 2 b ^ 2 + 5 b = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 b ^ 2 + 5 b = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Problem: between 100 to 200 how many no are divisible by both 3 and 2 and 100,200 are inclusive ?
Options: a ) 77 , b ) 78 , c ) 79 , d ) 80 , e ) 81
Rationale: prime numbers are 21 so 100 - 21 = 79 answer : c
Answer: c
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a + b ) / 2 ?
Options: a ) 100 , b ) 110 , c ) 105 , d ) 20 , e ) 215
Rationale: "yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a + b ) / 2 = 110 + 100 = 210 / 2 = 105 ans : c"
Answer: c
Problem: martin has to secure 80 % marks to clear his exam of class 9 th . he got 200 marks and failed by 200 marks . what is the maximum marks ?
Options: a ) 500 , b ) 505 , c ) 510 , d ) 515 , e ) 525
Rationale: a 500 to pass the exam ravish needs 200 + 200 = 400 marks . = > ( 400 / 80 ) * 100 = 500
Answer: a
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 60 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 104.8 % , d ) 150.5 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 60 percent to make square c length of each side of square c = 1.6 * 20 = 32 area of c = 32 ^ 2 = 1024 difference in areas of c and cummulative areas of a and b = 1024 - ( 400 + 100 ) = 524 percent is the area of square c greater than the sum of the areas of squares a and b = ( 524 / 500 ) * 100 % = 104.8 % answer c"
Answer: c
Problem: find the perimeter and area of a square of side 15 cm .
Options: a ) 144 , b ) 169 , c ) 196 , d ) 121 , e ) 225
Rationale: "we know that the perimeter of square = 4 ã — side side = 15 cm therefore , perimeter = 4 ã — 15 cm = 60 cm now , area of the square = ( side ã — side ) sq . units = 15 ã — 15 cm â ² = 225 cm â ² answer : e"
Answer: e
Problem: what is the remainder when 980 * 1050 * 880 * 1010 is divided by 22 ?
Options: a ) 15 , b ) 10 , c ) 12 , d ) 8 , e ) 3
Rationale: "oa is ' c ' . oe : take the remainder from each of 980 / 22 , 1050 / 22 and so on . . 980 / 22 gives remainder = 12 1050 / 22 gives remainder = 16 880 / 22 gives remainder = 0 1010 / 22 gives remainder = 20 the net remainder is the product of above individual remainders . i . e = 12 * 16 * 0 * 20 break them into pairs 12 * 16 / 22 gives remainder 16 and 0 * 20 / 22 gives remainder 20 so 16 * 20 / 22 gives remainder 12 . answer : c"
Answer: c
Problem: a pizzeria in castroville creates its own special blend of shredded cheese at a cost of $ 696.05 per kilogram . the blend includes mozzarella , at $ 504.35 per kilogram , and romano cheese , at $ 887.75 per kilogram . if the employees have already shredded 19 kilograms of mozzarella cheese , how many kilograms of romano cheese will they need to shred now ?
Options: a ) 19 kg , b ) 13 kg , c ) 10 kg , d ) 23 kg , e ) 15 kg
Rationale: 504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) solve the equation . 504.35 ( 19 ) + 887.75 x = 696.05 ( 19 + x ) 9 , 582.65 + 887.75 x = 13 , 224.95 + 696.05 x 9 , 582.65 + 191.7 x = 13 , 224.95 191.7 x = 3 , 642.3 x = 19 . answer is a .
Answer: a
Problem: product of two natural numbers is 17 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 17 ( 2 ) = 290 / 289 option a"
Answer: a
Problem: the perimeter of an isosceles right triangle is 10 + 10 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5 , b ) 6 , c ) 7.07 , d ) 8 , e ) 9
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 10 + 10 sqrt 2 or , a . ( 2 + sqrt 2 ) = 10 ( 1 + sqrt 2 ) , a = 10 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 10 * 2.414 / 3.414 = 0.707 * 10 then hypotenuse = 7.07 c"
Answer: c
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 15 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.5 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 15 = 405 hence , new average = 405 ⁄ 10 = 40.5 answer c"
Answer: c
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 998 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 998 y = 2 x + 2 996 = 2 x x = 498 answer : b . 498"
Answer: b
Problem: if two - third of a bucket is filled in 2 minutes then the time taken to fill the bucket completely will be .
