regisss/math_qa huggingface dataset:
Problem: if | 20 x - 10 | = 130 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 42 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 130 20 x - 10 = 130 or 20 x - 10 = - 130 20 x = 140 or 20 x = - 120 x = 7 or x = - 6 product = - 6 * 7 = - 42 answer is c"
Answer: c
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 60 and the turban . find the price of the turban .
Options: a ) 27 , b ) 30 , c ) 29 , d ) 10 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 60 . thus , 3434 ( 90 + x ) = 60 + x or 270 + 3 x = 240 + 4 x or x = 30 answer : b"
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1450 ?
Options: a ) rs . 1000 , b ) rs . 1250 , c ) rs . 1010 , d ) rs . 10000 , e ) none of these
Rationale: "explanation : 1450 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1250 answer : option b"
Answer: b
Problem: how many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 36 , c ) 40 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 600 * 3 / 50 = 36 sec answer : b"
Answer: b
Problem: a ship 450 m long is running at a speed of 24 km / hr . in what time will it pass a bridge 900 m long ?
Options: a ) 202.5 sec , b ) 205.5 sec , c ) 200 sec , d ) 1350 sec , e ) 900 sec
Rationale: total length = 450 + 900 = 1350 speed = 24 km / h = ( 24 * 5 ) / 18 = 20 / 3 m / s time = ( 1350 * 3 ) / 20 = 202.5 sec . answer : a
Answer: a
Problem: at company x , senior sales representatives visit the home office once every 12 days , and junior sales representatives visit the home office once every 8 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 24 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 40 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 40 , b ) 12 / 40 , c ) 8 / 40 , d ) 3 / 40 , e ) 7 / 40
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23,29 , 31,37 } n ( x ) = 12 , n ( s ) = 40 hence , the required probability is 12 / 40 . answer : b"
Answer: b
Problem: john can complete a given task in 10 days . jane will take only 20 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 8 , b ) 9 , c ) 8.5 , d ) 9.5 , e ) 10.5
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 4 * ( 1 / 10 ) = 2 / 5 of the work . so 3 / 5 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 12 = 8 / 60 time taken to complete 4 / 5 of the work = ( 3 / 5 ) / ( 8 / 60 ) = 9 / 2 days . so total number of days taken to complete the work = 9 / 2 + 4 = 8.5 days . c"
Answer: c
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 5 years at 20 % per annum is rs . 75 of money ?
Options: a ) 1489 , b ) 6845 , c ) 2598 , d ) 1875 , e ) 2600
Rationale: "p = 75 ( 100 / 20 ) 5 = > p = 1875 answer : d"
Answer: d
Problem: p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has . how much does p have ?
Options: a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60
Rationale: "p = ( 2 / 6 ) * p + 32 ( 4 / 6 ) * p = 32 p = 48 the answer is b ."
Answer: b
Problem: a salt manufacturing company produced a total of 2000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 80 , b ) 85 , c ) 83 , d ) 95 , e ) 00
Rationale: "total production of salt by the company in that year = 2000 + 2100 + 2200 + . . . . + 3100 = 30600 . average monthly production of salt for that year = 30600 / 365 â ‰ ˆ 84 answer : c"
Answer: c
Problem: how many terminating zeroes e does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Problem: the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 16 years old . what is the value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "14 n + 32 = 16 ( n + 1 ) 2 n = 16 n = 8 the answer is d ."
Answer: d
Problem: a 75 - liter solution of cool - drink is made from 8 % jasmine water . if 3 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 10.3 % , b ) 11.5 % . , c ) 10 % . , d ) 12.2 % , e ) 12 % .
Rationale: "denominator 75 + 3 + 12 90 numerator 75 * 0.08 = 6 - - - > jasmine water 6 + 3 = 9 - - - > new content of jasmine water in new solution ratio 9 / 90 answer : c"
Answer: c
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 216 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 5400 , d ) 2766 , e ) 1811
Rationale: "p = 216 ( 100 / 5 ) ^ 2 = > p = 5400 answer : c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 sec . what is the length of the train ?
Options: a ) 287 , b ) 699 , c ) 250 , d ) 168 , e ) 150
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 250 m answer : c"
Answer: c
Problem: rewrite ( 10 ^ 38 ) – 85 as a base 10 integer , what is the sum of the digits in that integer ?
