regisss/math_qa huggingface dataset:
Problem: if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: n ( n - 1 ) / 2 = 10 * 9 / 2 = 45 answer : e
Answer: e
Problem: 6 x – 5 y + 3 z = 22 4 x + 8 y – 11 z = 7 5 x – 6 y + 2 z = 12 given the equations above , x + y + z = ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 6 x – 5 y + 3 z ) - ( 5 x – 6 y + 2 z ) = 22 - 12 or , x + y + z = 10 option a is the ans
Answer: a
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 43 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 60 % then output equals 176 to restore new holidy demand output to original 100 . final - initial / final * 100 = 76 / 176 * 100 = 8 / 33 * 100 = 43 % approxiamately . option d is correct ."
Answer: d
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 405 , b ) 420 , c ) 440 , d ) 447 , e ) 490
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 38 t t = 14 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 14 = 490 miles answer : - e"
Answer: e
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,200
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 2500 net price of the car in 02 = 18700 + 2500 = $ 21200 correct option : e"
Answer: e
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 35 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: total time taken by jerry = ( 8 / 40 ) * 60 minutes + 15 minutes + ( 20 / 60 ) * 60 minutes = 47 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 47 / 60 ) hours = 28 * 60 / 47 = 35 miles per hour answer : option a
Answer: a
Problem: john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 50 %
Rationale: "increase = ( 20 / 40 ) * 100 = 50 % . e"
Answer: e
Problem: - 69 * 39 + 450 = ?
Options: a ) 2736 , b ) 2309 , c ) - 2801 , d ) - 2241 , e ) none of these
Rationale: "= > - 69 * ( 40 - 1 ) + 450 ; = > - ( 69 * 40 ) + 69 + 450 ; = > - 2760 + 519 = - 2241 . correct option : d"
Answer: d
Problem: when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 3 n = 3 ( 4 ) = 12 , which leaves a remainder of 4 when divided by 8 . answer b"
Answer: b
Problem: two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 72 min , d ) 75 min , e ) 130 min
Rationale: "1 / 40 - ( 1 / 45 + 1 / 60 ) = - 1 / 72 third pipe can empty in 72 minutes answer : c"
Answer: c
Problem: a car takes 6 hours to cover a distance of 450 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 450 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 450 / 9 = 50 kmph answer b ."
Answer: b
Problem: a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - .
Options: a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728
Rationale: since each ring consists of six different letters , the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216 . of these attempts , one of them is a successful attempt . maximum number of unsuccessful attempts = 216 - 1 = 215 . answer : c
Answer: c
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 240000 , c ) 153600 , d ) 154000 , e ) 154200
Rationale: "perimeter = distance covered in 10 min . = 12000 x 10 m = 2000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2000 or x = 200 . length = 600 m and breadth = 400 m . area = ( 600 x 400 ) m 2 = 240000 m 2 . b"
Answer: b
Problem: average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1250
Rationale: "0.16 x = 4 ( 850 - 800 ) 0.16 x = 200 x = 1250 answer e"
Answer: e
Problem: a person started from point a to point b and returned back to a with a speed of 60 kmh . if the distance between a and b is 120 km , calculate the time he travelled
Options: a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 6 hours , e ) 5 hours
Rationale: time = distance / speed total distance = ( from a - > b and from b - > a ) = 120 + 120 = 240 km speed = 60 kmh 240 / 60 = 4 answer : a
Answer: a
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15
Rationale: "the total number of ways to choose 5 managers is 7 c 5 = 21 we need to subtract the number of groups which include the two managers , which is 5 c 3 = 10 . 21 - 10 = 11 the answer is d ."
Answer: d
Problem: ravi and sunil are partners in a business . ravi invests rs . 15,000 for 8 months and sunil invested rs . 8000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 120000 : 80000 = 3 : 2 answer : c"
Answer: c
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 50 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 50 , then the total rent the motel charged for that night would have been reduced by 25 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 50 $ , then total difference in prices = 10 $ * 10 = 100 $ total rent the motel charged would have been reduced by 25 % . 25 x = 100 = > x = 400 answer a
Answer: a
Problem: if price of t . v set is reduced by 10 % , then its sale increases by 85 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 67 , e ) 48
Rationale: - a + b + ( ( - a ) ( b ) / 100 ) = - 10 + 85 + ( - 10 * 85 ) / 100 = - 10 + 85 - 8.5 = 67 answer : d
Answer: d
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 20 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 22.4 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 20 ) = 245 sell price = 300 gain = ( 55 / 245 ) * 100 = 22.4 % . answer : a"
Answer: a
Problem: which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ?