Options: a ) 3 minutes , b ) 70 seconds , c ) 60 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: "2 / 3 filled in 2 mint 1 / 3 filled in 1 mint then 2 / 3 + 1 / 3 = 2 + 1 = 3 minutes answer : a"
Answer: a
Problem: marla is hanging a banner diagonally across a rectangular room . the length of the room is 3 feet shorter than its width . if the total area of the room is 130 square feet , what is the length of the banner ( in feet ) ?
Options: a ) between 16 and 17
b ) between 17 and 18
c ) between 18 and 19
d ) between 19 and 20
e ) between 20 and 21
Rationale: to solve this , we first need to set up an equation for the area of the room . if x is the width , then we have x ( x - 3 ) = 130 . by putting the equation in standard form , we get x ^ 2 - 3 x - 130 = 0 . by using the quadratic formula , we get roots of - 10 and 13 . we know that x is the width , and x - 3 is the length , so by using the roots , we get 13 as the width ( x ) , and 10 as the length ( x - 3 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 13 ^ 2 + 10 ^ 2 = 169 + 100 = 269 the square root of 269 is less than 17 , since 17 ^ 2 = 289 . going down a number , we can compute 16 ^ 2 = 256 < 269 . therefore , the length of the diagonal must be between 16 and 17 . the correct answer is a .
Answer: a
Problem: if p gets 25 % more than q , then by what percent does q get less than p ?
Options: a ) 45 , b ) 34 , c ) 20 , d ) 76 , e ) 54
Rationale: let q get 1 unit . 25 % of 1 unit = 1 / 4 = 0.25 p gets ( 1 + 0.25 ) i . e . , 1.25 units . difference = ( 1.25 - 1 ) = 0.25 required percentage = 0.25 / 1.25 * 100 = 1 / 5 * 100 = 20 answer : c
Answer: c
Problem: before 5 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 58 , d ) 60 , e ) 64
Rationale: "a - 5 = 4 ( b - 5 ) - - > a - 4 b = - 15 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 23 - - > a = 3 ( 27 ) = 81 a - b = 81 - 23 = 58 answer : c"
Answer: c
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people b who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , b = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000
Answer: d
Problem: of 70 players on a football team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "37 are throwers and right handed 1 / 3 of remaining 33 , i . e 11 are left handed and remaining are right handed . basically , out of 70 , only 11 are left handed and remaining 70 - 11 = 59 are right handed . b is the answer"
Answer: b
Problem: the perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet . find the area of the rhombus .
Options: a ) 100 sqrt ( 5 ) ft . sq
b ) 400 sqrt ( 5 ) ft . sq
c ) 500 sqrt ( 5 ) ft . sq
d ) 200 sqrt ( 5 ) ft . sq
e ) 150 sqrt ( 5 ) ft . sq
Rationale: a perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet . the length of the side oc of the right triangle is equal to half the diagonal : 20 feet . let us now consider the right triangle boc and apply pythagora ' s theorem to find the length of side bo . 30 ^ 2 = bo ^ 2 + 20 ^ 2 bo = 10 sqrt ( 5 ) feet we now calculate the area of the right triangle boc and multiply it by 4 to obtain the area of the rhombus . area = 4 ( 1 / 2 ) bo * oc = 4 ( 1 / 2 ) 10 sqrt ( 5 ) * 20 = 400 sqrt ( 5 ) ft . sq answer is b
Answer: b
Problem: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , sam ' s new income would be what fraction of quentin ' s new income ?
Options: a ) 11 / 12 , b ) 12 / 11 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 9.6 and q 8.8 so 9.6 / 8.8 = 1.2 / 1.1 ans : b"
Answer: b
Problem: how many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 7 sets with 10 such number in each set will give 7 x 10 = 70 integers . c"
Answer: c
Problem: there are 200 female managers in a certain company . find the total number of female employees q in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) q = 300 , b ) q = 400 , c ) q = 500 , d ) q = 600 , e ) none of these
Rationale: { managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .
Answer: c
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 8,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 12000 , c ) 16160.8 , d ) 14000 , e ) 15000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 8,000 ( 1 + 0.04 / 4 ) ^ 4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 8,000 ( 1.0201 + 1 ) = 16160.8 hence answer is c ."
