regisss/math_qa huggingface dataset:
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Problem: the product of the squares of two positive integers is 1600 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : e - 4 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 1600 [ square root both sides ] xy = 40 40 = 1 x 40 , 4 x 10 , 40 x 1 , 10 x 4 , 5 x 8 , 8 x 5 , 20 x 2 , 2 x 20 cancel the repeats this leaves us with exactly 4 options . hence , e"
Answer: e
Problem: what percent is 20 % of 25 % ?
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: required percentage = 20 % / 25 % * 100 = 20 / 25 * 100 = 80 % answer is e
Answer: e
Problem: walking at 40 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 16 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: speed is inversly proprtional to time walking at 40 % of speed meand 2 / 5 s takes 5 / 2 t . it takes 24 minutes extra to cover the distance . then 5 / 2 t = t + 24 5 t = 2 t + 48 3 t = 48 t = 16 . option a is correct
Answer: a
Problem: the area of the largest circle that can be drawn inside a square of side 70 cm in length is :
Options: a ) 3600
b ) 2646
c ) 3850
d ) 4215
e ) 5205
Rationale: radius of required circle = 35 cm its area = 22 / 7 × 35 × 35 110 × 35 = 3850 cm ( power ) 2 answer is c .
Answer: c
Problem: there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b"
Answer: b
Problem: the speed of a train is 70 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 10.66 kmph , b ) 11.66 kmph , c ) 21.66 kmph , d ) 12.66 kmph , e ) 11.96 kmph
Rationale: "70 * 10 / 60 = 11.66 kmph answer : b"
Answer: b
Problem: what is the ratio e of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?
Options: a ) 1 / 4
b ) 3 / 8
c ) 1 / 2
d ) 3 / 5
e ) 2
Rationale: one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area e = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )
Answer: d
Problem: if the operation @ is defined for all a and b by the equation a @ b = ( a ^ b ) / 2 , then ( 3 @ 2 ) = ?
Options: a ) 4 , b ) 2 , c ) 9 / 2 , d ) - 9 / 2 , e ) - 8 / 2
Rationale: work within the parenthesis first so solve ( 3 @ 2 ) first ( 3 @ 2 ) = ( 3 ^ 2 ) / 2 = 9 / 2 so 9 / 2 is the answer . . . . this question is merely testing order of operations remember pemdas answer : c
Answer: c
Problem: a boat can travel with a speed of 10 km / hr in still water . if the speed of the stream is 8 km / hr , find the time taken by the boat to go 54 km downstream .
Options: a ) 4.25 hr , b ) 5.25 hr , c ) 3 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 10 km / hr speed of the stream = 8 km / hr speed downstream = ( 10 + 8 ) = 18 km / hr time taken to travel 68 km downstream = 54 â  „ 18 = 17 â  „ 4 = 3 hours answer is c"
Answer: c
Problem: there is enough provisions for 9600 women in an army camp for 400 days . if there were 4800 men less , how long will the provision last ?
Options: a ) 799 , b ) 800 , c ) 801 , d ) 802 , e ) 803
Rationale: we have , m 1 d 1 = m 2 d 2 9600 * 400 = 4800 * d 2 d 2 = 9600 * 400 / 4800 = 800 days . answer : b
Answer: b
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 3 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 3 + 1 ) = ( √ 8 * 18 ) / 4 = ( √ 144 ) / 4 = 12 / 4 = 3 . answer is d ."
Answer: d
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 60 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 48
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 48 hence answer is e"
Answer: e
Problem: a and b began business with rs . 6000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 357 , e ) 361
Rationale: "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 17 / 30 * 630 = 357 answer : d"
Answer: d
Problem: a , b and c rents a pasture for rs . 950 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 295 , b ) 199 , c ) 676 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 950 = 295 answer : a"
Answer: a
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 2 : 1 be mixed with another mixture q of milk and water in the ratio 1 : 5 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 3 : 5 , e ) 3 : 1
Rationale: "( 2 / 3 ) * p + ( 1 / 6 ) * q = ( 1 / 3 ) * p + ( 5 / 6 ) * q 2 p = 4 q p / q = 2 / 1 the answer is b ."
