Cheukting/mathqa huggingface dataset:
Question (physics): two cars , car 1 and car 2 move towards each other from q and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach q starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: q - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance qy = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Question (general): in a division sum , the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :
Options: a ) 200 , b ) 251 , c ) 250 , d ) 262 , e ) 254
Rationale: "diver = ( 8 * 3 ) + 3 = 27 3 * quotient = 27 quotient = 9 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 9 ) + 8 = 251 b"
Answer: b
Question (physics): the area of a sector of a circle of radius 5 cm formed by an arc of length 4.5 cm is ?
Options: a ) 8.78 , b ) 11.25 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 5 * 4.5 ) / 2 = 11.25 answer : b"
Answer: b
Question (general): if x = - 5 and y = 8 , what is the value of 2 ( x - y ) ^ 2 - xy ?
Options: a ) 358 , b ) 348 , c ) 368 , d ) 388 , e ) 378
Rationale: x = - 5 and y = 8 x - y = - 5 - 8 = - 13 x * y = - 5 * 8 = - 40 now we apply it in the equation 2 ( x - y ) ^ 2 - xy = 2 ( - 13 ) ^ 2 - ( - 40 ) = = > 2 * 169 + 40 = 338 + 40 = 378 answer : e
Answer: e
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 6 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 6 , b ) - 1 , c ) 0 , d ) 1 , e ) 6
Rationale: when x = 1 and when x = - 6 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 6 ) f ( 0 ) = - 6 the answer is a .
Answer: a
Question (probability): kim has 7 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 14 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 11 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "can be tackled in this way as well : probability of selecting any 1 out of 14 shoes = 14 / 14 = 1 probability of selecting the next shoe ( out of 14 available ) having the same color = 1 / 14 ( as after selecting the 1 st one , there is only 1 another shoe left with the same color ) . thus the total probability = 1 * 1 / 13 = 1 / 13 . a is the correct answer ."
Answer: a
Question (physics): find the distance covered by a man walking for 36 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 6 km , d ) 5 km , e ) 6 km
Rationale: distance = 10 * 36 / 60 = 6 km answer is c
Answer: c
Question (physics): a can finish a piece of work in 5 days . b can do it in 10 days . they work together for 1 day and then a goes away . in how many days will b finish the work ?
Options: a ) 8 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 9 days
Rationale: "1 / 5 + ( 1 + x ) / 10 = 1 = > x = 7 days answer : d"
Answer: d
Question (general): in an xy - coordinate plane , a line is defined by y = kx + 1 . if ( 4 , b ) , ( a , 5 ) , and ( a , b + 1 ) are 3 points on the line , where a and b are unknown , then k = ?
Options: a ) 1 / 2 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 5 / 2
Rationale: b = 4 k + 1 . . . ( 1 ) b + 1 = ak + 1 . . . ( 2 ) 5 = ak + 1 . . . ( 3 ) taking ( 2 ) and ( 3 ) 5 = b + 1 b = 4 taking ( 1 ) 4 = 4 k + 1 k = 3 / 4 answer : c
Answer: c
Question (general): david has $ 1,500 at the beginning of his trip , after spending money , he still has exactly $ 500 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 500 x + x - 500 = 1500 x = 1000 money not spend = 1000 - 500 = 500 answer : c"
Answer: c
Question (general): a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 18 more than the correct answer . find the number .
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 18 25 x = 16 x + 360 9 x = 360 x = 40 the answer is c ."
Answer: c
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 3 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 5 / 3 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 25 : 15 : 2 i . e . u : b = 25 : 2 answer : option e"
Answer: e
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 5 percent , but profits were 10 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 95 %
Rationale: "the profit 0 f 2009 interms of 2008 = 0.95 * 10 / 10 * 100 = 95 % e"
Answer: e
Question (general): a house wife saved $ 3.50 in buying an item on sale . if she spent $ 32.50 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 32.50 + 3.50 = $ 36 saving = 3.50 / 36 * 100 = 10 % approximately answer is c"
Answer: c
Question (physics): a garrison of 1000 men has provisions for 60 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1000 , b ) 2250 , c ) 60 , d ) 45 , e ) 1250
Rationale: "1000 - - - - 60 1000 - - - - 45 x - - - - - 20 x * 20 = 1000 * 45 x = 2250 1000 - - - - - - - 1250 answer : e"
Answer: e
Question (general): on an order of 99 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.1 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 100 dozens free . equivalent discount = 1 / 100 * 100 = 1 % . answer c ) 1 %"
Answer: c
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 35 , find the value of ab .
Options: a ) 12 , b ) 13 , c ) 10 , d ) 18 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 35 - 9 = 26 ab = 13 . answer is b ."