Answer: c
Problem: if the sum of two numbers is 24 and the sum of their squares is 404 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 86 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 24 and x 2 + y 2 = 404 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 24 ) 2 - 404 = 576 - 404 = 172 xy = 86 . answer d"
Answer: d
Problem: product of two natural numbers is 3 . then , the sum of reciprocals of their squares is
Options: a ) 10 / 9 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 3 , as 3 is a prime number , so a = 1 , b = 3 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 3 ( 2 ) = 10 / 9 option a"
Answer: a
Problem: if the least common multiple of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
Rationale: lcm of two prime numbers will basically be multiple of those numbers . lcm = 10 = 2 * 5 , both of which are prime . now we know x > y , so x = 5 and y = 2 . 2 x + y = 2 * 5 + 2 = 10 + 2 = 12 . answer : d
Answer: d
Problem: if the cost price is 96 % of selling price then what is the profit percentage .
Options: a ) 7.14 , b ) 7.41 , c ) 4.71 , d ) 4.17 , e ) none of them
Rationale: "selling price = rs 100 : then cost price = rs 96 : profit = rs 4 . profit = { ( 4 / 96 ) * 100 } % = 4.17 % answer is d ."
Answer: d
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 50 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 33 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 50 = > x = 11 so deepak age is = 3 ( 11 ) = 33 answer : option c"
Answer: c
Problem: if x ^ 3 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c"
Answer: c
Problem: a man buys a cycle for rs . 1750 and sells it at a loss of 8 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1610 , c ) s . 1190 , d ) s . 1202 , e ) s . 1092
Rationale: "s . p . = 92 % of rs . 1750 = rs . 92 x 1750 / 100 = rs . 1610 answer : option b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 12 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 66 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 12 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 12 = 4 / 9 ( t - 12 ) 10 t = 1188 - 528 = > t = 66 . answer : c"
Answer: c
Problem: a metallic sheet is of rectangular shape with dimensions 100 m x 50 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 10 m , the volume of the box ( in m cube ) is :
Options: a ) 42500 m cube , b ) 20000 m cube , c ) 44140 m cube , d ) 24000 m cube , e ) none of these
Rationale: "explanation : l = ( 100 - 20 ) m = 80 m , [ because 10 + 10 = 20 ] b = ( 50 - 20 ) m = 30 m , h = 10 m . volume of the box = ( 80 x 30 x 8 ) m cube = 24000 m cube . option d"
Answer: d
Problem: a rope of which a calf is tied is increased from 5 m to 9 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 180 , c ) 176 , d ) 200 , e ) 291
Rationale: "π ( 92 – 52 ) = 176 answer : c"
Answer: c
Problem: if the number of white balls in a box are 6 times the black balls , which of the below is the total number of balls , if there are 8 black balls in the box ?
Options: a ) a - 56 , b ) b - 57 , c ) c - 58 , d ) d - 59 , e ) e - 60
Rationale: let the number of black balls = x and the number of white balls = 6 x then , total number of balls in the box = x + 6 x = 7 x i . e . , the total number of balls must be a multiple of 7 from the given choices , only 56 is the multiple of 7 . hence , 56 are the number of balls in the box . answer is a .
Answer: a
Problem: a trader marked the selling price of an article at 50 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 7.3 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 150 * 100 ] % = 7.3 % answer a"
Answer: a
Problem: 45 % of 750 - 25 % of 480 = ?
Options: a ) 216 , b ) 217.5 , c ) 236.5 , d ) 245 , e ) 250
Rationale: "explanation : given expression = ( 45 / 100 * 750 ) - ( 25 / 100 * 480 ) = ( 337.50 - 120 ) = 217.50 answer is b"
Answer: b
Problem: among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 90 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 42 , c ) 56 , d ) 32 , e ) 40
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 90 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 90 = 110 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 60 = 40 . thus e is the correct answer choice"
Answer: e
Problem: 72 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 77 , b ) b ) 99 , c ) c ) 66 , d ) d ) 55 , e ) e ) 88
Rationale: "( 72 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 160 160 – 72 = 88 answer : e"
Answer: e
Problem: how many of the positive divisors of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120 . consider factors of 120 4 * 30 6 * 20 15 * 8 24 * 5 60 * 2 total we get 5 different ways and all are part of 4 . answer : c is correct option .
Answer: c
Problem: the sale price sarees listed for rs . 400 after successive discount is 15 % and 5 % is ?