Options: a ) 354 , b ) 357 , c ) 330 , d ) 370 , e ) 360
Rationale: we know that ( 10 ^ 38 ) is ending 00 , so ( 10 ^ 38 ) – 85 = 9 . . . . 9915 total number of digits in ( 10 ^ 38 ) – 85 is 38 , or 36 digits of 9 and two digits 1 and 5 . answer choice is 36 * 9 + 6 = 330 answer is c 330
Answer: c
Problem: he average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 26 , b ) 27 , c ) 88 , d ) 99 , e ) 12
Rationale: sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b
Answer: b
Problem: a man buy a book in rs 50 & sale it rs 70 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 40 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 70 profit = 70 - 50 = 20 % = 20 / 50 * 100 = 40 % answer : b"
Answer: b
Problem: a tank is filled by 3 pipes a , b , c in 6 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 42 hr , c ) 40 hr , d ) 20 hr , e ) 50 hr
Rationale: suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 6 7 / x = 1 / 6 x = 42 hours answer is b
Answer: b
Problem: first column specifies the no of days prior to departure information . second column specifies the percentage discount offered . 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % 14 - 29 days = = > 25 % 30 days or more = = > 40 % the table above shows the discount structure for advanced purchase of tickets at a particular airline . a passenger bought a ticket at this airline for $ 1050 . the ticket agent informed her that , had she purchased the ticket one day later , she would have paid $ 210 more . how many days before her departure did she purchase her ticket .
Options: a ) 6 , b ) 7 , c ) 13 , d ) 14 , e ) 29
Rationale: first i figured out the percentage change from the immediate previous amount for each of the period . thus it comes - 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % ( 90 % of the price ) 14 - 29 days = = > 17 % ( approx ) ( went from 90 % to 75 % ) 30 days or more = = > 20 % ( went from 75 % to 60 % ) if the passenger had to pay the extra amount , she had to pay = ( 210 + 1050 ) = 1260 now 210 is somehow between 10 % and 20 % of 1260 . so 17 % is the choice here . correct ans : 14 days answer : d
Answer: d
Problem: a no . when divided by 158 gives a remainder 50 , what remainder will be obtainedby dividingthe same no . 16 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "158 + 50 = 208 / 16 = 13 ( remainder ) d"
Answer: d
Problem: a man can row a distance of 6 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 : 41 , e ) 5
Rationale: "explanation : he covered 6 km in 1 hour , so he might cover 20 km in 3 hours 19 minutes . but he took 10 hours . he would have saved 10 â € “ 3 hours 19 minutes = 6 hours 41 minutes . answer : d"
Answer: d
Problem: 1395 x 1395
Options: a ) 1946025 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1395 x 1395 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 5 x 1400 x 5 ) = 1946025 . answer : option a"
Answer: a
Problem: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 20 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 2,316 , e ) 2,870
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 20 and c = 1 / 2 into the equation and simplify to get the answer 2870 . option e ."
Answer: e
Problem: a mixture of 70 litres of milk and water contains 10 % water . how many litres of water should be added to the mixture so that the mixture contains 12 1 / 2 % water ?
Options: a ) 2 , b ) 8 , c ) 6 , d ) 3 , e ) 4
Rationale: "a 2 quantity of milk in the mixture = 90 / 100 ( 70 ) = 63 litres . after adding water , milk would form 87 1 / 2 % of the mixture . hence , if quantity of mixture after adding x liters of water , ( 87 1 / 2 ) / 100 x = 63 = > x = 72 hence 72 - 70 = 2 litres of water must be added ."
Answer: a
Problem: if a = 2 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?
Options: a ) - 14 , b ) - 60 , c ) 0 , d ) 4 , e ) 14
Rationale: "if a = - 1 , then putting values in equation = - [ ( 2 ) ^ 2 + ( 2 ) ^ 3 + ( 2 ^ 4 ) + ( 2 ^ 5 ) ] = - [ 4 + 8 + 16 + 32 ] = - 60 answer = b = - 60"
Answer: b
Problem: how many even number in the range between 20 to 100 inclusive are not divisible by 3
Options: a ) 28 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 20 , 22,24 . . . 100 using ap formula , we can say 100 = 20 + ( n - 1 ) * 2 or n = 41 . for 6 , 24,36 . . . 96 using ap formu 24 la , we can say 96 = 24 + ( n - 1 ) * 6 or n = 13 . hence , only divisible by 2 but not 3 = 41 - 13 = 28 . hence , answer a"
Answer: a
Problem: a clock shows the time as 9 a . m . if the minute hand gains 7 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 63 min , d ) 50 min , e ) 55 min
Rationale: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 7 = 63 minutes . answer : c"
Answer: c
Problem: how much interest will $ 10,000 earn in 9 months at an annual rate of 4 % ?
