regisss/math_qa huggingface dataset:
Problem: the speed at which a man can row a boat in still water is 21 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 90 metres ?
Options: a ) 23.46 , b ) 27.46 , c ) 28.46 , d ) 12.46 , e ) 25.46
Rationale: speed of the boat downstream = 21 + 5 = 26 kmph = 26 * 5 / 18 = 7.22 m / s hence time taken to cover 90 m = 90 / 7.22 = 12.46 seconds . answer : d
Answer: d
Problem: if a man lost 4 % by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 1 , b ) 8 , c ) 9 , d ) 4 , e ) 32
Rationale: "96 % - - - - 48 144 % - - - - ? 96 / 144 * 48 = 32 answer : e"
Answer: e
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 28 metre of cloth ?
Options: a ) 175 seconds , b ) 219 seconds , c ) 155 seconds , d ) 115 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 28 : x = > x = { \ color { blue } \ frac { 28 \ times 1 } { 0.128 } } = > x = 218.75 so time will be approx 219 seconds answer : b"
Answer: b
Problem: the radius of a circular wheel is 1.75 m , how many revolutions will it make in traveling 1 km ?
Options: a ) 1000
b ) 2788
c ) 2677
d ) 2899
e ) 2771
Rationale: 2 * 22 / 7 * 1.75 * x = 11000 x = 1000 answer : a
Answer: a
Problem: a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 4.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.7 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 10 + 4.2 + 6.8 = 361 numerator : 340 ( 1 - . 88 - . 05 ) + 4.2 340 ( 0.07 ) + 4.2 23.8 + 4.2 28 ratio : 28 / 361 = 0.077 answer : b"
Answer: b
Problem: if the radius of a cylinder is doubled and so is the height , what is the new volume of the cylinder divided by the old one ?
Options: a ) 8 .
b ) 2
c ) 6
d ) 4
e ) 10
Rationale: let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi ∗ ( 2 r ) ^ 2 ∗ 2 h / pi ∗ r ^ 2 ∗ h = 8 : 1 . hence the answer is a .
Answer: a
Problem: how many odd prime numbers are there less than 100 ?
Options: a ) 78 , b ) 5 , c ) 24 , d ) 12 , e ) 15
Rationale: "odd prime number less than 100 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 there is 24 the odd prime number answer is c"
Answer: c
Problem: the average of first six multiples of 3 is
Options: a ) 10.5 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 3 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 63 / 6 . = 10.5 . answer a"
Answer: a
Problem: the product of two numbers is 192 and the sum of these two numbers is 28 . what is the smaller of these two numbers ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "solution let the number be x and ( 28 - x ) = then , x ( 28 - x ) = 192 ‹ = › x 2 - 28 x + 192 = 0 . ‹ = › ( x - 16 ) ( x - 12 ) = 0 ‹ = › x = 16 or x = 12 . answer b"
Answer: b
Problem: oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 9 feet long , 8 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 60
b ) 70
c ) 80
d ) 90
e ) 100
Rationale: the volume the tank is : length * width * depth = 9 * 8 * 5 = 360 cubic feet . 360 cubic feet / 4 cubic feet per hour = 90 hours . it will take 90 hours to fill the tank . the answer is d .
Answer: d
Problem: a trader purchased two colour televisions for a total of rs . 35000 . he sold one colour television at 30 % profit and the other 40 % profit . find the difference in the cost prices of the two televisions if he made an overall profit of 30 % ?
Options: a ) rs . 28985 , b ) rs . 40985 , c ) rs . 20985 , d ) rs . 21000 , e ) rs . 30985
Rationale: "let the cost prices of the colour television sold at 30 % profit and 40 % profit be rs . x and rs . ( 35000 - x ) respectively . total selling price of televisions = x + 30 / 100 x + ( 35000 - x ) + 40 / 100 ( 35000 - x ) = > 130 / 100 x + 140 / 100 ( 35000 - x ) = 35000 + 30 / 100 ( 35000 ) x = 27985 35000 - x = 6985 difference in the cost prices of televisions = rs . 20985 answer : c"
Answer: c
Problem: the speed of a boat in still water in 37 km / hr and the rate of current is 13 km / hr . the distance travelled downstream in 10 minutes is :
Options: a ) 10.44 km , b ) 10.6 km , c ) 11.4 km , d ) 11.22 km , e ) 8.33 km
Rationale: "explanation : speed downstream = ( 37 + 13 ) = 50 kmph time = 24 minutes = 10 / 60 hour = 1 / 6 hour distance travelled = time × speed = ( 1 / 6 ) × 50 = 8.33 km answer : option e"
Answer: e
Problem: a train 600 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 76 kmph , b ) 108 kmph , c ) 72 kmph , d ) 34 kmph , e ) 91 kmph
Rationale: "length = speed * time speed = l / t s = 600 / 20 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : b"
Answer: b
Problem: the average of 30 numbers is 25 . if each number is multiplied by 5 , find the new average ?
