Cheukting/mathqa huggingface dataset:
Question (general): in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 15 , c ) 25 , d ) 30 , e ) 35
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 15 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 15 x 1 ( a = 1 , b = 5 respectively we have = 5 ) . to ensure , let ' s check ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 15 x 3 = 45 ( a = 4 b = 5 respectively . hey ! that ' s 20 . but we do n ' t have this number in answer choices , move on ) . 15 x 5 = 75 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) 15 x 7 = 105 ( a = 0 , b = 5 . have 0 now . can create a pattern ) imo e ."
Answer: e
Question (general): let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 79 th number in this set ?
Options: a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 629
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 79 th number = 8 * ( 79 - 1 ) + 5 = 629 answer = e"
Answer: e
Question (physics): the area of a sector of a circle of radius 4 cm formed by an arc of length 4.5 cm is ?
Options: a ) 8.78 , b ) 8.67 , c ) 8.75 , d ) 8.98 , e ) 9
Rationale: "( 4 * 4.5 ) / 2 = 9 answer : e"
Answer: e
Question (general): when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 1 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 1 ) ^ 2 = ( 5 x + 4 ) ^ 2 = 5 y + 16 , for some integer y when we divide this by 5 , the remainder is 1 . the answer is b ."
Answer: b
Question (physics): when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tom is what percent greater than the quantifying chopped by tommy ? .
Options: a ) 44 % , b ) 100 % , c ) 125 % , d ) 225 % , e ) 400 %
Rationale: "tammy chops 4 lbs in 6 minutes tom chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : c"
Answer: c
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): √ ( 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (gain): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (gain): 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