Options: a ) $ 300 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: soln : - 9 months = 3 / 4 of year ; 4 % = 4 / 100 = 1 / 25 ; $ 10,000 ( principal ) * 1 / 25 ( interest rate ) * 3 / 4 ( time ) = $ 300 . answer : a
Answer: a
Problem: if the perimeter of a rectangular garden is 700 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 250 m , e ) 128 m
Rationale: "2 ( l + 100 ) = 700 = > l = 250 m answer : d"
Answer: d
Problem: you have been given a physical balance and 7 weights of 40 , 42 , 36 , 33 , 47 , 52 and 67 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 169 kgs .
Options: a ) 163 , b ) 166 , c ) 162 , d ) 164 , e ) 165
Rationale: "67 + 52 + 47 = 166 answer : e"
Answer: e
Problem: the average of first five multiples of 7 is
Options: a ) 21 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 . = 21 answer a"
Answer: a
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 102 . what should be the selling price of the article to gain 20 % ?
Options: a ) rs . 146 , b ) rs . 144 , c ) rs . 129 , d ) rs . 123 , e ) rs . 128
Rationale: "given that sp = rs . 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = rs . 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = rs . 144 answer : b"
Answer: b
Problem: sum of the squares of 3 no . ' s is 62 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 18 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 62 + 2 * 131 a + b + c = √ 324 = 18 d"
Answer: d
Problem: some persons can do a piece of work in 12 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "12 / ( 2 * 2 ) = 3 days answer : a"
Answer: a
Problem: how many multiples of 4 are there between 12 and 92 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 23 . 23 - 3 + 1 = 21 . the answer is a ."
Answer: a
Problem: a metered rikshaw charges rs 13.50 for the first 1 km and 2.50 per 1 / 3 km there after . what would the charge if this rikshaw is hired for 13 kms ? in approx ? ?
Options: a ) 103.5 rs , b ) 104.5 rs , c ) 105.5 rs , d ) 106.5 rs , e ) 107.5 rs
Rationale: for 1 st km : rs . 13.50 ramaining distance : 13 - 1 = 12 km 1 / 3 km costs 2.5 rs 1 km costs ( 2.5 * 3 ) remaining 12 km costs ( 2.5 * 3 ) * 12 = 90 rs total cost = 90 + 13.5 = 103.5 rs answer : a
Answer: a
Problem: two pipes a and b separately fill in 15 / 2 min and 5 min respactively and third pipe c can empty of 14 l / m if all the pipes are open when the cistern is full , it is emptied in 1 hr . how many litres does the cistern hold ?
Options: a ) 40 , b ) 30 , c ) 50 , d ) 80 , e ) 54
Rationale: let total water in cistern = x liter speed of a = 2 x / 15 l / m ( speed = liter / time ) speed of b = x / 5 l / m speed of c = 14 l / m according to question x + ( x / 5 + 2 x / 15 ) * 60 = 60 * 14 x + = 60 * 14 x = 40 liter answer : a
Answer: a
Problem: if 4 men can colour 48 m long cloth in 2 days , then 6 women can colour 36 m long cloth in ?
Options: a ) day , b ) day , c ) days , d ) days , e ) days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 6 = 1 day . b )"
Answer: b
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king ?
Options: a ) 1 / 26 , b ) 1 / 13 , c ) 3 / 52 , d ) 3 / 26 , e ) 15 / 26
Rationale: "p ( black card ) = 1 / 2 p ( king ) = 1 / 13 p ( black card then a king ) = 1 / 2 * 1 / 13 = 1 / 26 the answer is a ."
