regisss/math_qa huggingface dataset:
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 22 in two years , at the same percent rate per annum ?
Options: a ) s . 520 , b ) s . 480 , c ) s . 420 , d ) s . 100 , e ) s . 200
Rationale: explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 22 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 22 – 20 ) / 20 ] * 100 = 10 % p . a . let the principal be rs . x time = t = 2 years % rate = 10 % p . a . si = ( prt / 100 ) 20 = ( x * 10 * 2 ) / 100 x = rs . 100 answer : d
Answer: d
Problem: if x / ( 11 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d
Answer: d
Problem: 9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them .
Options: a ) rs . 115 , b ) rs . 116 , c ) rs . 117 , d ) rs . 118 , e ) none
Rationale: solution : let the average expenditure of all the nine be x . then , 12 × 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 × 13 ) = rs . 117 answer : option c
Answer: c
Problem: a cube of edge 6 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 36 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1 / 36 = 1 : 36 . answer b"
Answer: b
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 36 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 36 ⇔ 9 ( x - y ) = 36 ⇔ x - y = 4 answer a"
Answer: a
Problem: a snail , climbing a 66 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 42 , b ) 63 , c ) 77 , d ) 80 , e ) 91
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 62 days it will climb 62 feet on the 63 rd day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 63 b"
Answer: b
Problem: if 6 pr = 360 and if 6 cr = 15 , find r ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: solution : npr = ncr � r ! 6 pr = 15 * r ! 360 = 15 * r ! r ! = 360 / 15 = 24 r ! = 4 * 3 * 2 * 1 = > r ! = 4 ! therefore , r = 4 . answer : option c
Answer: c
Problem: what is the sum of all remainders obtained when the first 130 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 412 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 412 . answer : d ."
Answer: d
Problem: by selling 90 pens , a trader gains the cost of 15 pens . find his gain percentage ?
Options: a ) 16.66 % , b ) 17.66 % , c ) 18.66 % , d ) 19.66 % , e ) 20.66 %
Rationale: "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 15 pens = rs . 15 profit % = 15 / 90 * 100 = 16.66 % answer : a"
Answer: a
Problem: how many paying stones , each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board ?
Options: a ) 99 , b ) 18 , c ) 135 , d ) 17 , e ) 12
Rationale: "30 * 18 = 2 * 2 * x = > x = 135 answer : c"
Answer: c
Problem: a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 14 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 99 - 9 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . distance to be covered = 250 + 100 = 350 m . time taken = 350 / 25 = 14 sec . answer : a"
Answer: a
Problem: a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 88 , d ) 66 , e ) 23
Rationale: "speed of the train relative to man = ( 200 / 20 ) m / sec = 5 m / sec . [ 5 * ( 18 / 5 ) ] km / hr = 18 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 18 = = > x = 23 km / hr . answer : e"
Answer: e
Problem: a pupil ' s marks were wrongly entered as 73 instead of 65 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 16 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c"
Answer: c
Problem: the average salary of 16 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a
Answer: a
Problem: a shopkeeper sold an article at $ 100 with 30 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 77 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 130 = $ 77 ( approximately ) answer is d"
Answer: d
Problem: in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 1600 , b ) 1800 , c ) 2000 , d ) 2200 , e ) 2400
Rationale: "let v be the total number of votes . 0.2 v = 480 v = 2400 the answer is e ."
Answer: e
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 4 years and to $ 500 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 67 % , d ) 25 % , e ) 33 %
Rationale: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 4 years the principal p amounts to $ 400 and after a time of 6 years ( question says after another 6 years so 4 + 2 ) p becomes $ 500 . formulating the above data amount ( a 1 ) at end of 4 years a 1 = p ( 1 + 4 r / 100 ) = 400 amount ( a 2 ) at end of 6 years a 2 = p ( 1 + 2 r / 100 ) = 500 dividing a 2 by a 1 we get ( 1 + 4 r / 100 ) / ( 1 + 2 r / 100 ) = 5 / 4 after cross multiplication we are left with 4 r = 100 which gives r = 25 % option : d"
Answer: d
Problem: twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ?
Options: a ) 1299
b ) 1305
c ) 1311
d ) 1317
e ) 1323
Rationale: the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e .
Answer: e
Problem: if the area of circle is 616 sq cm then its circumference ?
Options: a ) 76
b ) 55
c ) 88
d ) 21
e ) 11
Rationale: the area of circle = pie * r ^ 2 = 616 = > r = 14 2 * 22 / 7 * 14 = 88 answer : c
Answer: c
Problem: the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ?