Answer: b
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 320 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 640 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 320 ) = 2 + 2 ( extra ) = > 2 x - 640 = x = > x = 640 . answer : b"
Answer: b
Question (physics): 45 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 17 , b ) 97 , c ) 18 , d ) 55 , e ) 72
Rationale: "( 45 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 100 100 – 45 = 55 answer : d"
Answer: d
Question (physics): one hour before john started walking from p to q , a distance of 38 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 19 miles , d ) 19,6 miles , e ) 24 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 38 - 3 = 35 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 35 miles so it will take them 35 / 5 = 7 hours to meet . in 7 hrs , ann would have covered 7 hrs * 3 miles per hour = 21 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 21 = 24 miles . answer ( e )"
Answer: e
Question (general): simplify 586645 * 9999
Options: a ) 5865863355 , b ) 5665863355 , c ) 4865863355 , d ) 4665863355 , e ) none of these
Rationale: explanation : although it is a simple question , but the trick is to save time in solving this . rather than multiplying it we can do as follows : 586645 * ( 10000 - 1 ) = 5866450000 - 586645 = 5865863355 option a
Answer: a
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is :
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 = 189 or x = 1575 . ∴ p . w . = rs . 1575 . ∴ sum due = p . w . + t . d . = rs . ( 1575 + 189 ) = rs . 1764 . answer b"
Answer: b
Question (general): if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 23 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 − 100 ) / 130 ∗ 100 . hence , the consumption should be reduced to 23 % . answer : b"
Answer: b
Question (physics): pipe a that can fill a tank in two hour and pipe b that can fill the tank in an hour are opened simultaneously when the tank is empty . pipe b is shut 30 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 36 mins , b ) 35 mins , c ) 40 mins , d ) 32 mins , e ) 30 mins
Rationale: the last 30 minutes only pipe a was open . since it needs 2 hour to fill the tank , then in 30 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : e
Answer: e
Question (other): two family reunions are happening at the taj hotel , the oates reunion and the hall reunion . all 150 guests at the hotel attend at least one of the reunions . if 70 people attend the oates reunion and 52 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 28
Rationale: no of people in oates reunion = 70 no of people in hall reunion = 52 attending both = x all guests attend at least one . therefore , 150 = 70 + 52 - ( both ) both = 28 answer e
Answer: e
Question (geometry): you buy a piece of land with an area of â ˆ š 1024 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 1024 . answer e"
Answer: e
Question (general): divide rs . 720 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 180 , e ) s . 900
Rationale: "a + b + c = 720 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 720 = > 180 answer : d"
Answer: d
Question (general): the least common multiple of positive integer e and 3 - digit integer n is 690 . if n is not divisible by 3 and e is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and e is 690 = 2 * 3 * 5 * 23 . e is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to e . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Question (general): half a number plus 5 is 15 . what is the number ?
Options: a ) 8 , b ) 20 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 15 ( 1 / 2 ) x = 15 - 5 ( 1 / 2 ) x = 10 x = 20 correct answer is b"
Answer: b
Question (physics): a car takes 6 hours to cover a distance of 630 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 70 kmph
Rationale: "time = 6 distence = 630 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 630 / 9 = 70 kmph e"
Answer: e
Question (gain): population of a city in 20004 was 1100000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2384525 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2384525 / 2 e"
Answer: e
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 750 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 15 minutes = 15 / 18 * 15 * 60 = 750 m answer is d"
Answer: d
Question (physics): a room 4 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 38636 , b ) 38640 , c ) 38647 , d ) 38591 , e ) 38675
Rationale: "explanation : area of the room = ( 447 x 777 ) cm 2 . size of largest square tile = h . c . f . of 447 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 447 × 777 ) / ( 3 × 3 ) = 38591 answer : option d"
Answer: d
Question (gain): the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 13 % ?
Options: a ) 31.5 % , b ) 35.9 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 87 gain % = 23 / 64 * 100 = 35.9 % . b"
Answer: b
Question (general): the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length r of a cube whose surface area is equal to 6 z ?
Options: a ) r = 16 , b ) r = 8 √ 2 , c ) r = 8 , d ) r = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Question (gain): a candidate got 25 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 8000
Rationale: "25 % - - - - - - - - - - - l 75 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 50 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 8000 answer : e"
Answer: e
Question (general): 8 , 24 , 12 , 36 , 18 , 54 , ( . . . . )
Options: a ) 27 , b ) 68 , c ) 107 , d ) 108 , e ) 28
Rationale: "8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 answer is a"
Answer: a
Question (other): 39 ! is divided by 41 . then what is the remainder for this ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a
Answer: a
Question (general): the ratio 5 : 20 expressed as percent equals to
Options: a ) 50 % , b ) 125 % , c ) 25 % , d ) none of above , e ) 30 %
Rationale: "explanation : actually it means 5 is what percent of 20 , which can be calculated as , ( 5 / 20 ) * 100 = 5 * 5 = 25 option c"
Answer: c
Question (gain): a sum of money becomes 7 / 6 of itself in 2 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 7 , c ) 50 / 6 , d ) 50 / 8 , e ) 50 / 3
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 2 years . rate = ( 100 * x ) / ( x * 6 * 2 ) = 50 / 6 % . answer : c"
Answer: c
Question (physics): a train travels 325 km in 3.5 hours and 470 km in 4 hours . find the average speed of train ?