Answer: b
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 350 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 2,900 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 350 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 350 x 8 = 2800 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 2900 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 2900 ( answer b )"
Answer: b
Problem: ifaequals the sum of the even integers from 2 to 80 , inclusive , andbequals the sum of the odd integers from 1 to 79 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 40 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 80 - 2 ) / 2 + 1 = 40 even integers . ( 80 + 2 ) / 2 = 41 is the average of the even set . sum = avg * ( # of elements ) = 41 * 40 = 1640 = a odd numbers : ( 79 - 1 ) / 2 + 1 = 40 odd integers . ( 79 + 1 ) / 2 = 40 is the average of the odd set . sum = avg * ( # of elements ) = 40 * 40 = 1600 = b a - b = 1640 - 1600 = 40 . answer : d"
Answer: d
Problem: if 31 % of a number is 46.5 , the number is ?
Options: a ) 150 , b ) 155 , c ) 160 , d ) 165 , e ) none
Rationale: "answer let 31 % of a = 46.5 ⇒ ( 31 x a ) / 100 = 46.5 ∴ a = ( 46.5 x 100 ) / 31 = 150 correct option : a"
Answer: a
Problem: if an average hard drive had a capacity of 0.6 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 6144 , e ) 1536
Rationale: "0.6 * 2 ^ 10 = 0.6 * 1024 = 614.4 the answer is d ."
Answer: d
Problem: two digits in father ' s age are the same as the digit in the son ' s age , but in reverse order . in 5 years father will be twice as old as son will be then . what is the difference in their current age ?
Options: a ) 18 , b ) 16 , c ) 34 , d ) 25 , e ) 12
Rationale: father ' s age = 10 x + y so son ' s age = 10 y + x . . after 5 years , 10 x + y + 5 = 2 * ( 10 y + x + 5 ) . . . . so 5 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 3 . . . so ages are 31 and 13 and ans as found correctly by u is a . . 18
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 300 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 18 ) m = 300 m . answer : c"
Answer: c
Problem: the average monthly income of a and b is rs . 5050 . the average monthly income of b and c is rs . 6250 and the average monthly income of a and c is rs . 5200 . what is the monthly income of a ?
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6200
Rationale: "explanation : let monthly income of a = a monthly income of b = b monthly income of c = c a + b = 2 × 5050 . . . . ( equation 1 ) b + c = 2 × 6250 . . . . ( equation 2 ) a + c = 2 × 5200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > a + b + a + c - ( b + c ) = ( 2 × 5050 ) + ( 2 × 5200 ) - ( 2 × 6250 ) = > 2 a = 2 ( 5050 + 5200 - 6250 ) = > a = 4000 i . e . , monthly income of a = 4000 answer is c"
Answer: c
Problem: x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 1 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 1 are 3 , 2 , and 1 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 24 the answer is a ."