Options: a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90
Rationale: let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c .
Answer: c
Problem: anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 5 + 6 + 11 = 22 . answer is a ."
Answer: a
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,000 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 120 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 120 / 800 * 1 / 600 = 1 / 8,000 . answer : b ."
Answer: b
Problem: a man is walking at the rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) 2500 meters
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 10 â ˆ — 5 / 18 = 25 / 9 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 25 / 9 â ˆ — 900 = 2500 meter option e"
Answer: e
Problem: 826924 × 9999 = ?
Options: a ) 8248402936 , b ) 8268413076 , c ) 8268413071 , d ) 8064329671 , e ) 8244563371
Rationale: "b 8268413076 826924 × 9999 = 826924 × ( 10000 - 1 ) = 826924 × 10000 - 826924 × 1 = 8269240000 - 826924 = 8268413076"
Answer: b
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 144 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 40 % , e ) 72 %
Rationale: answer : d 144 ° divided by 360 ° equals 0.4 , therefore the sector is equal to 40 % of the total
Answer: d
Problem: a train speeds past a pole in 15 seconds and a platfrom 100 m long in 25 seconds . its length is :
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) none
Rationale: "sol . let the length of the train be x metres and its speed be y m / sec . they , x / y = 15 ⇒ y = x / 15 ∴ x + 100 / 25 = x / 15 ⇔ x = 150 m . answer d"
Answer: d
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 . 55 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 50 , 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 . 55 . thus , 3434 ( 90 + x ) = 55 + x or 270 + 3 x = 220 + 4 x or x = 50 answer : d
Answer: d
Problem: in a ratio which is equal to 2 : 4 , if the antecedent is 50 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 100 , d ) 51 , e ) 80
Rationale: "we have 2 / 4 = 50 / x 2 x = 50 * 4 x = 100 consequent = 100 answer is c"
Answer: c
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 1.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 18 , c ) 1 / 10 , d ) 2 , e ) 30
Rationale: "pete covered 1.5 * 60 = 90 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 90 = 1 / 18 . answer : b ."
Answer: b
Problem: the average of 50 numbers is 38 . if two numbers 45 and 55 are discarded , the average of the remaining set of numbers is
Options: a ) 38.5 , b ) 37.5 , c ) 37.0 , d ) 36.5 , e ) none of these
Rationale: average of the remaining set of numbers [ 50 x 38 - ( 45 + 55 ) ] / ( 50 - 2 ) = ( 1900 - 100 ) / 48 = 37.5 answer : b
Answer: b
Problem: i bought two books ; for rs . 420 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 245 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 420 - x ) 119 / 100 x = 245 answer : b"
Answer: b
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 6 years will be
Options: a ) 2 : 3 , b ) 7 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 11 : 9
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 6 ) : ( 12 + 6 ) = 22 : 18 = 11 : 9 answer : e"
Answer: e
Problem: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 5 m 3 , then the rise in the water level in the tank will be :
Options: a ) 31.25 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 5 x 50 ) m 3 = 250 m 3 rise in water level = 250 / 40 ã — 20 = 0.3125 m = 31.25 cm answer : a"
Answer: a
Problem: if the price of petrol increases by 20 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 16.7 % , b ) 20 % , c ) 24.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 20 ) i . e 120 . now , his consumption should be reduced to : - = ( 120 − 100 ) / 120 ∗ 100 . hence , the consumption should be reduced to 16.7 % . answer : a"
Answer: a
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 35 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.3 * 0.6 = 0.18 of the class are female science majors . then 0.22 of the class are male science majors . 0.4 x = 0.22 x = 0.55 = 55 % the answer is c .