Options: a ) 297 , b ) 879 , c ) 323 , d ) 762 , e ) 269
Rationale: "400 * ( 85 / 100 ) * ( 95 / 100 ) = 323 answer : c"
Answer: c
Problem: efrida and frazer who live 15 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 13
Rationale: it ' s a simple geometry problem . look at the diagram below : answer : e .
Answer: e
Problem: the sum of two consecutive integers is 15 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 15 2 n + 1 = 15 2 n = 14 n = 7 answer : b"
Answer: b
Problem: a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 5 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 39 / 5 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 3 ) / ( b + 3 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 5 ) / ( a + 5 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 39 / 5 ans : ( c )"
Answer: c
Problem: a space shuttle orbits the earth at about 2 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 7,200 , b ) 8,880 , c ) 10,800 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 2 * 3600 = 28,800 answer : a"
Answer: a
Problem: a train 220 m long is running with a speed of 59 kmph . . in what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec
Rationale: "explanation : speed of the train relative to man = ( 59 + 7 ) kmph = 66 × 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 × 3 / 55 ) sec = 12 sec answer : option c"
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 35 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 34 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 35 x dollars for thefirst 35 hoursplus 7 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 7 x / 1.5 x = 4 additional hours , so harry worked for total of 30 + 4 = 34 hours . answer : c ."
Answer: c
Problem: in what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 8 sec
Rationale: "t = 80 / 36 * 18 / 5 = 8 sec answer : e"
Answer: e
Problem: two equilateral triangles of side 12 cm are placed one on top of another , such that a 6 pointed star is formed . if the six verticals lie on a circle what is the area of the circle not enclosed by the star ?
Options: a ) 68
b ) 83
c ) 57
d ) 61
e ) 62
Rationale: area of star = √ 3 / 4 * ( 12 ) ^ 2 + 3 * √ 3 / 4 * ( 12 / 3 ) ^ 2 = 48 √ 3 if r be radius of circle then r = 6 / cos 30 = > r = 12 / √ 3 = > r ^ 2 = 48 area of circle = pi * 48 area of the circle not enclosed by the star = 48 * pi - 48 √ 3 = 48 ( 3.14 - 1.732 ) = 68 ( approax ) answer : a
Answer: a
Problem: jaclyn buys $ 30 000 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 ) 712.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 712.50 answer : a"
Answer: a
Problem: the average of 6 observations is 12 . a new seventh observation is included and the new average is decreased by 1 . the seventh observation is :
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "explanation : seventh observation = ( 7 × × 11 - 6 × × 12 ) = 5 correct option : c"
Answer: c
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 5 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28350 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d ."
Answer: d
Problem: how many factors of 880 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Problem: how many multiples of 9 are there between 18 and 270 ?
Options: a ) 12 , b ) 27 , c ) 42 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 18 and 270 are inclusive . if 18 and 270 are inclusive , then the answer is ( 270 - 18 ) / 9 + 1 = 29 . if 18 and 270 are not inclusive , then the answer is ( 261 - 27 ) / 9 + 1 = 27 . since oa is b , then we have not inclusive case ."
Answer: b
Problem: if it takes 30 construction workers 70 days to build a skyscraper , how long would it take 50 workers ?
Options: a ) 52 days , b ) 47 days , c ) 42 days , d ) 37 days , e ) 32 days
Rationale: 30 * 70 = 50 * x x = 42 answer : c
Answer: c
Problem: there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ?
Options: a ) 50 , b ) 74 , c ) 37 , d ) 77 , e ) 68
Rationale: e 68 68 regions . each new tangent increases the non - enclosed areas by two
Answer: e
Problem: 2 cow ’ s and 8 goats are brought for rs . 1400 . if the average price of a goat be rs . 60 . what is the average price of a cow .
Options: a ) rs . 480 , b ) rs . 960 , c ) rs . 960 , d ) rs . 460 , e ) rs . 560
Rationale: explanation : average price of a goat = rs . 60 total price of 8 goats = 8 * 60 = rs . 480 but total price of 2 cows and 8 goats = rs . 1400 total price of 2 cows is = 1400 - 480 = 980 average price of a cow = 980 / 2 = rs . 460 answer : option d
Answer: d
Problem: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ?