Options: a ) 115 , b ) 125 , c ) 135 , d ) 145 , e ) 155
Rationale: "sum of the 30 numbers = 30 * 25 = 750 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : b"
Answer: b
Problem: √ ( 21 ) ^ 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 21 ) ^ 2 = ? or , ? = 21 answer d"
Answer: d
Problem: a and b began business with rs . 3000 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 . 798 find the share of a .
Options: a ) 240 , b ) 388 , c ) 379 , d ) 304 , e ) 122
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 798 = 304 answer : d"
Answer: d
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 68 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 37.5 , c ) 92 , d ) 136 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 68 - 40 ) / ( 40 - 36 ) = 28 / 4 = 7 / 1 = number of microtron stocks / number of dynaco stocks so for every 7 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 7 ) th i . e . 300 / 8 = 37.5 must be dynaco stock . answer ( b )"
Answer: b
Problem: the speed of a boat in still water is 15 km / hr and the rate of the current is 3 km / hr . the distance travelled downstream in 12 minutes is
Options: a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) none
Rationale: "speed downstream = ( 15 + 3 ) km / hr = 18 km / hr . distance travelled = ( 18 x 12 / 60 ) hours = 3.6 km . answer d"
Answer: d
Problem: a certain animal in the zoo has consumed 39 pounds of food in 6 days . if it continues to eat at the same rate , in how many more days will its total consumption be 117 pounds ?
Options: a ) 8 , b ) 7 , c ) 12 , d ) 9 , e ) none of the above
Rationale: ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 441 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 ) 21 , e ) 24
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 = 441 / 3 = 147 sq m l b = 147 i . e . , l * l / 3 = 147 l ^ 2 = 441 = > l = 21 . d"
Answer: d
Problem: in a class of 42 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 1 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 42 avg # of books per student = 2 total # of books = 42 * 2 = 84 # of student borrowed at least 3 books = 42 - 2 - 12 - 10 = 18 # of books borrowed by above 18 students = 84 - ( 12 * 1 ) + ( 10 * 2 ) = 52 considering that 17 out of above 18 students borrowed only 3 books , # of books borrowed = 17 * 3 = 51 so maximum # of books borrowed by any single student = 52 - 51 = 1 option a"
Answer: a
Problem: a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 * 7 / 17 . what was the number erased ?
Options: a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4
Rationale: explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a
Answer: a
Problem: find the number which is nearest to 3105 and is exactly divisible by 21 ?
Options: a ) 3100 , b ) 2500 , c ) 2545 , d ) 5800 , e ) 3108
Rationale: on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer e
Answer: e
Problem: the lengths of the diagonals of a rhombus are 20 and 48 meters . find the perimeter of the rhombus ?
Options: a ) 150 merters
b ) 125 meters
c ) 96 meters
d ) 104 meters
e ) 152 meters
Rationale: below is shown a rhombus with the given diagonals . consider the right triangle boc and apply pythagora ' s theorem as follows bc 2 = 10 ^ 2 + 24 ^ 2 and evaluate bc bc = 26 meters . we now evaluate the perimeter p as follows : p = 4 * 26 = 104 meters . answer is d
Answer: d
Problem: cp of 3 buffaloes are $ 30,000 . by selling 1 at a loss of 15 % and other at a profit of 19 % , he foundthat sp of both buffaloes is the same . find the cp of each ?