Answer: c
Problem: a cargo ship carrying 4 kinds of items , doohickies , geegaws , widgets , and yamyams , arrives at the port . each item weighs 2 , 11 , 5 , and 7 pounds , respectively , and each item is weighed as it is unloaded . if , in the middle of the unloading process , the product of the individual weights of the unloaded items equals 104 , 350400 pounds , how many widgets have been unloaded ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 25 , e ) 20 , 870,080
Rationale: we need to know the number of widgets ( which weigh 5 pounds each ) . the number of times that 5 divides the number is related to the number of times that 10 divides the number . when we divide 104 , 350,400 by 100 , we get 104 , 350,400 = 1 , 043,504 * 5 ^ 2 * 2 ^ 2 . 1 , 043,504 is not divisible by 5 , thus there are 2 widgets . the answer is a .
Answer: a
Problem: what is the sum of all the composite numbers up to 18 ?
Options: a ) 228 , b ) 112 , c ) 80 , d ) 96 , e ) 100
Rationale: explanation : 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112 answer : b
Answer: b
Problem: if 10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 100 , b ) 10,000 , c ) 100,000 , d ) 0.01 , e ) 0.0001
Rationale: "10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 10,000 microns = 1 , 000,000 angstroms 1 micron = 100 answer : a"
Answer: a
Problem: this year , mbb consulting fired 5 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees , each earning 1 $ . after the cut , 95 are left , each earning 1.1 $ . 1.1 * 95 = 104.5 100 * 1 = 100 this gives you the answer . answer : c"
Answer: c
Problem: during a certain two - week period , 75 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 2 / 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 5 a , b ) 10 a , c ) 15 a , d ) 18 a , e ) 25 a
Rationale: "movies : 75 % comedies . 25 % remaining genre . now in this 25 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 2 x / 3 . total 5 x / 3 . 5 x / 3 = 25 ; x = 15 action movies : 15 % drama movies : 10 % we can say that out of 100 z , : comedies : 75 z action : 15 z drama : 10 z now action movies were a this means : a = 15 z . z = a / 15 comedies : 75 z = 75 * ( a / 15 ) 5 a a is the answer ."
Answer: a
Problem: rs 60000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 60000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 60000 + y so y = 10000 then x = 50000 - 10000 = 40000 first part = 40000 answer : b"
Answer: b
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.2 % , b ) 0.4 % , c ) 0.6 % , d ) 0.8 % , e ) 1 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 ) * x * ( 96 / 100 ) * y = ( 504 / 500 ) ( xy ) error in measurement = ( 504 / 500 ) xy - xy = ( 4 / 500 ) xy error % = [ ( 4 / 500 ) xy * ( 1 / xy ) * 100 ] % = ( 4 / 5 ) % = 0.8 % . answer d 0.8 %"
Answer: d
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability g is 2 / 3 . d"
Answer: d
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 4 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 4 , d ) 8 , e ) 10
Rationale: "explanation : the least number of trees that are required = lcm ( 2 , 4,4 ) = 4 . answer : c"
Answer: c
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ?
Options: a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c .
Answer: c
Problem: a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6
Rationale: to find the least amount that must be added to the account to split the money evenly among 9 of its vendors , the total divisible by 9 simply add the individual digits of the total = 3 + 2 + 9 + 8 + 6 + 4 = 32 if you add 4 , the number is divisible by 9 ( 32 + 4 ) correct option : d
Answer: d
Problem: an escalator moves towards the top level at the rate of 10 ft . sec and its length is 112 feet . if a person walks on the moving escalator at the rate of 4 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 112 / ( 10 + 4 ) = 8 sec answer : d"
Answer: d
Problem: if - 2 / ( a - 6 ) = 4 / ( a + 4 ) , then a = ?
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 5 / 3 , d ) 8 / 3 , e ) 7 / 3
Rationale: "multiply all terms of the given equation by ( a - 6 ) ( a + 4 ) , simplify and solve ( a - 6 ) ( a + 4 ) [ - 2 / ( a - 6 ) ] = ( a - 6 ) ( a + 4 ) [ 4 / ( a + 4 ) ] - 2 ( a + 4 ) = 4 ( a - 6 ) a = 8 / 3 correct answer d"
Answer: d
Problem: what is the total surface area in square meters of a rectangular solid whose length is 5 meters , width is 4 meters , and depth is 1 meters ?