Answer: a
Problem: a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 15.33 , d ) rs . 12.31 , e ) none
Rationale: "solution 90 : 12 = 115 : x x = ( 12 ã — 115 / 90 ) = rs . 15.33 hence , s . p per kg = rs . 15.33 answer c"
Answer: c
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 20 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 10 / 1 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 20 + 1 / 20 = 1 / 10 therefore they take 10 ratio = 10 / 1 = d"
Answer: d
Problem: two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 128 , e ) 180
Rationale: l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 20 = 128 . answer : d
Answer: d
Problem: a cylindrical bucket of height 36 cm and radius 21 cm is filled with sand . the bucket is emptied on the ground and a conical heap of sand is formed , the height of the heap being 12 cm . the radius of the heap at the base is :
Options: a ) 63 cm
b ) 53 cm
c ) 56 cm
d ) 66 cm
e ) none of these
Rationale: volume of the bucket = volume of the sand emptied volume of sand = π ( 21 ) 2 × 36 let r be the radius of the conical heap . then , 1 ⁄ 3 π r 2 × 12 = π ( 21 ) 2 × 36 or r 2 = ( 21 ) 2 × 9 or r = 21 × 3 = 63 answer a
Answer: a
Problem: a man opens a shop . he buys water bottles for 50 cents each , fruit for 25 cents each , and snacks for a dollar each . he wants to start a bundle of selling a bottle a water , 3 snacks and 2 fruits for d dollars . every 5 th bundle sold will be sold for 2 dollars and a complimentary snack at the owner ' s expense . what should he charge at least to not lose any money ?
Options: a ) 4.6 , b ) 3.0 , c ) 4.1 , d ) 3.2 , e ) 2.9
Rationale: w = 0.50 f = 0.25 s = 1.00 b = w + 2 f + 3 s = 4.00 they pay , he pays 4 , net loss 0 fifth bundle = 2 they pay , he pays 5 , net loss 3 dollars 3 / 5 = 60 cents . charging 60 more cents on each bundle will be safe . answer : a
Answer: a
Problem: there is 60 % increase in an amount in 6 years at simple interest . what will be the compound interest of $ 12,000 after 3 years at the same rate ?
Options: a ) $ 2160 , b ) # 3120 , c ) $ 3972 , d ) $ 6240 , e ) none of these
Rationale: "let p = $ 100 . then , s . i . $ . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = $ 12000 . t = 3 years and r = 10 % p . a . c . i . = $ 12000 x 1 + 10 3 - 1 100 = $ 12000 x 331 1000 = 3972 answewr : c 3972"
Answer: c
Problem: a person is traveling at 75 km / hr and reached his destiny in 4 hr then find the distance ?
Options: a ) 300 km , b ) 200 km , c ) 250 km , d ) 400 km , e ) 220 km
Rationale: "t = 4 hrs d = t * s = 75 * 4 = 300 km answer is a"
Answer: a
Problem: a can do a piece of work in 80 days . he works at it for 10 days & then b alone finishes the remaining work in 42 days . in how much time will a and b , working together , finish the work ?
Options: a ) 30 days , b ) 20 days , c ) 25 days , d ) 35 days , e ) 45 days
Rationale: "work done by a in 10 days = 10 / 80 = 1 / 8 remaining work = ( 1 - ( 1 / 8 ) ) = 7 / 8 now , work will be done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days therefore , a ’ s one day ’ s work = 1 / 80 b ’ s one day ’ s work = 1 / 48 ( a + b ) ’ s one day ’ s work = 1 / 80 + 1 / 48 = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer : a"
Answer: a
Problem: a box contains 11 apples , 10 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: p ( choosing a red apple 6 times in a row ) = 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 11 < 0.5 the answer is d .
Answer: d
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 11 minutes 20 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: "bob ' s time = 680 secs . his sis ' time = 576 secs . percent increase needed = ( 680 - 576 / 680 ) * 100 = 104 / 640 * 100 = 15 % . ans ( e ) ."
Answer: e
Problem: if the price of a certain computer increased 30 percent from x dollars to 351 dollars , then 2 x =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = x after 30 % price increase price = x + ( 30 / 100 ) * x = 1.3 x = 351 ( given ) i . e . x = 351 / 1.3 = $ 270 i . e . 2 x = 2 * 270 = 540 answer : option a"
Answer: a
Problem: in the mundane goblet competition , 6 teams compete in a “ round robin ” format : that is , each team plays every other team exactly once . a team gets 3 points for a win , 1 point for a tie ( a draw ) , and 0 points for a loss . what is the difference between the maximum total points and the minimum total points that can be gained by all teams ( added together ) in the mundane goblet competition ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 75
Rationale: no oa yet : my method : max points : a b c d e f 15 12 9 6 3 0 = 45 points min points a b c d e f 5 5 5 5 5 5 = 30 45 - 30 = 15 points = = = = > ( a ) ans
Answer: a
Problem: how many integers between 324,805 and 458,705 have tens digit 2 and units digit 3 ?