Answer: a
Problem: a man is 28 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 28 . = > 2 ( x + 4 ) = ( x + 28 + 4 ) = > 2 x + 8 = x + 32 = > x = 24 years answer : option d"
Answer: d
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 529 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 23
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 529 / 3 = 176.33 sq m l b = 176.33 i . e . , l * l / 3 = 176.33 l ^ 2 = 529 = > l = 23 e"
Answer: e
Problem: walking at 5 / 6 th of its usual speed a cab is 8 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 40 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 8 m ut / 5 = 8 m ut = 40 m answer is c"
Answer: c
Problem: a and b can do a piece of work in 4 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 4.05 days , b ) 5.05 days , c ) 14.76 days , d ) 8.05 days , e ) 15.05 days
Rationale: "a + b = 1 / 4 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 4 + 1 / 12 + 1 / 16 = 19 / 48 a + b + c = 19 / 96 96 / 19 = 5.05 days answer : b"
Answer: b
Problem: a certain machine produces 780 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 4 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 74,880 , d ) 100,000 , e ) 168,000
Rationale: "since 7 days consist of 24 * 4 hours the total is 96 hours . since every hour the machine produces 780 units of product p the total product during 96 hours is 96 * 780 = 74,880 . correct option : d"
Answer: d
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 39 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "first , let ' s translate the expression 21 # 39 , using the definition given : 21 # 39 = 21 × 24 × 27 × 30 × 33 × 36 × 39 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 39 = 3 ^ 7 ( 7 × 8 × 9 × 10 × 11 × 12 × 13 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 39 = 3 ^ 7 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 × ( 2 ^ 2 × 3 ) × 13 ) let ' s group the prime bases : 21 # 39 = 2 ^ 6 × 3 ^ 10 × 5 × 7 × 11 × 13 the sum of the exponents is 6 + 10 + 1 + 1 + 1 + 1 = 20 the answer is d ."
Answer: d
Problem: the cost of 3 pens and 5 pencils is rs . 200 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) rs . 600
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 200 15 x + 5 x = rs . 200 x = 200 / 20 = 10 : . cost of 1 pen = 5 x = 5 x 10 = 50 : . cost of 12 pens , i . e . ( one dozen ) = 50 x 12 = rs . 600 answer : option e"
Answer: e
Problem: the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 5 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: "let the average age of the whole team be x years . 11 x - ( 25 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c ."
Answer: c
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 72 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 48 % , b ) 54 % , c ) 60 % , d ) 64 % , e ) 68 %
Rationale: 72 % is 8 % - points below 80 % and 17 % - points above 55 % . so the ratio of solution p to solution q is 17 : 8 . mixture p is 17 / 25 = 68 % of the volume of mixture pq . the answer is e .
Answer: e
Problem: there are 3 girls and 6 boys . how many kids are there ?
Options: a ) 10 , b ) 19 , c ) 20 , d ) 9 , e ) 12
Rationale: d
Answer: d
Problem: two numbers n and 16 have lcm = 48 and gcf = 8 . find n .
Options: a ) 11 , b ) 32 , c ) 24 , d ) 48 , e ) 50
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 8 n = 48 * 8 / 16 = 24 correct answer c"
Answer: c
Problem: if y > 0 , ( 2 y ) / 5 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: can be reduced to 2 y / 5 + 3 y / 10 = 2 y / 5 = 70 % d
Answer: d
Problem: convert 200 inches into centimeter ?
Options: a ) 512 cm , b ) 520 cm , c ) 508 cm , d ) 510 cm , e ) 554 cm
Rationale: "1 inch = 2.54 cm 200 inches = 200 * 2.54 = 508 cm answer is c"
Answer: c
Problem: if an object travels at seven feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 25200 , e ) 18000
Rationale: "speed = 7 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 7 = 25200 answer d"
Answer: d
Problem: evaluate : 2344 - 12 * 3 * 2 = ?
Options: a ) 2337 , b ) 1227 , c ) 3327 , d ) 5457 , e ) 7677
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 2344 - 12 * 3 * 2 = 2344 - 8 = 2337 correct answer a"
Answer: a
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 20 % of the final price - - > ( final price ) * 0.8 = $ 18 - - > ( final price ) = $ 22.5 . answer : d ."
Answer: d
Problem: the product of x and y is a constant . if the value of x is increased by 80 % , by what percentage must the value of y be decreased ?
Options: a ) 45 % , b ) 55 % , c ) 35 % , d ) 40 % , e ) 44.44 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.8 x ( 180 ) i . e . 180 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 180 = 55.55 i . e . y decreases from 100 to 55.55 i . e . decrease of 44.44 % answer : option e"
Answer: e
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 90 km / hr
Options: a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 4 seconds
Rationale: "first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 100 / 25 = 4 seconds answer : e"
Answer: e
Problem: the roof of an apartment building is rectangular and its length is 7 times longer than its width . if the area of the roof is 847 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 66 . , d ) 44 . , e ) 46 .