Options: a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235
Rationale: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b
Answer: b
Problem: p alone can complete a job in 6 days . the work done by q alone in one day is equal to one - fifth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "p ' s rate is 1 / 6 q ' s rate is 1 / 30 the combined rate is 1 / 6 + 1 / 30 = 1 / 5 if they work together , the job will take 5 days . the answer is e ."
Answer: e
Problem: 60 % of a number is added to 150 , the result is the same number . find the number ?
Options: a ) 375 , b ) 277 , c ) 266 , d ) 99 , e ) 121
Rationale: ": ( 60 / 100 ) * x + 150 = x 2 x = 750 x = 375 answer : a"
Answer: a
Problem: x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 2 are 3 , 2 , and 2 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 36 the answer is b ."
Answer: b
Problem: what is the smallest integer that is multiple of 87 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e
Problem: two employees x and y are paid a total of rs . 600 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.72 , b ) s . 250.72 , c ) s . 272.72 , d ) s . 300.72 , e ) s . 310.72
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 600 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 600 ⇒ y [ 12 / 10 + 1 ] = 600 ⇒ 22 y / 10 = 600 ⇒ 22 y = 6000 ⇒ y = 6000 / 22 = rs . 272.72 c"
Answer: c
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 32
Rationale: "800 * ( 20 / 100 ) = 160 - - - - 5 ? - - - - 1 = > rs . 32 answer : e"
Answer: e
Problem: mary ' s income is 40 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 84 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 84 ( 40 percent more than tim ' s income ) . thus , mary ' s income ( 84 ) is 84 % of juan ' s income ( 100 ) . answer : e ."
Answer: e
Problem: kim has 40 percent more money than sal and sal has 20 percent less money than phil . if sal and phil have a combined total of $ 1.80 , how much money does kim have ?
Options: a ) $ 1.00 , b ) $ 1.12 , c ) $ 1.20 , d ) $ 1.32 , e ) $ 1.40
Rationale: phil = x sal = 0.8 x kim = ( 1.4 ) * 0.8 x = 1.12 x x + 0.8 x = 1.8 - - > x = 1 kim = 1.12 answer : b
Answer: b
Problem: the sides of a rectangle are in the ratio 4 : 3 and its area is 972 sq . m find the perimeter of rectangle
Options: a ) 120 m
b ) 122 m
c ) 124 m
d ) 126 m
e ) 128 m
Rationale: explanation : let 4 x and 3 x be sides of the rectangle we know that area of rectangle = l × b 4 x × 3 x = 972 12 x 2 = 972 x 2 = 81 x = 9 therefore length = 4 x = 4 × 9 = 36 m breadth = 3 x = 3 × 9 = 27 m therefore perimeter = 2 ( l + b ) = 2 ( 36 + 27 ) = 126 m answer : option d
Answer: d
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 14 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,240 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 14 : x + x - 2 = 14 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : a ."
Answer: a
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 35 % . staff are allowed a further 30 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.555 d , b ) 0.765 d , c ) 0.455 d , d ) 0.785 d , e ) 0.805 d
Rationale: "effective discount = a + b + ab / 100 = - 35 - 30 + ( - 35 ) ( - 30 ) / 100 = - 54.5 sale price = d * ( 1 - 54.5 / 100 ) sale price = . 455 * d answer ( c )"
Answer: c
Problem: the number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 84 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 6 and 28 = 84 answer c"
Answer: c
Problem: if k ^ 3 is divisible by 336 , what is the least possible value of integer k ?
Options: a ) 56 , b ) 70 , c ) 84 , d ) 96 , e ) 120
Rationale: "k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c ."
Answer: c
Problem: there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 40
Rationale: given the constraints of this question , we have to consider 6 possible outcomes . . . 1 green ball : 6 options grrrrr rgrrrr rrgrrr rrrgrr rrrrgr rrrrrg 2 green balls : 5 options ggrrrr rggrrr rrggrr rrrggr rrrrgg 3 green balls : 4 options gggrrr rgggrr rrgggr rrrggg 4 green balls : 3 options ggggrr rggggr rrgggg 5 green balls : 2 options gggggr rggggg 6 green balls : 1 option gggggg 6 + 5 + 4 + 3 + 2 + 1 = 21 options . b
Answer: b
Problem: a man walked diagonally across a square lot . approximately , what was the percent saved by not walking along the edges ?