Options: a ) 116 kmph , b ) 106 kmph , c ) 186 kmph , d ) 126 kmph , e ) 176 kmph
Rationale: explanation : as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 325 + 470 = 795 km thus , total speed = 7.5 hrs average speed = 795 / 7.5 = > 106 kmph . answer : b
Answer: b
Question (general): a bucket full of nuts was discovered by the crow living in the basement . the crow eats a sixth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "in one hour , the crow eats 1 / 48 of the nuts . ( 1 / 4 ) / ( 1 / 48 ) = 12 hours the answer is b ."
Answer: b
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7560 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 960 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7560 / 18 + 7560 / 14 = 420 + 540 = 960 hours answer : option e"
Answer: e
Question (general): jennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 20
Rationale: "1 / 5 x $ 150 = $ 30 for sandwich 1 / 6 x $ 150 = $ 25 for museum 1 / 2 x $ 150 = $ 75 for book $ 30 + $ 25 + $ 75 = $ 130 spent $ 150 - $ 130 = $ 20 left over correct answer e"
Answer: e
Question (physics): excluding the stoppages , the speed of a bus is 32 km / hr and including the stoppages the speed of the bus is 16 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 10 min , c ) 12 min , d ) 30 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 32 km / hr speed of the bus with stoppage = 16 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 32 ) hr = 1 / 2 hr = 30 min answer : d"
Answer: d
Question (general): what is the sum of all the multiples of 10 between 0 and 75 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 280
Rationale: "the multiples of 10 between 0 and 99 are 10 , 20 , 30 , 40 , 50 , 60 , 70 . if these are all added together , the result is 280 . final answer : e"
Answer: e
Question (general): the sum of the non - prime numbers between 10 and 20 , non - inclusive , is
Options: a ) 60 , b ) 75 , c ) 90 , d ) 105 , e ) 120
Rationale: "sum of consecutive integers from 11 to 19 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 11 + 19 ) / 2 * 9 = 15 * 9 = 135 sum of non - prime numbers b / w 10 and 20 , non inclusive = = = > 135 - 60 ( i . e . , 11 + 13 + 17 + 19 , being the prime # s in the range ) = 75 answer : b"
Answer: b
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 2210 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 340 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 2210 x = 80 required perimeter = 2 ( 80 + 90 ) = 340 c"
Answer: c
Question (geometry): the sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq . m . find the perimeter of rectangle .
Options: a ) 121 , b ) 123 , c ) 125 , d ) 122 , e ) 126
Rationale: "let 6 x and 5 x be sides of the rectangle 6 x × 5 x = 1331 11 xpower 2 = 1331 xpower 2 = 1331 / 11 = 121 = > x = 11 length = 6 x = 6 × 11 = 66 breadth = 5 x = > 5 × 11 = 55 perimeter = 2 ( l + b ) = > 2 ( 66 + 55 ) = 121 m answer is a ."
Answer: a
Question (geometry): the ratio of the volumes of two cubes is 729 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 81 : 126 , c ) 81 : 189 , d ) 81 : 176 , e ) 81 : 117
Rationale: "ratio of the sides = ³ √ 729 : ³ √ 1331 = 9 : 11 ratio of surface areas = 92 : 112 = 81 : 121 answer : a"
Answer: a
Question (gain): at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 4 years ?
Options: a ) 4 % , b ) 3.57 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 4 xr ) / 100 r = 3.57 % answer : option b"
Answer: b
Question (general): roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be three times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: "r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d ."
Answer: d
Question (general): having scored 95 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 23 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 95 = 19 ( n + 4 ) = > n = 19 so , average score after 19 th innings = x + 4 = 23 . answer : c"
Answer: c
Question (geometry): if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the shorter sides ?
Options: a ) 4
b ) 7
c ) 8
d ) 13
e ) 26
Rationale: assume the sides to be x and y . perimeter = 2 x + 2 y = 42 hence x + y = 21 - ( i ) area = xy = 104 - ( ii ) since these are the sides of a billboard , we are dealing with positive numbers only and the options tell us that they are integers . 104 can be written as a product of two numbers as 104 * 1 or 52 * 2 or 26 * 4 or 13 * 8 of these , only 13 * 8 satisfies the equation ( i ) hence the lengths are 13 and 8 length of shorter side = 8 answer : c
Answer: c