Options: a ) 1,352 , b ) 1,359 , c ) 1,329 , d ) 1,349 , e ) 1,348
Rationale: "there is one number in hundred with 2 in the tens digit and 3 in the units digit : 23 , 123 , 223 , 323 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 134,900 - one number per each hundred gives 133,900 / 100 = 1,349 numbers . answer : d ."
Answer: d
Problem: a can do a job in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 4 days work = 7 / 60 * 4 = 7 / 15 remaining work = 1 - 7 / 15 = 8 / 15 answer is b"
Answer: b
Problem: diana is painting statues . she has 3 / 6 of a gallon of paint remaining . each statue requires 1 / 6 gallon of paint . how many statues can she paint ?
Options: a ) 3 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 3 / 6 ÷ 1 / 6 = 3 / 6 * 6 / 1 = 3 / 1 = 3 answer is a ."
Answer: a
Problem: what is the units digit of ( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 ?
Options: a ) 0 , b ) 3 , c ) 2 , d ) 1 , e ) 4
Rationale: "( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 = 6 ! ( 4 ! + 5 ! ) / 12 = 720 ( 24 + 120 ) / 12 = ( 720 * 144 ) / 12 = 720 * 12 units digit of the above product will be equal to 0 answer a"
Answer: a
Problem: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 9 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 180 , b ) 210 , c ) 240 , d ) 270 , e ) 300
Rationale: the relative speed of jack and christina is 5 + 3 = 8 feet per second . the distance between them is 240 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 8 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 9 * 30 = 270 feet . answer : d .
Answer: d
Problem: a slot machine in a las vegas casino has an average profit of $ 600 for each 8 - hour shift for the 5 days sunday through thursday , inclusive . if the average per - shift profit on friday and saturday is 25 % greater than on the other days of the week and the slot machine is in operation every hour of every day , what is the total weekly profit that the casino makes from the slot machine ?
Options: a ) a - 4500 , b ) b - 9000 , c ) c - 13500 , d ) d - 15500 , e ) e - 27000
Rationale: correct answer is c - 13500 . total profit per weekday = $ 600 x 3 ( shifts ) = $ 1800 total profit per week ( apart from saturdaysunday ) = $ 1800 x 5 = $ 9000 total profit per shift on weekends = $ 600 x 125 / 100 = $ 750 total profit on weekends = $ 750 x 3 ( shifts ) x 2 ( saturday , sunday ) = $ 4500 . hence the answer is - $ 4500 + $ 9000 = $ 13500 . ( c )
Answer: c
Problem: if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 118.5 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 9 * 1.25 = 11.25 . the average price of the bond on may 1 st and july 1 st = ( 9 + 11.25 ) / 2 = 10.125 . the price of the bond on june 1 st ( 12 ) is 32 / 27 times ( 118.5 % ) the average price of the bond on may 1 st and july 1 st . answer : c ."
Answer: c
Problem: the average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 47.55 kg , b ) 48 kg , c ) 48.55 kg , d ) 49.25 kg , e ) 59.25 kg
Rationale: "16 * 50.25 + 8 * 45.15 / 24 = 48.55 answer : c"
Answer: c
Problem: how much water should be added to 13 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 13 + x ) ) ) 2 = 5 % * ( 13 + x ) - - - - - - - - > x = 27 ans b"
Answer: b
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 40 .
Options: a ) 3 , b ) 4 , c ) 7 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 40 , remainder will be - 4 i . e . n will be 4 less than a multiple of 40 . so you must add 7 to n to make it a multiple of 40 c"
Answer: c
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.7 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 4 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.7 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.7 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.9 = 4 / 9 required ratio = 4 / 9 : 1 = 4 : 9 . answer : e"
Answer: e
Problem: what is the hcf of 2 / 3 , 4 / 10 and 6 / 5
Options: a ) 7 / 45 , b ) 1 / 15 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 10 , 5 ) = 2 / 30 = 1 / 15 answer : option b"
Answer: b
Problem: at veridux corporation , there are 215 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 50 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 215 â € “ 90 = 125 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 215 â € “ 40 = 175 must be associates . now , in the â € œ associate â €  row , 135 + e = 175 , which means e = 40 â € ” the other 40 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 40 = 90 , which means b = 50 . there are fifteen female managers in this company . thus , the answer = 50 ( a ) ."