Options: a ) 20 %
b ) 30 %
c ) 40 %
d ) 50 %
e ) 55 %
Rationale: let the side of the square ( abcd ) be x metres . then , ab + bc = 2 x metres . ac = 2 x = ( 1.41 x ) m . saving on 2 x metres = ( 0.59 x ) m . saving % = ( 0.59 x ) / 2 x x 100 % = 30 % ( approx . ) b )
Answer: b
Problem: rs . 500 amounts to rs . 670 in 5 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 150 , b ) 550 , c ) 760 , d ) 450 , e ) 260
Rationale: ( 500 * 5 * 2 ) / 100 = 50 500 + 50 = 550 answer : b
Answer: b
Problem: the lcm and hcf of two numbers are 10000 and 1000 respectively . find the larger of the two numbers if their sum is 11000 .
Options: a ) 10000 , b ) 562 , c ) 352 , d ) 576 , e ) 594
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 10000 * 1000 = 10000000 so the answer which we are looking for has to be a factor of 10000000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 10000000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.3 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 10 ) = 7 / 30 the cistern will be filled in 30 / 7 hrs i . e . , 4.3 hrs . answer : a"
Answer: a
Problem: a software engineer starts from home at 3 pm for every walk on a route which has level road for some distance and a then a hillock . he walks speed of 4 kmph on level ground and then at a speed of 3 kmph on the uphill and then down the hill at a speed of 6 kmph to the level ground and then at a speed of 4 kmph to the home if he reaches home at 9 pm . what is the distance one way of his route ?
Options: a ) 12 km , b ) 15 km , c ) 18 km , d ) 24 km , e ) data inadequate
Rationale: time = distance / speed so , let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so , ( x / 4 + y / 3 ) + ( y / 6 + x / 4 ) = 6 x + y = 12 km . answer : a
Answer: a
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 60 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 60 - c = 100 c = 20 option d ."
Answer: d
Problem: there are 30 balls which are red , blue or green . if 11 balls are green and the sum of red balls and green balls is less than 25 , at most how many red balls are there ?
Options: a ) 14 , b ) 13 , c ) 16 , d ) 17 , e ) 8
Rationale: "r + g + b = 30 g = 11 r + g < 25 = > r + 11 < 25 = > r < 14 = > at most 13 red balls answer : b"
Answer: b
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 3000 resolutions ?
Options: a ) 2187 m , b ) 3704 m , c ) 4179 m , d ) 4224 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 3000 resolutions . = 3000 * 2 * 22 / 7 * 22.4 = 422400 cm = 4224 m answer : d"
Answer: d
Problem: half a number plus 6 is 11 . what is the number ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 6 = 11 ( 1 / 2 ) x = 11 - 6 ( 1 / 2 ) x = 5 x = 10 correct answer is c
Answer: c
Problem: n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 10 ?
Options: a ) 8 , b ) 12 , c ) 10 , d ) 16 , e ) 18
Rationale: n ^ ( n / 2 ) = 10 apply log n / 2 logn = log 10 nlogn = 2 log 10 = log 10 ^ 2 = log 100 logn = log 100 now apply antilog n = 100 / n now n = 10 . answer : c
Answer: c
Problem: the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ?
Options: a ) 48 , b ) 50 , c ) 56 , d ) 62 , e ) 64
Rationale: 1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 550 = 56 c
Answer: c
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6840 . find the actual price of the good .
Options: a ) rs . 6000 , b ) rs . 9000 , c ) rs . 10800 , d ) rs . 10000 , e ) rs . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6840 1 = 6840 / 68.4 100 = ( 6840 * 100 ) / 68.4 = rs . 10,000 . answer : option d"
Answer: d
Problem: a rope of which a calf is tied is increased from 9 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 1212 , c ) 1408 , d ) 2707 , e ) 2591
Rationale: "π ( 232 – 92 ) = 1408 answer : c"
Answer: c
Problem: what is the value of 3 x ^ 2 − 1.6 x + 0.3 for x = 0.8 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 0.94 , e ) 2.46
Rationale: "3 x ^ 2 - 1.6 x + 0.3 for x = 0.6 = 3 ( 0.8 * 0.8 ) - 2 * 0.8 * ( 0.8 ) + 0.3 = 0.8 * 0.8 + 0.3 = 0.94 correct option : d"
Answer: d
Problem: in a school of 900 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 144 , b ) 153 , c ) 162 , d ) 171 , e ) 180
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 900 * 18 / 100 = 162 the answer is c ."