Options: a ) 48 , b ) 64 , c ) 70 , d ) 80 , e ) 84
Rationale: let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d
Answer: d
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 6 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 3 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 168 , d ) 691 , e ) 871
Rationale: n / p = 18 6 / p = 18 p + 6 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 3 solving these two equations we get p = 9 n = 168 answer is c .
Answer: c
Problem: in an examination , 25 % of total students failed in hindi , 35 % failed in english and 40 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 60 % , d ) 80 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d"
Answer: d
Problem: population of a city in 20004 was 1400000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2818075 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e"
Answer: e
Problem: the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 134 , c ) 141 , d ) 190 , e ) 28
Rationale: "π * 15 * 3 = 141 answer : c"
Answer: c
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?
Options: a ) 56 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a"
Answer: a
Problem: if ( 55 ^ 55 + 55 ) is divided by 56 , then the remainder is : ?
Options: a ) 54 , b ) 55 , c ) 53 , d ) 56 , e ) 57
Rationale: solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a
Answer: a
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( a ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Problem: the least common multiple of positive integer m and 3 - digit integer n is 690 . if n is not divisible by 3 and m is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is :
Options: a ) rs . 50 , b ) rs . 160 , c ) rs . 200 , d ) rs . 225 , e ) rs . 325
Rationale: "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent f of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d"
Answer: d
Problem: the difference between the local value and the face value of 9 in the numeral 62975148 is
Options: a ) 899999 , b ) 899991 , c ) 899891 , d ) 899981 , e ) 899000
Rationale: "explanation : ( local value of 9 ) - ( face value of 9 ) = ( 900000 - 9 ) = 899991 b )"
Answer: b
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 234 km , e ) 255 km
Rationale: "( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b"
Answer: b
Problem: the compound ratio of 3 : 4 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 9 : 10 , e ) 1 : 4
Rationale: "3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d"
Answer: d
Problem: the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 × 2460 = 0.17 × 2460 = rs . 422 answer : option b"
Answer: b
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 16 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d"
Answer: d
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1400 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
Answer: b
Problem: if the simple interest on a sum of money for 5 years at 9 % per annum is rs . 800 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 947.55 , b ) rs . 957.55 , c ) rs . 857.55 , d ) rs . 657.55 , e ) rs . 357.55
Rationale: "sum = ( 800 * 100 ) / ( 5 * 9 ) = rs . 1 , 777.78 c . i . on rs . rs . 1 , 777.78 for 5 years at 9 % = rs . 2 , 735.33 . = rs . 2 , 735.33 - 1 , 777.78 = rs . 957.55 answer : b"
Answer: b
Problem: find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a
Options: a ) rs . 2.20 , b ) rs . 3.20 , c ) rs . 4.20 , d ) rs . 5.20 , e ) rs . 3.25
Rationale: p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b
Answer: b
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 10 machines to produce 100 units ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 24 , e ) 96
Rationale: "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a"
Answer: a
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 1040 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 2340 / 9 = 1040 correct choice is ( c )"
Answer: c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 666 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666 answer : a"
Answer: a
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 5 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 25 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '"
Answer: a
Problem: a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 10 / 3
Rationale: "sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e"
Answer: e
Problem: if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
Options: a ) 900 , b ) 800 , c ) 600 , d ) 300 , e ) none
Rationale: "answer ∵ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 ∴ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d"
Answer: d
Problem: in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]
Options: a ) 4 , b ) 7 , c ) 12 , d ) 14 , e ) 28
Rationale: if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d
Answer: d
Problem: in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ."
Answer: b
Problem: 9 log 9 ( 4 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d"
Answer: d
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
Options: a ) 96 , b ) 106 , c ) 128 , d ) 137 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d"
Answer: d
Problem: yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 588 , e ) 658
Rationale: "total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d"
Answer: d
Problem: the area of a square is 4900 sq cm . find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square ?
Options: a ) 5 : 8 , b ) 5 : 10 , c ) 5 : 13 , d ) 5 : 7 , e ) 5 : 16
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4900 a = ( 4900 ) ^ 1 / 2 = 70 l = a and b = a - 20 b : l = a - 20 : a = 50 : 70 = 5 : 7 answer : d"
Answer: d
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 18 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 3000 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b"
Answer: b
Problem: the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
Options: a ) 84
b ) 86
c ) 82
d ) 80
e ) none of them
Rationale: let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a
Answer: a
Problem: r is the set of positive even integers less than 20 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none
b ) two
c ) three
d ) five
e ) seven
Rationale: squares < 20 { 1,4 , 9,16 } s = { 1,4 , 9,16 } r = { 2 , . . . . . 18 } hence c .