Answer: a
Problem: a number when divided by a divisor leaves a remainder of 30 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 43 , e ) 59
Rationale: let the number is n , the divisor = d , i will make the two equations - n = xd + 30 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 43 as d is also integer and 43 is a prime number , the d should be 43 to satisfy the above equation . hence answer is ' d '
Answer: d
Problem: a student got twice as many sums wrong as he got right . if he attempted 36 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 36 3 x = 36 x = 12 . answer : a"
Answer: a
Problem: if 6 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 4 , c ) - 3 , d ) - 9 , e ) 6
Rationale: the phrase “ 6 is one solution of the equation ” means that one value of x is 6 . thus , we first must plug 6 for x into the given equation to determine the value of k . so we have 6 ^ 2 + ( 3 ) ( 6 ) + k = 10 36 + 18 + k = 10 54 + k = 10 k = - 44 next we plug - 44 into the given equation for k and then solve for x . x ^ 2 + 3 x – 44 = 10 x ^ 2 + 3 x – 54 = 0 ( x + 9 ) ( x - 6 ) = 0 x = - 9 or x = 6 thus , - 9 is the other solution . answer d .
Answer: d
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 120
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 8 * 180 / 12 = 120 ounces of water e"
Answer: e
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability q this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability of cgd / ( cg ) q - > 3 / 19 answer d"
Answer: d
Problem: in the youth summer village there are 125 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 100 , e ) 90
Rationale: "total = 125 not working = 50 having family = 25 like to sing in shower = 75 working = 125 - 50 = 75 not having family = 125 - 25 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 a"
Answer: a
Problem: solution y is 20 percent liquid x and 80 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 20 % , b ) 21 1 / 2 % , c ) 22 % , d ) 24 % , e ) 25 %
Rationale: "in 8 kilograms of solution y there are 0.2 * 8 = 1.6 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.2 * 2 = 0.4 kilograms of solution x are added , so in the new solution of 8 kilograms there are 1.6 + 0.4 = 2 kilograms of solution x , which is 2 / 8 * 100 = 25 % of this new solution . answer : e ."
Answer: e
Problem: 20.036 divided by 0.04 gives :
Options: a ) 50.09 , b ) 5.06 , c ) 50.06 , d ) 100.9 , e ) 500.9
Rationale: "= 20.036 / 0.04 = 2003.6 / 4 = 500.9 answer is e ."
Answer: e
Problem: the ratio between the sale price and the cost price of an article is 12 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 6 , d ) 5 : 7 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 12 x . then , gain = rs . 5 x required ratio = 5 x : 7 x = 5 : 7 answer : d"
Answer: d
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6800 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6791 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6800 * 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 . answer : d"
Answer: d
Problem: when 17 is divided by positive integer x , the remainder is 1 . for how many values of x is this true ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when 17 is divided by x , the remainder is 1 i . e . 1 orange left over after grouping , so x must be greater than 1 . it also means that 16 is completely divisible by x . factors of 16 are 1 , 2 , 4 , 8 , 16 . out of these , x can be 2 , 4 , 8 , and 16 . answer ( d ) .
Answer: d
Problem: sakshi can do a piece of work in 12 days . tanya is 20 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "ratio of times taken by sakshi and tanys = 120 : 100 = 6 : 5 suppose tanya takes x days to do the work . 6 : 5 : : 12 : x = > x = 10 days . hence , tanya takes 10 days to complete the work . answer : a"
Answer: a
Problem: a river 4 m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 10666 , b ) 11678 , c ) 12345 , d ) 10678 , e ) 19099
Rationale: "( 4000 * 4 * 40 ) / 60 = 10666 m 3 answer : a"
Answer: a
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c"
Answer: c
Problem: what least number should be subtracted from 1398 so that the remainder when divided by 7 , 9 , and 11 will leave in each case the same remainder 5 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "the lcm of 7 , 9 , and 11 is 693 . the next multiple is 2 * 693 = 1386 . 1386 + { remainder } = 1386 + 5 = 1391 , which is 7 less than 1398 . answer : b ."
Answer: b
Problem: if the sides of a triangle are 32 cm , 27 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 162 cm 2 , d ) 666 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 32 cm , 27 cm and 12 cm is right angled , where the hypotenuse is 32 cm . area of the triangle = 1 / 2 * 27 * 12 = 162 cm 2 answer : c"
Answer: c
Problem: 9.99 x 9.9 x 9 ÷ 9.9 ÷ 0.3 = ?