Answer: c
Problem: if c is 14 % of a and 40 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "answer = d 14 a / 100 = 40 b / 100 b = 14 a / 40 = 35 a / 100 = 35 %"
Answer: d
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 7 / 15
Rationale: i think e - 7 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 2 x so old = x , new = x now 1 / 3 of x are occupied and 1 / 5 of x are occupied which simplifies to ( 1 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 1 / 5 of x occupied in the new ward . add them up to get 8 / 15 of x there are x beds in new tower so ratio is : ( 8 / 15 ) x / x = 8 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new towerb = 7 / 15 . e
Answer: e
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 222 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 4.75
Rationale: "required run rate = 222 - ( 3.2 x 10 ) = 190 = 4.75 40 40 e"
Answer: e
Problem: if the sum of a number and its square is 342 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 87 , e ) 18
Rationale: "explanation : let the integer be x . then , x + x 2 = 342 x 2 + x - 342 = 0 ( x + 19 ) ( x – 18 ) = 0 x = 18 answer : e"
Answer: e
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.6 , d ) 12 , e ) 12.5
Rationale: "mean = 16.2 two standard deviations is 2.3 + 2.3 = 4.6 there could be two calues for this . mean + two standard deviations = 20.8 mean - two standard deviations = 11.6 answer choice has 11.6 and so c is the answer ."
Answer: c
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 99 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "7 c + 6 p = 99 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 * 3 + 6 * 13 = 21 + 78 = 99 hence c is the answer"
Answer: c
Problem: p and q started a business investing rs . 85,000 and rs . 25,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 5
Rationale: "p : q = 85000 : 25000 = 17 : 5 . answer : e"
Answer: e
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 10 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 22 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: if the total quantity was 100 then 40 x 10 % + 60 x 30 % = 22 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer
Answer: a
Problem: the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years , what will be the total interest at the end of the tenth year ?
Options: a ) rs . 600 , b ) rs . 900 , c ) 1200 rupees , d ) rs . 1500 , e ) none
Rationale: solution 22.22 let the sum be rs . x . now , s . i . = rs . 600 , t = 10 years . rate = % = ( 100 x 600 / x x 10 ) % = ( 6000 / x ) % s . i . for first 5 years = rs . ( x x 5 x 6000 / x x 100 ) = rs . 300 . s . i . for first 5 years = rs . ( 3 x x 5 x 6000 / x x 100 ) = rs . 900 . ∴ total interest = rs . 1200 . answer c
Answer: c
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value w of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "w - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Problem: out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: description : = > 8 x = 2 ( x + 2 ) + 5 + 3 ( x + 4 ) = > 3 x = 21 , x = 7 = > x + 4 = 11 x = 11 - 4 = 7 answer c
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 30 sec . what is the length of the train ?
Options: a ) 535 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 500 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 30 = 500 m answer : e"
Answer: e
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 3 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 23
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 8 = 21 the answer is d ."
Answer: d
Problem: what is the smallest number which when increased by 3 is divisible by 9 , 35 , 25 and 21 ?
Options: a ) 1572 , b ) 1782 , c ) 1992 , d ) 2122 , e ) 2342
Rationale: "when increased by 3 , the number must include at least 3 ^ 2 * 5 ^ 2 * 7 = 1575 the answer is a ."
Answer: a
Problem: if | r + s | = | r - s | , then r * s must be equal to :
Options: a ) - 2 , b ) 2 , c ) 0 , d ) - 3 , e ) 3
Rationale: solution 1 : distance perspective | r - s | = | r + s | = = > the distance of r and s is equal to the distance of r and - s . < = = = = = = = ( - s ) = = = = = = = 0 = = = = = = = ( s ) = = = = = = > only 0 is the value that has a distance equal to s and - s . solution 2 : | r - s | = | r + s | ( square both ) r ^ 2 - 2 rs + s ^ 2 = r ^ 2 + 2 rs + s ^ 2 4 rs = 0 rs = 0 answer : c
Answer: c
Problem: 8 cups of milk are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of milk should be poured into the 8 - cup bottle ?
Options: a ) 16 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 4 / 3 , e ) 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : a
Answer: a