Rationale: "answer is c : 66 let w be the width , so length is 7 w . therefore : w * 7 w = 847 , solving for , w = 11 , so 7 w - w = 6 w = 6 * 11 = 66"
Answer: c
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 3000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 600 , e ) 1200
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 3000 = > 5 parts out of 15 parts is rs . 3000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 3000 ) = rs . 1200 answer : e"
Answer: e
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 9 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = 9 years . answer : c"
Answer: c
Problem: the circumferences of two circles are 660 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2996 sq m , b ) 4774 sq m , c ) 4312 sq m , d ) 2768 sq m , e ) 2786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 660 and 2 ∏ l = 704 s = 660 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 330 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 330 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 330 - 352 ) ( 330 + 352 ) / ∏ = ( 22 ) ( 682 ) / ( 22 / 7 ) = 4774 sq m answer : b"
Answer: b
Problem: p is 30 % more efficient than q . p can complete a work in 23 days . if p and q work together , how much time will it take to complete the same work ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 13 , e ) 15
Rationale: "work done by p in 1 day = 1 / 23 let work done by q in 1 day = q q × ( 130 / 100 ) = 1 / 23 = > q = 100 / ( 23 × 130 ) = 10 / ( 23 × 13 ) work done by p and q in 1 day = 1 / 23 + 10 / ( 23 × 13 ) = 23 / ( 23 × 13 ) = 1 / 13 = > p and q together can do the work in 13 days option d"
Answer: d
Problem: suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have
Options: a ) 4
b ) 6
c ) 9
d ) 10
e ) 5
Rationale: to arrange them as described i did as follows on my scratch paper ( see the file attached ) , where i counted 4 sides and bottom , hence 4 + 1 = 5 . e
Answer: e
Problem: the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 48 , e ) 50
Rationale: "so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 difference = 50 - 25 = 25 answer : b ."
Answer: b
Problem: how many positive integers less than 10,000 are such that the product of their digits is 30 ?
Options: a ) 12 , b ) 24 , c ) 36 , d ) 38 , e ) 50
Rationale: "30 = 1 * 30 , 2 * 15 , 3 * 10 , 5 * 6 we have the option of using single digits 1,2 , 3,5 and 6 no : of four digit numbers such that the product is 30 the possible combinations are using digits ( 1,2 , 3,5 ) & ( 1,1 , 5 , 6 ) such that the product 30 . no : of different combinations possible using ( 1,2 , 3,5 ) = 4 ! = 24 no : of different combinations possible using ( 5,6 , 1,1 ) = 4 ! / 2 ! = 12 ( ' 1 ' is repeated twice ) total 4 digit numbers so that the product is 30 is 24 + 12 = 36 no : of three digit numbers such that the product is 30 the possible combinations are using digits ( 2,3 , 5 ) & ( 1 , 5,6 ) no : of different combinations possible using ( 2 , 3,5 ) = 3 ! = 6 no : of different combinations possible using ( 1 , 5,6 ) = 3 ! = 6 total 3 digit numbers so that the product is 30 is 6 + 6 = 12 no : of 2 digit numbers such that the product is 30 is 2 ( 56 and 65 ) total numbers under 10000 such that the product is 30 is 36 + 12 + 2 = 50 e"
Answer: e
Problem: the speed at which a man can row a boat in still water is 16 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 100 metres ?
Options: a ) 23 , b ) 27 , c ) 28 , d ) 12 , e ) 18
Rationale: speed of the boat downstream = 16 + 4 = 20 kmph = 20 * 5 / 18 = 5.55 m / s hence time taken to cover 100 m = 100 / 5.55 = 18 seconds . answer : e
Answer: e
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "per quarter , interest = 2 % so for a year , interest = 8 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 8 % answer = 8.25 % = answer : d"
Answer: d
Problem: the sale price sarees listed for rs . 390 after successive discount is 14 % and 15 % is ?