Options: a ) $ 10,500 , b ) $ 11,500 , c ) $ 11,600 , d ) $ 12,100 , e ) $ 12,500
Rationale: let the c . p of 1 st buffalo = x ∴ c . p of 2 nd buffalo = 30,000 - x s . p of 1 st buffalo = ( 100 - loss % ) - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = 100 - 15 x - - - - - - - - - - - = 85 x / 100 100 s . p of 2 nd buffalo = ( 100 - profit % ) - - - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = ( 100 + 19 ) ( 30,000 - x ) 119 ( 30,000 - x ) - - - - - - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - 100 100 s . p of 1 st buffalo = s . p of 2 nd buffalo 85 x / 100 = 119 ( 30,000 - x ) / 100 ⇒ 85 x = 119 ( 30,000 - x ) ⇒ 85 x = 3 , 570,000 - 119 x ⇒ 85 x + 119 x = 3 , 570,000 ⇒ 204 x = 3 , 570,000 ⇒ x = 3 , 570,000 / 204 ⇒ x = $ 17,500 c . p of 1 st buffalo = $ 17,500 c . p of 2 nd buffalo = 30,000 - 17,500 = $ 12,500 e
Answer: e
Problem: a courtyard is 21 meter long and 14 meter board is to be paved with bricks of dimensions 14 cm by 8 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 26250 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2100 ã — 1400 / 14 ã — 8 ) = 26250 option d"
Answer: d
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.3 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 2 : 6 , b ) 2 : 3 , c ) 4 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.3 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.3 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.5 = 4 / 5 required ratio = 4 / 5 : 1 = 4 : 5 . answer : c"
Answer: c
Problem: if a ( a - 8 ) = 9 and b ( b - 8 ) = 9 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 8 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 9 or if a = 9 then b = - 1 but in each case a + b = - 1 + 9 = 8 answer : option c"
Answer: c
Problem: how many positive integers less than 253 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . the numbers 244 and 248 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice b is correct here .
Answer: b
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 2 hours ?
Options: a ) 2.4 . , b ) 3.2 . , c ) 4.2 . , d ) 5.5 . , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 2 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 2 = 3.2 desks b is the correct answer ."
Answer: b
Problem: a is twice as good a work man as b and together they finish a piece of work in 14 days . the number of days taken by a alone to finish the work is :
Options: a ) 11 , b ) 21 , c ) 28 , d ) 42 , e ) none of these
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 14 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 14 x 2 / 3 ) = 1 / 21 hence , a alone can finish the work in 21 days . answer b"
Answer: b
Problem: one night a certain hotel rented 2 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 20 % , b ) 25 % , c ) 33 % , d ) 36 % , e ) 40 %
Rationale: "the rooms which were not rented is 3 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 3 / 5 ) = 1 / 3 = 33 % the answer is c ."
Answer: c
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 6 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 4.8 miles , d ) 9.2 miles , e ) 10 miles
Rationale: "answer : d ) 9.2 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 6 * 20 / ( 6 + 20 ) = 9.2 m / hr the distance between schoolhome should be half of that . ie . 9.2 miles answer d"
Answer: d
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 12 : 8 , b ) 8 : 16 , c ) 9 : 16 , d ) 8 : 12 , e ) 16 : 9
Rationale: "water : soap = 3 : 2 soap : salt = 12 : 8 = > for 12 soap , salt = 8 = > for 2 soap , salt = ( 8 / 12 ) * 2 = 16 / 12 = 4 / 3 so , water : soap : salt = 3 : 2 : 4 / 3 = 9 : 6 : 4 after open container , water : soap : salt = 2.25 : 6 : 4 so , water : salt = 2.25 : 4 = 9 : 16 answer : c"
Answer: c
Problem: during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d .
Answer: d
Problem: the owner of a furniture shop charges his customer 18 % more than the cost price . if a customer paid rs . 6000 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6290 , d ) rs . 5084 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 6000 ( 100 / 118 ) = rs . 5084 . answer : d"
Answer: d
Problem: find the simple interest on $ 10000 at 7 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 700 , e ) $ 1000
Rationale: "p = $ 10000 r = 7 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 7 * 1 / 100 = $ 700 answer is d"
Answer: d
Problem: two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is
Options: a ) 60 days , b ) 15 days , c ) 6 days , d ) 51 days , e ) 50 days
Rationale: two men and 7 children complete a certain piece of work in 4 days or 8 men and 28 children complete a certain piece of work in 1 days 4 men and 4 children complete the same work in only 3 days . or 12 men and 12 children complete the same work in only 3 days . so 8 men + 28 children = 12 men + 12 children 1 man = 4 children 4 men and 4 children complete the same work in only 3 days or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days or 5 men complete the same work in 3 days or 1 man will complete the same work in 5 * 3 = 15 days answer : b
Answer: b
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 15 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.85 * 150 x = 127.5 x hence total profit = 27.5 % option a
Answer: a
Problem: the total surface area of a solid hemisphere of diameter 14 cm , is :
Options: a ) 462 cm ²
b ) 530 cm ²
c ) 1345 cm ²
d ) 1788 cm ²
e ) none
Rationale: sol . total surface area = 3 ∏ r ² = [ 3 * 22 / 7 * 7 * 7 ] cm ² = 462 cm ² answer a
Answer: a
Problem: a certain company ’ s profit in 1996 was 25 percent greater than its profit in 1995 , and its profit in 1997 was 30 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 62.5 % , c ) 33 % , d ) 35 % , e ) 38 %
Rationale: "profit in 1995 - 100 profit in 1996 - 125 % increae profit in 1997 in comparison to 1995 = 25 + 125 * 30 % = 62.5 correct option : b"
Answer: b
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container h ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .
Answer: c
Problem: after decreasing 90 % in the price of an article costs rs . 320 . find the actual cost of an article ?
Options: a ) 2777 , b ) 2987 , c ) 3200 , d ) 9977 , e ) 1671
Rationale: "cp * ( 10 / 100 ) = 320 cp = 32 * 100 = > cp = 3200 answer : c"
Answer: c
Problem: the perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 35
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : d"
Answer: d
Problem: what will be the fraction of 50 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 50 * 1 / 100 = 1 / 2 answer : option e"
Answer: e
Problem: if 0.45 : x : : 4 : 2 , then x is equal to
Options: a ) 0.225 , b ) 0.228 , c ) 0.254 , d ) 0.256 , e ) none
Rationale: "sol . ( x × 4 ) = ( 0.45 × 2 ) ⇒ x = 0.9 / 4 = 0.225 . answer a"
Answer: a
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Problem: if 0.75 : x : : 5 : 12 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.8 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 12 ) x = 9 / 5 = 1.80 answer : c"
Answer: c
Problem: the average age of 32 students in a group is 14 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 36 , c ) 47 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 33 ã — 15 â € “ 32 ã — 14 ) years = 47 years . answer c"
Answer: c
Problem: two employees x and y are paid a total of rs . 650 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.45 , b ) s . 250.45 , c ) s . 295.45 , d ) s . 300.45 , e ) s . 310.45
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 650 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 650 ⇒ y [ 12 / 10 + 1 ] = 650 ⇒ 22 y / 10 = 650 ⇒ 22 y = 6500 ⇒ y = 6500 / 22 = rs . 295.45 c )"
Answer: c
Problem: the average speed of a car is 1 3 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 320 km , c ) 360 km , d ) 550 km , e ) 600 km
Rationale: sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 × 2 = 50 km the speed of a car in an hour = 8 / 5 * 50 = 80 km so , the distance covered by car in 4 h is 80 × 4 = 320 km ans . ( b )
Answer: b
Problem: a certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 340 , b ) 380 , c ) 472 , d ) 528 , e ) 630
Rationale: "1 c 8 * 2 c 12 = 8 * 66 = 528 the answer is ( d )"
Answer: d
Problem: which number need to add to 859622 to get a number exactly divisible by 456 ?
Options: a ) 456456 , b ) 576834 , c ) 562783 , d ) 634567 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Problem: in a factory , there are 40 % technicians and 60 % non - technicians . if the 60 % of the technicians and 40 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: total = 100 t = 40 nt = 60 40 * ( 60 / 100 ) = 24 60 * ( 40 / 100 ) = 24 24 + 24 = 48 = > 100 - 48 = 52 % answer : c
Answer: c
Problem: a can do a work in 8 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 400,200 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 8 : 4 ratio of their wages a : b = 2 : 1 a ' s share = ( 2 / 5 ) 1000 = 400 b ' s share = ( 1 / 5 ) 1000 = 200 correct option is c"
Answer: c
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1235 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . a )"
Answer: a
Problem: if the area of a square with sides of length 11 centimeters is equal to the area of a rectangle with a width of 11 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 11 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 11 ^ 2 = l * 11 = > l = 121 / 11 = 11 answer c"
Answer: c
Problem: tanks p and b are each in the shape of a right circular cylinder . the interior of tank p has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank p is what percent of the capacity of tank b ?