Options: a ) 48 m 2 , b ) 40 m 2 , c ) 50 m 2 , d ) 58 m 2 , e ) 62 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 5 * 4 + 4 * 1 + 5 * 1 ) = 2 ( 20 + 4 + 5 ) = 2 * 29 = 58 m 2 answer : d"
Answer: d
Problem: in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 17 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 34 = > 2 x = 34 = > x = 17 d"
Answer: d
Problem: what is the units digit of ( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 = 6 ! ( 7 ! + 4 ! ) / 2 = 240 ( 1680 + 24 ) / 2 = 204480 units digit of the above product will be equal to 0 answer a"
Answer: a
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25
Rationale: "12 * 63 = 756 756 % 21 = 36 answer : b"
Answer: b
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . v = 4 + 4 + 4 = 12 . answer a"
Answer: a
Problem: a tank can supply water to a village for 30 days . if a leak at the bottom of the tank drains out 15 liters per day , the supply lasts for 20 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 18
Rationale: "losing 15 liters per day results in a loss of 300 liters in 20 days . so , those 300 liters were for 10 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 30 = 900 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 900 / 50 = 18 days . the answer is e ."
Answer: e
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 12348 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 5,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 12348 pi r = 21 so area = 4 . pi . r ^ 2 = 1764 . pi = 1764 x 3.14 = 5000 ( approx ) e"
Answer: e
Problem: a room of 2 m 40 cm long and 4 m 20 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 23 , b ) 25 , c ) 28 , d ) 60 , e ) 240
Rationale: "explanation : area of the room = 240 * 420 sq cm size of largest square tile = h . c . f of 240 cm and 420 cm = 60 cm area of 1 tile = 60 * 60 sq cm no . of tiles required = ( 240 * 420 ) / ( 60 * 60 ) = 28 answer : c ) 28"
Answer: c
Problem: how many times in a day , the hands of a clock are shows opposite directions ?
Options: a ) 12 , b ) 20 , c ) 21 , d ) 23 , e ) 22
Rationale: "sol . in 12 hours , the hands coincide or are in opposite direction 11 times . â ˆ ´ in 24 hours , the hands coincide or are in opposite direction 22 times a day . ( between 5 and 7 they point in opposite directions at 6 o ' clock only ) answer e"
Answer: e
Problem: the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is :
Options: a ) 4 / 0 , b ) 4 / 1 , c ) 4 / 5 , d ) 4 / 2 , e ) 4 / 3
Rationale: "explanation : let the required fraction be x . then , ( 1 / x ) - x = 9 / 20 1 - x ^ ( 2 ) / x = 9 / 20 = > 20 - 20 * x ^ ( 2 ) = 9 * x . 20 * x ^ ( 2 ) + 9 * x - 20 = 0 . = > ( 4 * x + 5 ) ( 5 * x - 4 ) = 0 . = > x = 4 / 5 . answer : c ) 4 / 5"
Answer: c
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ?
Options: a ) 1500 , b ) 2000 , c ) 2500 , d ) 2800 , e ) 3000
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 3 x , rs . 5 x and rs . 4 x respectively . then , 5 x - 4 x = 1000 x = 1000 . b ' s share = rs . 3 x = rs . ( 3 x 1000 ) = rs . 3000 . answer : e"
Answer: e
Problem: a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 70 , d ) 500 , e ) 980
Rationale: average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 686 x = 70 pairs were sold . answer : c
Answer: c
Problem: one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 7 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 24 / 7
Rationale: "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 4 - - > ( 1 ) , w + 2 g = 1 / 4 - - > ( 2 ) and m + g = 1 / 8 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 24 , m = 1 / 12 and w = 1 / 6 . so , n = 1 / ( 7 / 24 ) = 24 / 7 option , e"
Answer: e
Problem: what is the least number to be subtracted from 1300 to make it a perfect square ?
Options: a ) 80 , b ) 25 , c ) 75 , d ) 63 , e ) 90
Rationale: "the numbers less than 1300 and are squares of certain number is 1225 . the least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225 = 75 . answer : c"
Answer: c
Problem: the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) kg , b ) 70 kg , c ) 80 kg , d ) 90 kg , e ) 93 kg
Rationale: "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . e )"
Answer: e
Problem: the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square ?