Options: a ) 276 , b ) 299 , c ) 310 , d ) 3.33 , e ) 365
Rationale: "explanation : ? = ( 9.99 x 9.9 x 9 ) / ( 9.9 x 0.9 x 0.3 ) = 3.33 answer : option d"
Answer: d
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1233 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 137 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1233 or 9 x = 1233 or x = 137 . required number = 137 . answer : d"
Answer: d
Problem: two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ?
Options: a ) 30 / 28 , b ) 40 / 28 , c ) 25 / 28 , d ) 27 / 28 , e ) 32 / 28
Rationale: there are 6 consonants and 2 vowels in barkhint . probability that at least one of the selected letters is a consonant = 1 - ( probability of both vowels ) probability of both vowels = 2 c 2 / 8 c 2 = 1 / 28 so , answer is 1 - 1 / 28 = 27 / 28 answer : d
Answer: d
Problem: if ( a + b ) = 4 , ( b + c ) = 8 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 1 .
Rationale: "given a + b = 4 b + c = 8 c + d = 3 then ( a + b ) - ( b + c ) + ( c + d ) = 4 - 8 + 3 = - 1 option e . . ."
Answer: e
Problem: ( 69842 x 69842 - 30158 x 30158 ) / ( 69842 - 30158 ) = ?
Options: a ) 100000 , b ) 69842 , c ) 39684 , d ) 30158 , e ) none
Rationale: answer given expression = [ ( 69842 ) 2 - ( 30158 ) 2 ] / [ ( 69842 - 30158 ) ] = [ ( 69842 - 30158 ) ( 69842 + 30158 ) ] / ( 60842 - 30158 ) = 100000 correct option : a
Answer: a
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 6 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 135 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 6 ) m = 135 m . answer d"
Answer: d
Problem: a train running at the speed of 20 km / hr crosses a post in 10 seconds . what is the length of the train ?
Options: a ) 150 , b ) 250 , c ) 415 , d ) 200 , e ) 312
Rationale: "speed = ( 20 x 5 / 18 ) = 50 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 9 x 10 m = 200 m . answer : d"
Answer: d
Problem: 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 69 % , e ) 75 %
Rationale: initially 92 % and 8 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 92 so , the required % is [ ( 3 / 4 ) ∗ 92 / 100 ] ∗ 100 = 69 % answer : d
Answer: d
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 20 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 160 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,16 r = x / 100 * 0.1 r answer b"
Answer: b
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 750 ( before payroll deductions ) ?
Options: a ) 1600 , b ) 1625 , c ) 1650 , d ) 1655 , e ) 1675
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 760 x = 260 / 0.16 = 1625 the answer is b ."
Answer: b
Problem: 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened to fillthe tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs
Rationale: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c
Answer: c
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 354
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 15 ) . larger number = ( 23 x 15 ) = 345 . answer : option d"
Answer: d
Problem: an assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the time to produce the first 60 cogs is 60 / 15 = 4 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 5 hours = 24 cogs per hour . the answer is c ."
Answer: c
Problem: 210 students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 19 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?
Options: a ) 36 , b ) 4 , c ) 16 , d ) 38 , e ) 40
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 19 ^ 2 / 2 - 17 ^ 2 / 2 = 72 / 2 = 36 ans a ."
Answer: a
Problem: increasing the original price of a certain item by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 44.0
Rationale: "we ' re told that the original price of an item is increased by 20 % and then that price is increased by 20 % . . . . if . . . . starting value = $ 100 + 20 % = 100 + . 20 ( 100 ) = 120 + 20 % = 120 + . 20 ( 120 ) = 120 + 24 = 144 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 44 / 100 = 44 % final answer : e"
Answer: e
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 112 ) * 63 = 27 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 63 will have a volume a little more than 24 , that is 27 answer : a"
Answer: a
Problem: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m , what is its area ?
Options: a ) 4290 , b ) 2535 , c ) 2530 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 266 m ⇒ breadth = 55 m length = 55 + 23 = 78 m area = 78 × 55 = 4290 m 2 answer is a ."
Answer: a
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability z that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days z = 15 / 64 ans a it is ."
Answer: a
Problem: if a ^ 2 is divisible by 240 what is the least possible value of integer a ?
Options: a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e 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 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d"
Answer: d