Options: a ) 75 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: b . for p , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi p / b = 160 pi / 200 pi = 0.8
Answer: b
Problem: x and y are both integers . if x / y = 59.40 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 450 , b ) 616 , c ) 672 , d ) 900 , e ) 1024
Rationale: remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : a
Answer: a
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 1.00 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 4 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 1.00 ( 1 - x ) = 0.75 0.2 x = 1.00 - 0.75 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 6 ."
Answer: d
Problem: what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ?
Options: a ) 30 liters , b ) 50 liters , c ) 60 liters , d ) 70 liters , e ) 80 liters
Rationale: "acid in 20 liters = 80 % of 20 = 16 liters suppose x liters of water be added . then 16 liters of acid in 20 + x liters of diluted solution 20 % of 20 + x = 16 20 + x = 80 x = 60 liters answer is c"
Answer: c
Problem: if the compound interest on a certain sum of money for 5 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 1500 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 5 yrs = ( 3000 x 10 x 5 ) / 100 = 1500 / - answer : a ."
Answer: a
Problem: the percentage profit earned by selling an article for rs . 1620 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1812.5 , c ) 2000 , d ) 5600 , e ) 3400
Rationale: "c . p . be rs . x . then , ( 1620 - x ) / x * 100 = ( x - 1280 ) / x * 100 1620 - x = x - 1280 2 x = 2900 = > x = 1450 required s . p . = 125 % of rs . 1450 = 125 / 100 * 1450 = rs . 1812.5 . answer b"
Answer: b
Problem: a trader bought a car at 25 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 105 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 75 s = 75 * ( 140 / 100 ) = 105 100 - 105 = 5 % answer : c"
Answer: c
Problem: a 750 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 300 , b ) 875 , c ) 360 , d ) 770 , e ) 380
Rationale: "speed = 750 / 18 = 125 / 3 m / sec . let the length of the platform be x meters . then , ( x + 750 ) / 39 = 125 / 3 = > x = 1625 m . l = 1625 - 750 = 875 answer : option b"
Answer: b
Problem: john bought a total of 20 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 20 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 9 , e ) 12
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 20 - x ) 0.60 / 20 = 0.65 solving for x , we get x = 5 - - > mangoes 5 , oranges 15 now , number of oranges to be returned be y 0.80 * 5 + ( 15 - y ) * 0.60 / 20 - y = 0.72 solving for y , y = 12 ans : e"
Answer: e
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 10 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 855 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 10 ) = ( 8550 / 10 ) = 855 answer : option d"
Answer: d
Problem: when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "let possible value of x is 76 least possible value of x / 18 is 76 / 18 = > 4 quotient with remainder 4 thus answer is ( d ) 4"
Answer: d
Problem: 26 : 62 : : 32 : ?
Options: a ) 49 , b ) 25 , c ) 36 , d ) 64 , e ) 23
Rationale: "ans 23 reverse of 32 answer : e"
Answer: e
Problem: a reduction of 50 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.75 , b ) 8.75 , c ) 7.75 , d ) 3.75 , e ) 1.75
Rationale: "explanation : 40 * ( 50 / 100 ) = 20 - - - 64 ? - - - 12 = > rs . 3.75 answer : d"
Answer: d
Problem: marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 54.2 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 65 ; projected revenue = 120 . actual / projected * 100 = 65 / 120 * 100 = 54.2 % . answer : a ."
Answer: a
Problem: mr . shah decided to walk down the escalator of a tube station . he found â that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stairs he would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins â to descend to the time he steps off the last step at the bottom , find out the height of the stair way in steps ?
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: ( s 1 * t 2 ~ s 2 * t 1 ) / ( t 2 ~ t 1 ) = ( 26 * 18 ~ 34 * 30 ) / ( 18 ~ 30 ) = 46 answer : c
Answer: c
Problem: the average age of 18 students of a class is 18 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 18 th student is
Options: a ) 101 , b ) 66 , c ) 110 , d ) 160 , e ) 12
Rationale: "explanation : age of the 18 th student = [ 18 * 18 - ( 14 * 5 + 16 * 9 ) ] = ( 324 - 214 ) = 110 years . answer : c"
Answer: c
Problem: what is 15 percent of rs . 34 ?
Options: a ) rs . 3.40 , b ) rs . 3.75 , c ) rs . 4.50 , d ) rs . 5.10 , e ) none
Rationale: "sol . 15 % of rs . 34 = rs . ( 15 / 100 x 34 ) = rs . 5.10 answer d"
Answer: d
Problem: on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "d = ( d - r ) / q = ( 123 - 4 ) / 7 = 119 / 7 = 17 c"
Answer: c
Problem: a reduction of 10 % in the price of tea enables a dealer to purchase 25 kg more tea for rs . 22500 . what is the reduced price per kg of tea ?