Options: a ) 285 , b ) 277 , c ) 290 , d ) 662 , e ) 262
Rationale: "390 * ( 86 / 100 ) * ( 85 / 100 ) = 285 answer : a"
Answer: a
Problem: with both inlets open , a water tank will be filled with water in 42 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 7,000 , b ) 10,500 , c ) 11,750 , d ) 12,000 , e ) 13,000
Rationale: "the work done by inlet a and b together in 1 min = 1 / 42 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 42 ) - ( 1 / 120 ) = 1 / 65 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 65 ) - ( 1 / 120 ) = 50 cubic meter = 7000 cubic meter answer : option a"
Answer: a
Problem: if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 91 and a perimeter of 40 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 91 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . let ' s test answer b : 7 if . . . the shorter side = 7 . . . the area = 91 . . . . 91 / 7 = 13 = the longer side perimeter = 7 + 7 + 13 + 13 = 40 b"
Answer: b
Problem: the ratio of the volumes of two cubes is 27 : 125 . what is the ratio of their total surface areas ?
Options: a ) 9 : 25 , b ) 9 : 35 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 27 : 3 √ 125 = 3 : 5 ratio of surface areas = 3 ^ 2 : 5 ^ 2 = 9 : 25 answer : option a"
Answer: a
Problem: the ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50 . if in a day , rs . 1 , 325 are collected from the passengers travelling between the two stations , then the amount collected from the second class from the second class passengers is
Options: a ) 1,250 , b ) 1,000 , c ) 850 , d ) 750 , e ) 350
Rationale: explanation : let the fares be 3 x and x respectively for the first and second class . suppose in a day passengers travelling between the two stations be 1 and 50 . then by given condition , 3 x × 1 + x × 50 = 1,325 = > x = 25 the amount collected from second class = 25 × 50 = rs . 1250 answer : a
Answer: a
Problem: find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2
Rationale: "1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e"
Answer: e
Problem: a club wants to mix 20 pounds of candy worth $ 10.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 10 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 200 + 5 w = > w = 80 answer e"
Answer: e
Problem: the reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 166
Rationale: "reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 so , hcf = 12 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 12 * 312 / 24 = 156 answer : d"
Answer: d
Problem: a can do a piece of work 20 days . b can do work in 35 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16.32 days , c ) 12.72 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 140 , ratio = 20 : 35 = 4 : 7 no of days = 140 / ( 4 + 7 ) = 90 / 5 = 12.72 days answer : c"
Answer: c
Problem: the sale price shirts listed for rs . 1000 after successive discount is 15 % and 2 % is ?
Options: a ) 338 , b ) 823 , c ) 833 , d ) 337 , e ) 733
Rationale: "1000 * ( 85 / 100 ) * ( 98 / 100 ) = 833 answer : c"
Answer: c
Problem: what is the ratio of 4 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 4 : 49 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "4 / 7 / 21 / 3 = 4 / 49 . . . imo option a ."
Answer: a
Problem: exactly 5 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 92 % , e ) 90 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 5 % of all reporters reporters covering politics / all reporters = 5 / 70 = 1 / 14 reporters not covering politics / all reporters = 13 / 14 = 92 % = d"
Answer: d
Problem: kanul spent $ 35000 in buying raw materials , $ 40000 in buying machinery and 20 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 87952 , b ) $ 93750 , c ) $ 89542 , d ) $ 95820 , e ) $ 84256
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 35000 + 40000 80 % of x = 75000 80 x / 100 = 75000 x = $ 93750 answer is b"
Answer: b
Problem: the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 18 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 18 a - c = 18 answer is d"
Answer: d
Problem: the sector of a circle has radius of 21 cm and central angle 150 o . find its perimeter ?
Options: a ) 91.5 , b ) 91.4 , c ) 97 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 150 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 55 + 42 = 97 cm answer : c"
Answer: c
Problem: tom drives from town w to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between w and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point w to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Problem: the average of first 12 natural numbers is ?