Options: a ) 5 : 24 , b ) 5 : 19 , c ) 5 : 13 , d ) 5 : 22 , e ) 5 : 18
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 = 6400 a = ( 6400 ) ^ 1 / 2 = 80 l = 3 a and b = a - 30 b : l = a - 30 : 2 a = 50 : 240 = 5 : 24 answer : a"
Answer: a
Problem: if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 3 / 5 , d ) 5 , e ) 6
Rationale: ( 1 / x + 1 / y ) = 15 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 15 / 5 = = > ( x + y ) / 5 = 15 / ( 5 * 5 ) = 3 / 5 . c
Answer: c
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 26 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 200 km , e ) 234 km
Rationale: "0.5 x / 10 + 0.5 x / 10 = 20 - - > x / 10 + x / 10 = 40 - - > 2 x = 10 x 40 - - > x = ( 10 x 40 ) / 2 = 200 km . answer : d ."
Answer: d
Problem: a bookseller sells his books at a 10 % markup in price . if he sells a book for $ 11.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 5.00
Rationale: "let the cost price of book = x selling price of book = 11 $ markup % = 10 ( 110 / 100 ) x = 11 = > x = 10 answer c"
Answer: c
Problem: there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 , 49 for a total of 7 doors . the answer is d .
Answer: d
Problem: a train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 8 sec , c ) 10 sec , d ) 12 sec , e ) 14 sec
Rationale: "speed of the train relative to man = ( 59 + 7 ) kmph = 66 * 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 * 3 / 55 ) sec = 12 sec answer : d ."
Answer: d
Problem: the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.0 cm . what is the area of the triangle ?
Options: a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.0 * 28 / 2 = 28 cm 2 answer : a"
Answer: a
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 17.19 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 20 = 9 * 3 / 1 = 27 time difference = 17.19 ans : d"
Answer: d
Problem: the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 5 , d ) 9 , e ) 1
Rationale: s = ( 1 + 2 + 7 ) / 2 = 5 answer : c
Answer: c
Problem: a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 75 kmph , d ) 80 kmph , e ) 85 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 125 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2250 x = 70 kmph answer is b"
Answer: b
Problem: what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ?
Options: a ) 0 , b ) 8 , c ) 4 , d ) 6 , e ) 3
Rationale: i think answer on this one should be b too . since we know that 14 ^ 7 > 15 ^ 4 , as will said one should always check if the number is positive .
Answer: b
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "300 = ( 750 * 5 * r ) / 100 r = 8 % . answer : a"
Answer: a
Problem: the amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 25 hours , b ) 30 hours , c ) 20 hours , d ) 26 hours , e ) 32 hours
Rationale: "let the persons be a , b , c . hours worked : a = 4 * 120 / 12 = 40 hours b = 3 * 120 / 12 = 30 hours c = 5 * 120 / 12 = 50 hours c is the hardest worker and b worked for the least number of hours . so the difference is 50 - 30 = 20 hours . answer : c"
Answer: c
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e"
Answer: e
Problem: a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c"
Answer: c
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much r does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) r = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d ."
Answer: d
Problem: if ( n + 2 ) ! / n ! = 110 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b"
Answer: b
Problem: ( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d
Answer: d
Problem: i bought two books ; for rs . 360 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 210 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 360 - x ) 119 / 100 x = 210 answer : b"
Answer: b
Problem: if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by :
Options: a ) 6 only , b ) 12 only , c ) 6 and 12 both , d ) by 18 only , e ) 15 only
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer c ) 6 and 12 both ."
Answer: c
Problem: | 13 - 3 | - | 4 - 10 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e"
Answer: e
Problem: a fill pipe can fill 1 / 6 of cistern in 90 minutes in how many minutes , it can fill 5 / 6 of the cistern ?
Options: a ) 450 min , b ) 360 min , c ) 240 min , d ) 306 min , e ) 500 min
Rationale: "1 / 6 of the cistern can fill in 90 min 5 / 6 of the cistern can fill in = 90 * 6 * 5 / 6 = 450 min answer is a"
Answer: a
Problem: increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by
Options: a ) 12.1 % , b ) 12.36 % , c ) 12.94 % , d ) 13.65 % , e ) 14.56 %
Rationale: 1.06 * 1.06 * x = 1.1236 * x the answer is b .
Answer: b
Problem: the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees .
Options: a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3
Rationale: mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a
Answer: a
Problem: ravi and sunil are partners in a business . ravi invests rs . 18,000 for 8 months and sunil invested rs . 10000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 36 : 25 , c ) 3 : 2 , d ) 4 : 5 , e ) 20 : 45
Rationale: "= ( 18000 * 8 ) : ( 10000 * 10 ) = 144000 : 100000 = 36 : 25 answer : b"
Answer: b
Problem: if | x | = 5 x - 3 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . c"
Answer: c
Problem: the area of a square is 4489 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 43 : 134
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 = 4489 a = 67 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 43 : 134 answer : e"
Answer: e
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 12 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 36
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 12 = > m = 36 answer e"
Answer: e
Problem: a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .
Options: a ) 4
b ) 5
c ) 6
d ) 7
e ) 2
Rationale: first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 12 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 3 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 2 inches . add the totals together to get the rectangular cube surface area of 17 inches . since a square cube has 6 sides , divide the surface area by 6 . this calculates to 2.833 inches as the surface area of each side of the cube . the square root of 2.833 is 1.683 . rounding to the nearest whole number that makes each side of the cube measuring 2 inches . the correct answer is ( e ) .
Answer: e
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 7.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 1,600 , d ) $ 1,250 , e ) $ 1,500
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 7 = $ 3500 profit : 3500 - 1900 = $ 1600 option c is correct"
Answer: c
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 100 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 79.55 $ , b ) 80.63 $ , c ) 81.63 $ , d ) 80.27 $ , e ) 83.15 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 100 x = 81.27 hence , the correct option is d"
Answer: d
Problem: a garrison of 2000 men has provisions for 54 days . at the end of 21 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1300
Rationale: "2000 - - - - 54 2000 - - - - 33 x - - - - - 20 x * 20 = 2000 * 33 x = 3300 2000 - - - - - - - 1300 answer : e"
Answer: e
Problem: a person buys an article at $ 200 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 240 , b ) 260 , c ) 220 , d ) 300 , e ) 360
Rationale: "c 220 cost price = $ 200 profit = 10 % of 200 = $ 20 selling price = cost price + profit = 200 + 20 = 220"
Answer: c
Problem: 200 liters of a mixture contains milk and water in the ratio 4 : 1 . if 20 liters of this mixture be replaced by 20 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 6 : 1 , b ) 1 : 6 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 1
Rationale: "quantity of milk in 200 liters if mix = 200 * 4 / 5 = 160 liters quantity of milk in 210 liters of new mix = 160 + 20 = 180 liters quantity of water in it = 210 - 180 = 30 liters ratio of milk and water in new mix = 180 : 30 = 6 : 1 answer is a"
Answer: a
Problem: if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a"
Answer: a
Problem: when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"
Answer: c
Problem: two identical trains aa and bb running in opposite direction at same speed tale 2 min to cross each other completely . the number of bogies of aa are increased from 12 to 16 . how much more time would they now require to cross each other ?
Options: a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 20 sec , e ) 25 sec
Rationale: total initial bogies is 12 + 12 = 2412 + 12 = 24 additional bogies = 16 â ˆ ’ 12 = 4 24 bogies is 12 + 12 = 24 additional bogies = 16 - 12 = 4 24 bogies take 2 min 2 * 60 / 24 * 4 = 20 sec answer d
Answer: d
Problem: express 5 mps in kmph ?
Options: a ) 22 , b ) 88 , c ) 90 , d ) 18 , e ) 24
Rationale: "5 * 18 / 5 = 18 kmph answer : d"
Answer: d
Problem: a person starting with rs . 64 and making 6 bets , wins 3 times and loses 3 times , the wins and loses occurring in random order . the chance for a win is equal to the chance for a loss . if each wager is for 1 / 2 the money remaining at the time of the bet , then the final result is ?
Options: a ) rs . 23 , b ) rs . 37 , c ) rs . 45 , d ) rs . 67 , e ) rs . 77
Rationale: as the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5 , we will multiply initial amount by 1.5 thrice and by 0.5 thrice ( in any order ) . the overall resultant will remain same . so final amount with the person will be ( in all cases ) : = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = rs 2727 hence the final result is : 64 − 27 = 3764 − 27 = 37 : a loss of rs . 37 b
Answer: b
Problem: a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 90 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 90 km downstream = 90 / 30 hrs = 3 hrs . answer : c"
Answer: c
Problem: how many ounces of a 60 % salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 60 + . 6 x = . 4 ( 60 + x ) x = 60 answer d"
Answer: d