Options: a ) rs . 70 , b ) rs . 80 , c ) rs . 90 , d ) rs . 100 , e ) none
Rationale: solution : 1 st method : let the original price of tea be rs . x / kg . after reduction the price becomes = x - 10 % of x = 9 x / 10 per kg . now , ( 22500 / ( 9 x / 10 ) ) - 22500 / x = 25 or , 22500 [ 10 / 9 x - 1 / x ] = 25 or , 25 * 9 x = 22500 ; or , x = ( 22500 / 2589 ) = rs . 100 . hence , new price = 90 per kg . thought process method : let the original price be rs . 100 per kg , he get tea = 22500 / 100 = 225 kg . after reduction the price becomes = 90 per kg , he get tea = 22500 / 90 = 250 kg . so , reduction price is rs . 90 per kg as it enables him to buy 25 kg of more tea . answer : option c
Answer: c
Problem: at 12 : 30 , the hour hand and the minute hand of a clock form an angle of
Options: a ) 120 ° , b ) 135 ° , c ) 125 ° , d ) 150 ° , e ) 180 °
Rationale: "answer : 180 degree answer : e"
Answer: e
Problem: 896.7 – 573.07 – 95.007 = ?
Options: a ) 228.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 896.7 - ( 573.07 + 95.007 ) = 896.7 - 668.077 = 228.623 . answer a"
Answer: a
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2200 , what will be c ' s share of the earnings ?
Options: a ) $ 488.9 , b ) $ 480.9 , c ) $ 588.9 , d ) $ 680.9 , e ) $ 788.9
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2200 = $ 488.9 hence : a"
Answer: a
Problem: two pipes a and b can fill a tank in 36 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hrs , b ) 22 hrs , c ) 23 hrs , d ) 24 hrs , e ) 21 hrs
Rationale: "1 / ( 1 / 36 + 1 / 45 ) = 180 / 9 = 20 hrs answer : a"
Answer: a
Problem: a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 18 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 18 the total number of traditionalists is 6 p / 18 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Problem: a man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 5.33 kmph , b ) 6.00 kmph , c ) 5.00 kmph , d ) 6.00 kmph , e ) 4.00 kmph
Rationale: "m = 6.5 s = 1.5 ds = 8 us = 4 as = ( 2 * 8 * 4 ) / 12 = 5.33 answer : a"
Answer: a
Problem: in order to obtain an income of rs . 1250 from 10 % stock at rs . 210 , one must make an investment of
Options: a ) 5363 , b ) 26250 , c ) 28678 , d ) 29002 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 210 . to obtain rs . 1250 , investment = = rs . 26250 . answer : b"
Answer: b
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 400 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 8,250 , c ) rs . 15,600 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 400 x 20.625 ) = rs . 8,250 . answer b"
Answer: b
Problem: given that 268 x 74 = 19632 , find the value of 2.68 x . 74 .
Options: a ) 1.9632 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9632 answer a"
Answer: a
Problem: a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: xc 1 * ( x - 1 ) c 1 = 56 x ^ 2 - x - 56 = 0 ( x - 8 ) ( x + 7 ) = 0 x = 8 , - 7 - 7 ca n ' t possible . hence 8 should be the answer b
Answer: b
Problem: a businessman earns $ 26800 in december , thus decreasing his average annual ( january to december ) earnings by $ 1200 . his average annual earnings would be source : cmat preparation
Options: a ) $ 29000 , b ) $ 33500 , c ) $ 40000 , d ) $ 41000 , e ) $ 42300
Rationale: ( x - 26,800 ) / 11 - x / 12 = 1,200 x = 480,000 x / 12 = 40,000 answer : c .
Answer: c
Problem: a can complete a certain job in 16 days . b is 60 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: let , total work unit = 160 units a can finish in 16 days = 160 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 60 / 100 ) * 10 = 16 unit work days in which b will complete the work alone = 160 / 16 = 10 days answer : option e
Answer: e
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 7 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 88.2 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 7 % of 400 = 28 therefore , total number of rotten fruits = 90 + 28 = 118 therefore number of fruits in good condition = 1000 - 118 = 882 therefore percentage of fruits in good condition = ( 882 / 1000 × 100 ) % = ( 88200 / 1000 ) % = 88.2 % answer : b"
Answer: b
Problem: sandy had $ 231 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 270 , b ) $ 290 , c ) $ 310 , d ) $ 330 , e ) $ 350
Rationale: "let the money sandy took for shopping be x . 0.7 x = 231 x = 330 the answer is d ."