Options: a ) 5.2 , b ) 6.5 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 12 natural no . = 156 / 2 = 78 average = 78 / 12 = 6.5 answer : b"
Answer: b
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 65 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 55 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 65 - { both correctly } + 5 { both correctly } = 55 . answer : b ."
Answer: b
Problem: what is the average of 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1 , 1.20 , and 11.25 ?
Options: a ) 21.06 , b ) 23 , c ) 26 , d ) 23.69 , e ) 22.56
Rationale: "add 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1,12 , and 11.25 grouping numbers together may quicken the addition sum = 231.75 231.75 / 11 = 21.06 a"
Answer: a
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 5 % ?
Options: a ) 20 % , b ) 29 % , c ) 10 % , d ) 80 % , e ) 42.5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 95 2 / 3 sp 1 = 95 sp 1 = 142.5 100 - - - 42.5 = > 42.5 % answer : e"
Answer: e
Problem: a jewelry store purchased a pair of earrings for $ 240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price . after some time a jewelry store owner decided to decrease the selling price by 20 percent . what was the jewelry store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 16 , e ) $ 18
Rationale: sale price ( sp ) = 240 + markup ( mp ) - - > mp = sp - 240 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 240 3 sp / 4 = 240 sp = 320 now a discount of 20 % is given so new sp is . 8 * 320 = 256 profit = 256 - 240 = 16 answer is d
Answer: d
Problem: if 1 / 4 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 12 are from africa , 1 / 6 are from asia and the remaining 36 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: "1 / 4 + 1 / 8 + 1 / 12 + 1 / 6 = ( 6 + 3 + 2 + 4 ) / 24 = 15 / 24 let x be the number of passengers on the ship . 36 = ( 9 / 24 ) x = 3 x / 8 x = 96 the answer is b ."
Answer: b
Problem: a hare and a tortoise have a race along a circle of 100 yards diameter . the tortoise goes in one direction and the hare in the other . the hare starts after the tortoise has covered 1 / 5 of its distance and that too leisurely . the hare and tortoise meet when the hare has covered only 1 / 8 of the distance . by what factor should the hare increase its speed so as to tie the race ?
Options: a ) 37.9 , b ) 37.2 , c ) 37.1 , d ) 37.82 , e ) 37.8
Rationale: assume the circumference of the circle is 200 meters . hare and tortoise started at the same point but moves in the opposite direction . it is given that by that time tortoise covered 40 m ( 1 / 5 th of the distance ) , hare started and both met after hare has covered 25 . this implies , in the time hare has covered 25 m , hare has covered 200 - 40 - 25 = 135 meters . so hare : tortoise speeds = 25 : 135 = 5 : 27 now hare and tortoise has to reach the starting point means , hare has to cover 175 meters and tortoise has to cover only 25 meters in the same time . as time = distancespeed = 2527 = 1755 × kdistancespeed = 2527 = 1755 × k ie . , hare has to increase its speed by a factor k . solving we get k = 37.8 answer : e
Answer: e
Problem: a certain rectangular crate measures 20 feet by 20 feet by 20 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 20 x 20 i . e . of radius 20 / 2 = 10 e"
Answer: e
Problem: jack got paid today for his part - time job as a juggler , and noticed that 20 % of his paycheck went to taxes . jack wants to spend 80 % of what ' s left on a new bike , and put the rest into savings . if jack puts $ 20 into savings , how much was his original paycheck before taxes ?
Options: a ) $ 125 , b ) $ 135 , c ) $ 145 , d ) $ 155 , e ) $ 165
Rationale: let p be jack ' s original paycheck value . the value after taxes t is given by t = p - 20 % p let s be the amount put into savings , given by s = t - 80 % t for s = $ 20 , solve for p $ 20 = ( p - 20 % p ) - 80 % ( p - 20 % p ) p = $ 125 correct answer a
Answer: a
Problem: find a sum for 1 st 5 prime no . ' s ?