Answer: c
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e"
Answer: e
Problem: find the area , diameter = 13 m .
Options: a ) 132.00 square meter , b ) 132.04 square meter , c ) 132.78 square meter , d ) 132.24 square meter , e ) 113.43 square meter
Rationale: "diameter = 13 meter . radius = diameter / 2 . = 13 / 2 . = 6.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 6.5 area of a circle = 3.14 ã — 6.5 ã — 6.5 . = 3.14 ã — 42.25 . = 132.78 square meter answer : c"
Answer: c
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 45 , find the other ?
Options: a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 45 = 160 answer is b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 40 , b ) 36 , c ) 32 , d ) 28 , e ) 24
Rationale: "let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ."
Answer: b
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b"
Answer: b
Problem: to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
Options: a ) rs . 10,000 , b ) rs . 10,800 , c ) rs . 14,400 , d ) rs . 16,000 , e ) none of these
Rationale: solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a
Answer: a
Problem: if the least common addition 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 ) 14 , d ) 17 , e ) 21
Rationale: "( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d"
Answer: d
Problem: what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 40 seconds ?
Options: a ) 308 , b ) 320 , c ) 332 , d ) 344 , e ) 356
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ."
Answer: d
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d ."
Answer: d
Problem: if 10 men can reap 120 acres of land in 15 days , how many acres of land can 20 men reap in 30 days ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 1200 , e ) 480
Rationale: "10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e"
Answer: e
Problem: the profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 975 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 × 150 ⁄ 100 = 975 answer b"
Answer: b
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 1 , e ) 1 : 3
Rationale: "( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ."
Answer: d
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )"
Answer: b
Problem: find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .
Options: a ) 366 , b ) 236 , c ) 367 , d ) 365 , e ) 386
Rationale: "explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e"
Answer: e
Problem: the speed of a car is 90 km in the first hour and 75 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 82.5 kmph , c ) 75 kmph , d ) 65 kmph , e ) 77 kmph
Rationale: "s = ( 90 + 75 ) / 2 = 82.5 kmph b"
Answer: b
Problem: a larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 64 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 288 , e ) 120
Rationale: "volume of larger cube = 64 = 4 ^ 3 side of larger cube = 4 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 4 ^ 2 = 96 surface area of 27 smaller cubes = 64 * 6 * 1 = 384 difference = 384 - 96 = 288 answer : d"
Answer: d
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 8 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 34 hr , e ) 36 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d"
Answer: d
Problem: two buses each 3125 m long are running in opposite directions on parallel roads . their speeds are 40 km / hr and 35 km / hr respectively . find the time taken by the slower bus to pass the driver of the faster one ?
Options: a ) 50 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 45 sec
Rationale: relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a
Answer: a
Problem: if the perimeter of a rectangular garden is 500 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 167 m , e ) 150 m
Rationale: "2 ( l + 100 ) = 500 = > l = 150 m answer : e"
Answer: e
Problem: a man goes from a to b at a speed of 15 kmph and comes back to a at a speed of 12 kmph . find his average speed for the entire journey ?
Options: a ) 13.7 kmph , b ) 13.3 kmph , c ) 13.8 kmph , d ) 13.9 kmph , e ) 12.3 kmph
Rationale: distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b
Answer: b
Problem: a cube is divided into 729 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that the cube is coloured with green colour on one set of adjacent faces , red on the other set of adjacent faces , blue on the third set . so , how many cubelets are there which are painted with exactly one colour ?
Options: a ) 293 , b ) 294 , c ) 295 , d ) 296 , e ) 298
Rationale: "total cubes created are 729 so a plane of big cube has 9 * 9 cubes out of that ( n - 2 ) * ( n - 2 ) = 7 * 7 = 49 are painted only one side and a cube has six sides = 6 * 49 = 294 answer : b"
Answer: b
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 4 students are girls . how many boys are there ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 120 , e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 4 = 120 total boys : 160 - 120 = 40 answer is a"
Answer: a
Problem: the perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 729 , d ) d ) 75 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 60 / 2 = 35 cm 2 answer : option d"
Answer: d
Problem: the product z of two prime numbers is between 10 and 30 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24 , then what is z ?
Options: a ) 21 , b ) 15 , c ) 14 , d ) 10 , e ) 6
Rationale: "the smallest possible product is 21 which is 3 * 7 . all other products are too big . the answer is a ."