Answer: d
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 12 pumps work to empty the tank in 1 day ?
Options: a ) 4 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 12 pumps then 48 / 12 = 4 hrs . answer : a"
Answer: a
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 70 / kg . how much did a kg of coffee cost in june ?
Options: a ) 70 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 700 gm ) of tea and 1 / 2 kg ( 700 gm ) of coffee ( equal quantities ) = 70 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 70 = > x = 70 thus proved . . . option a ."
Answer: a
Problem: a sum of rs . 66000 is divided into 3 parts such that the simple interests accrued on them for 6 , two and 11 years respectively may be equal . find the amount deposited for 11 years .
Options: a ) 6500 , b ) 2000 , c ) 4500 , d ) 3000 , e ) 6000
Rationale: let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e
Answer: e
Problem: what is the number of integers from 1 to 100 ( inclusive ) that are divisible by neither 5 nor by 6 ?
Options: a ) 35 , b ) 47 , c ) 58 , d ) 26 , e ) 34
Rationale: "in 100 consecutive numbers , number of multiples of 5 = 100 / 5 = 20 ( ignore decimals ) in 100 consecutive numbers , number of multiples of 6 = 100 / 6 = 16 number of multiples of 5 * 6 i . e . 30 = 100 / 30 = 3 number of integers from 1 to 100 that are divisible by neither 5 nor by 6 = 100 - ( 29 + 16 - 3 ) { using the concept of sets here ) = 58 answer is c"
Answer: c
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what percent z of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c
Answer: c
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 16 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7 , d ) 7.8 , e ) 9
Rationale: "answer is c . x / x + 36 = 1 / 5 x = 9 16 - 9 = 7"
Answer: c
Problem: the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?
Options: a ) 15.5 , b ) 15.4 , c ) 15.25 , d ) 10.4 , e ) 15.6
Rationale: total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d
Answer: d
Problem: the sum of the squares of three consecutive natural number is 2030 . what is the middle number ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26"
Answer: b
Problem: in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 60 kmph being 130 m and 120 m in length respectively ?
Options: a ) 6.9 sec , b ) 7.1 sec , c ) 7.2 sec , d ) 7.4 sec , e ) 7.5 sec
Rationale: "d = 130 m + 120 m = 250 m * 1 / 1000 = 0.25 kms rs = 60 + 60 = 120 kmph t = ( 0.25 / 120 ) * 3600 = 7.5 sec answer : e"
Answer: e
Problem: the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . what is the average percent increase of population per year ?
Options: a ) 4 % , b ) 6 % , c ) 5 % , d ) 50 % , e ) none of these
Rationale: "explanation : increase in the population in 10 years = 2 , 62,500 - 1 , 75,000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) × 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c"
Answer: c
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 67 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a"
Answer: a
Problem: rob also compared the empire state building and the petronas towers . what is the height difference between the two if the empire state building is 435 m tall and the petronas towers is 458 m tall ?
Options: a ) 9 , b ) 17 , c ) 23 , d ) 45 , e ) 12
Rationale: 458 - 435 = 23 . answer is c .
Answer: c
Problem: a and b together can do a work in 4 days . if a alone can do it in 20 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 5 , c ) 6 , d ) 8 , e ) 25
Rationale: "b 5 1 / 4 â € “ 1 / 20 = 1 / 5 = > 5"
Answer: b
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?
Options: a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780
Rationale: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .
Answer: d
Problem: a train passes a station platform in 34 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 166 , e ) 210
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 34 = 15 = > x = 210 m . answer : e"
Answer: e
Problem: find the area , diameter = 11 m .
Options: a ) 113.00 square meter
b ) 95.07 square meter
c ) 93.08 square meter
d ) 93.24 square meter
e ) 113.43 square meter
Rationale: diameter = 11 meter . radius = diameter / 2 . = 11 / 2 . = 5.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 5.5 . area of a circle = 3.14 ã — 5.5 ã — 5.5 . . = 3.14 ã — 30.25 . = 95.07 square meter answer : b
Answer: b