Options: a ) 23 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"
Answer: b
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability w that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer w : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel two times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 2 and w = 2 s then we have 1 / ( 2 * s ) + 1 / s = 1 / 2 < = > 3 / ( 2 * s ) = 1 / 2 < = > s = 3 ans : b"
Answer: b
Problem: if a train , travelling at a speed of 90 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 135 m , b ) 125 m , c ) 129 m , d ) 120 m , e ) 165 m
Rationale: "explanation : d = 90 * 5 / 18 * 5 = 125 m answer : option b"
Answer: b
Problem: karthik read 7 / 13 th of a book in 1 st week and 5 / 9 th of the remaining book in 2 nd week . if there were 96 pages unread after 2 nd week , how many pages were there in the book ?
Options: a ) 518 , b ) 452 , c ) 468 , d ) 502 , e ) 396
Rationale: solution 96 pages were unread so on second week have 5 / 9 so unread pages = 1 - 5 / 9 = 4 / 9 96 * 9 / 4 = 216 then , on first week unread pages were 216 total pages = 216 * 13 / 6 = 468 so answer is c
Answer: c
Problem: find the quotient : 0.0204 / 17
Options: a ) 0.012 , b ) 0.12 , c ) 0.0012 , d ) 0.00012 , e ) none of them
Rationale: 204 / 17 = 12 . dividend contains 4 places of decimal . 0.2040 / 17 = 0.0012 . answer is c .
Answer: c
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 400 km ?
Options: a ) 300 , b ) 400 , c ) 250 , d ) 350 , e ) 450
Rationale: "50 kmph consumption is 1 lt / hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance . 1 lt costs $ 30 so 8 lt costs $ 240 extra expenses for 1 hr - $ 20 8 hrs - $ 160 total expense - $ 240 + $ 160 = $ 400 answer : b"
Answer: b
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 59.29 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 59.29 x 100 ) paise = 5929 paise . number of members = 5929 = 77 . answer : c"
Answer: c
Problem: if a ^ 2 + b ^ 2 = 30 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 30 - 20 = 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 30 + 20 = 50 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 50 + 10 = 60 d"
Answer: d
Problem: a can do a work in 30 days , b can do it in 20 days . they together under took to do a piece of work for rs . 1000 , what is the share of b ?
Options: a ) rs . 500 , b ) rs . 400 , c ) rs . 800 , d ) rs . 600 , e ) rs . 200
Rationale: explanation : share of their work days = 30 : 20 share of their work = 20 : 30 share of b ’ s money = 3 / 5 * 1000 = 600 answer : option d
Answer: d
Problem: 3 x ^ 2 - 6 x + 3 = 0 find the above equation find the value of x
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 ± √ ( ( - 6 ) 2 - 4 × 3 × 3 ) ) / ( 2 × 3 ) = ( 6 ± √ ( 36 - 36 ) ) / 6 = ( 6 ± 0 ) / 6 x 1 = x 2 = 1 b
Answer: b
Problem: the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is :
Options: a ) 8 % , b ) 1 % , c ) 20 % , d ) 80 % , e ) none
Rationale: "explanation : let the business value changes from x to y . then , 4 % of x = 5 % of y or 4 / 100 × x = 5 / 100 × y or y = 4 / 5 x change in business = ( x − 4 / 5 x ) = 1 / 5 x percentage slump in business = ( 1 / 5 x × 1 / x × 100 ) % correct option : c"
Answer: c
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: equate the fat : 0.1 x + 0.45 * 8 = 0.2 ( x + 8 ) - - > x = 20 . answer : e .
Answer: e
Problem: if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle .
Options: a ) 40 cm
b ) 45 cm
c ) 50 cm
d ) 52 cm
e ) 57 cm
Rationale: explanation : let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( 1 ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( 2 ) solving 1 & 2 , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : option c
Answer: c
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 110 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 7 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 70 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 110 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 7 + 4 = 11 kms / hr time taken = 110 / 11 = 10 hrs distance traveled by brad = brad ' s speed * time taken = 7 * 10 = 70 kms . . . answer - d"
Answer: d
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 15 % . staff are allowed a further 10 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.75 d , b ) 0.76 d , c ) 0.765 d , d ) 0.775 d , e ) 0.805 d
Rationale: "successive doscounts = - a - b + ab / 100 putting the values , total discount = - 15 - 10 + 150 / 100 = - 25 + 1.5 = 23.5 % discount hence the final price of the dress = d - 0.235 d = 0.765 d correct option : c"
Answer: c
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 11
Options: a ) 11 / 25 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
Rationale: total number of cases = 10 * 10 = 100 favourable cases = [ ( 2,10 ) , ( 3,9 ) , ( 3,10 ) , ( 4,8 ) , ( 4,9 ) , ( 4,10 ) , ( 5,7 ) , ( 5,8 ) , ( 5,9 ) , ( 5,10 ) , ( 6,6 ) , ( 6,7 ) , ( 6,8 ) , ( 6,9 ) , ( 6,10 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) , ( 7,8 ) , ( 7,9 ) , ( 7,10 ) , ( 8,4 ) , ( 8,5 ) , ( 8,6 ) , ( 8,7 ) , ( 8,8 ) , ( 8,9 ) , ( 8,10 ) , ( 9,3 ) , ( 9,4 ) , ( 9,5 ) , ( 9,6 ) , ( 9,7 ) , ( 9,8 ) , ( 9,10 ) , ( 10,2 ) , ( 10,3 ) , ( 10,4 ) , ( 10,5 ) , ( 10,6 ) , ( 10,7 ) , ( 10,8 ) , ( 10,9 ) , ( 10,10 ) ] = 44 so probability = 44 / 100 = 11 / 25 answer is a
Answer: a
Problem: sandy had $ 210 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 240 , b ) $ 300 , c ) $ 360 , d ) $ 420 , e ) $ 480
Rationale: "let the money sandy took for shopping be x . 0.7 x = 210 x = 300 the answer is b ."
Answer: b
Problem: if a ã — b = 2 a - 3 b + ab , then 2 ã — 5 + 5 ã — 2 is equal to :
Options: a ) 18 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 2 ã — 5 + 5 ã — 2 = ( 2 ã — 2 - 3 ã — 5 + 2 ã — 5 ) + ( 2 ã — 5 - 3 ã — 2 + 5 ã — 3 ) = ( 4 - 15 + 10 + 10 - 6 + 15 ) = 18 . answer : a"
Answer: a
Problem: if ( n + 2 ) ! / n ! = 156 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 156 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 ) = 156 from here , we might just test the answer choices . since ( 13 ) ( 12 ) = 156 , we can see that n = 11 d"
Answer: d
Problem: 18 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 230 , b ) 274 , c ) 306 , d ) 354 , e ) 424
Rationale: "2 * 18 c 2 = 2 * 153 = 306 the answer is c ."
Answer: c
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 3 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 3 + 3 = 28 meter answer is d ."
Answer: d
Problem: a 6 - liter solution is 40 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4
Rationale: let x be the amount of pure alcohol required . 0.4 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.4 x = 1.2 liters the answer is a .
Answer: a
Problem: the present population of a town is 2100 . population increase rate is 5 % p . a . find the population of town before 1 years ?
Options: a ) 1500 , b ) 1600 , c ) 2000 , d ) 2100 , e ) 2500
Rationale: "p = 2100 r = 5 % required population of town = p / ( 1 + r / 100 ) ^ t = 2100 / ( 1 + 5 / 100 ) = 2100 / ( 21 / 20 ) = 2000 ( approximately ) answer is c"
Answer: c
Problem: a math teacher has 25 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 25 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 25 - 17 = 8 answer ( a )"
Answer: a
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.3 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 34 = 66 . answer : b ."
Answer: b