Answer: a
Problem: how many integers from 0 to 44 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 13 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 43 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 43 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 42 or , n - 1 = 12 or , n = 13 a"
Answer: a
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c"
Answer: c
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 7 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 30 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e"
Answer: e
Problem: a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 33 , b ) 37 , c ) 41 , d ) 45 , e ) 49
Rationale: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ."
Answer: d
Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
Options: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
Rationale: "n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 or 1 girl from 10 = 13 c 2 + 10 c 1 = 88 ans - a"
Answer: a
Problem: a student gets 70 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "a student gets 70 % in one subject , 80 % in the other . average of 2 subjects is 75 % , if they have equal weightage . to get an overall of 75 % , he should get 75 % in third subject to maintain same % age . . if they have equal weightage . answer : a"
Answer: a
Problem: carina has 85 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a"
Answer: a
Problem: how much water must be added to 56 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 14 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 56 litres of milk = ( 1 ⁄ 4 × 56 ) litres = 14 litres . answer c"
Answer: c
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2000 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2000 = ( p * 5 * 4 ) / 100 p = 2500 answer : b"
Answer: b
Problem: if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"
Answer: d
Problem: jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 926 . answer : e ."
Answer: e
Problem: the sum of the numbers is 110 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 30 , b ) 54 , c ) 72 , d ) 84 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a"
Answer: a
Problem: total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26
Rationale: "dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b"
Answer: b
Problem: the ratio of the radius of two circles is 5 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 25 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 5 : 3 π r 12 : π r 22 r 12 : r 22 = 25 : 9 answer : c"
Answer: c
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 512,000 locusts ?
Options: a ) 18 , b ) 15 , c ) 13 , d ) 14 , e ) 12
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 + 14 hours : 512,000 answer : d"
Answer: d
Problem: if the price of gasoline increases by 20 % and a driver intends to spend only 14 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 1 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d .
Answer: d
Problem: a cube is divided into 343 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
Rationale: "each side of the cube has 7 x 7 = 49 cubelets . only the interior cubelets are painted one colour . on each side , 5 x 5 = 25 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 25 = 150 the answer is b ."
Answer: b
Problem: the average of 7 consecutive numbers is 20 . the largest of these numbers is :
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c"
Answer: c
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 5 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 1 and - 5 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 5 i . e x ^ 2 + 4 x - 5 = 0 is the quadratic equation which needs to be solved . ( x - 1 ) ( x + 5 ) = 0 hence x = 1 . c = - 5 imo d"
Answer: d
Problem: 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height . what is the diameter of each sphere ?
Options: a ) 2 cm , b ) 4 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 1 cm ^ 3 r = 1 cm d = 2 cm the answer is a ."
Answer: a
Problem: 9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ?
Options: a ) 690.48 , b ) 690.49 , c ) 690.5 , d ) 690.51 , e ) 690.52
Rationale: if the bill was $ 690.47 dollars , how much money should be removed with 1 cent as the smallest unit ? this is equivalent to finding the first number that is divisible by 9 that occurs after 690.47 . 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 6 + 9 + 0 + 4 + 7 = 26 . if you add 1 , the number is divisible by 9 ( 26 + 1 ) . 27 is divisible by 9 . hence , we need to add 1 cent from this number for it to be divisible by 9 . correct option : a
Answer: a
Problem: evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 )
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13"
Answer: e
Problem: 16 people can write 52 book in 12 days working 8 hour a day . then in how many day 206 can be written by 64 people ?
Options: a ) 309 / 26 , b ) 309 / 28 , c ) 309 / 22 , d ) 319 / 26 , e ) 339 / 26
Rationale: "work per day epr hour per person = 52 / ( 12 * 8 * 16 ) / / eq - 1 people = 64 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 206 / ( p * 8 * 64 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 309 / 26 answer : a"
Answer: a
Problem: total dinning bill for 7 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c"
Answer: c
Problem: what is the area of square field whose side of length 20 m ?
Options: a ) 200 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 400 sq m
Rationale: "20 * 20 = 400 sq m answer : e"
Answer: e
Problem: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 812 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 9.6 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 12 miles per hour time = t 2 = distance / speed = x / 12 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : d"
Answer: d
Problem: in a survey of 345 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 40 / 69
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 291 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 345 we have to find not part time and not uninsured . in other words not part time and insured = x / 345 = ( 291 - 104 + 13 ) / 345 = 40 / 69 answer is e ."
Answer: e