Cheukting/mathqa huggingface dataset:
Question (general): if x is equal to the sum of the integers from 10 to 20 , inclusive , and y is the number of even integers from 10 to 20 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 175 , c ) 180 , d ) 190 , e ) 200
Rationale: sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 10 + ( 11 - 1 ) * 1 } = 11 * 15 = 165 = x number of even number = ( 20 - 10 ) / 2 + 1 = 6 = y x + y = 165 + 6 = 171 a
Answer: a
Question (general): 49 * 49 * 49 * 49 = 7 ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 8
Rationale: "sol . 49 * 49 * 49 * 49 = ( 72 * 72 * 72 * 72 ) = 7 ( 2 + 2 + 2 + 2 ) = 78 . so , the correct answer is 8 . answer d"
Answer: d
Question (general): find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case .
Options: a ) 266 , b ) 268 , c ) 270 , d ) 272 , e ) 274
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 33 , 8 ) + 2 = 266 . answer : a"
Answer: a
Question (gain): 50 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 240 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 50 / 100 ) * x + 120 = x x = 240 answer : a"
Answer: a
Question (general): there are 4 runners on a track team who run an average of 4.5 seconds per 40 yards . if another runner joins their team who runs 4.3 seconds per 40 yards , what will the new average 40 yard time be ?
Options: a ) 4.46 , b ) 4.39 , c ) 4.42 , d ) 4.49 , e ) 4.33
Rationale: ( sum of the 4 times ) / 4 = 4.5 sum of the 4 times = 18 new sum = 18 + 4.3 = 22.3 new average = 22.3 / 5 = 4.46 ans : a
Answer: a
Question (physics): a train is moving at 4 / 5 of its usual speed . the train is 30 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 30 minutes represents 1 / 4 of the usual time . the usual time is 2 hours . the answer is c ."
Answer: c
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 50 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 732 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 50 + 52 + 54 + . . . . . upto 12 terms ) this is an a . p with first term , a = 50 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 50 + { 12 - 1 ) x 2 ] = 6 ( 122 ) = 732 kms . answer : c"
Answer: c
Question (general): what is the least integer greater than – 3 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 3 ) + ( 0.5 ) = - 2.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 3 to - 2.5 ) . next , the question asks for the least integer that is greater than - 2.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 2.5 is - 2 . final answer : a"
Answer: a
Question (general): if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 90 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 50 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 60 , b ) $ 70 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b"
Answer: b
Question (gain): in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 8 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23.9 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 8 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.92 = 0.22 ; { % of customers who sample candy } = 0.239 . answer : b ."
Answer: b
Question (general): | x + 3 | – | 4 - x | = | 8 + x | how many u solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Question (geometry): the area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is ?
Options: a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36
Rationale: "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 12 will be divided into 3 parts = 6 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 18 * 4 = 36 e"
Answer: e
Question (general): a sum of money is sufficient to pay a ' s wages for 21 days and b ' s wages for 28 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 days , b ) 12 1 / 4 days , c ) 14 days , d ) 24 1 / 2 days , e ) none of these
Rationale: let total money be rs . x a ' s 1 day ' s wages = rs . x / 21 , b ' s 1 day ' s wages = rs . x / 28 ( a + b ) ' s 1 day ' s wages = rs . ( x / 21 + x / 28 ) = rs . x / 12 ; money is sufficient to pay the wages of both for 12 days . correct option : a
Answer: a
Question (general): in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 24 . what is the total number of students in the school ?
Options: a ) 50 , b ) 80 , c ) 120 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a"
Answer: a
Question (other): the l . c . m . of two numbers is 48 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : option c"
Answer: c
Question (general): if x + ( 1 / x ) = 5 , what is the value of r = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) r = 21 , b ) r = 22 , c ) r = 23 , d ) 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Question (general): how many multiples of 2 are there between 1 and 56 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 27 , d ) 26 , e ) 28
Rationale: "27 multiples of 2 between 1 and 56 exclusive . from 2 * 1 upto 2 * 27 , ( 1,2 , 3,4 , . . . , 27 ) . hence , 27 multiples ! correct option is c"
Answer: c
Question (general): the average of marks obtained by 120 boys was 39 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 39 24 x = 4680 - 1800 = > x = 2880 / 24 x = 120 . hence , the number of boys passed = 120 . answer : c"
Answer: c
Question (geometry): the area of a circular place is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 / meter approximately .
Options: a ) rs . 4233
b ) rs . 4350
c ) rs . 4457
d ) rs . 4670
e ) rs . 4756
Rationale: area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c
Answer: c
Question (probability): from a pack of 52 cards , two cards are drawn at random together at random what is the probability of both the cards being kings ?
Options: a ) 1 / 221 , b ) 8 / 221 , c ) 4 / 589 , d ) 4 / 587 , e ) 7 / 654
Rationale: "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 2 kings out of 4 n ( e ) = 4 c 2 = ( 4 * 3 ) / ( 2 * 1 ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 1326 = 1 / 221 answer ( a )"
Answer: a
Question (geometry): the length of a rectangle is halved , while its breadth is tripled . wat isthe % change in area ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 67 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Question (general): 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 10 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 74
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 63 + 11 = 74 answer : e"
Answer: e
Question (physics): 10 men and 15 women together can complete a work in 5 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 150 days , c ) 177 days , d ) 187 days , e ) 225 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 5 15 women ' s 1 day work = ( 1 / 5 - 10 / 100 ) = 1 / 10 1 woman ' s 1 day work = 1 / 150 1 woman alone can complete the work in 150 days . answer : b"
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 25 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 25 s = ( 27 x + 17 y ) / ( x + y ) = 25 = ( 27 x + 17 y ) / = 25 ( x + y ) = 2 x = 8 y = x / y = 8 / 2 = 4 / 1 i . e 4 : 1 answer : b"
Answer: b
Question (gain): on selling 20 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 48 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 70
Rationale: "( c . p . of 20 balls ) - ( s . p . of 20 balls ) = ( c . p . of 5 balls ) c . p . of 15 balls = s . p . of 20 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 15 = rs . 48 . answer : option a"
Answer: a
Question (general): the average of first 13 natural numbers is ?
Options: a ) 5.2 , b ) 5.5 , c ) 7 , d ) 9 , e ) 10
Rationale: "sum of 13 natural no . = 182 / 2 = 91 average = 91 / 13 = 7 answer : c"
Answer: c
Question (gain): tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 54000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 24000 , c ) 34000 , d ) 35000 , e ) 30000
Rationale: sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 54000 = 30000 e
Answer: e
Question (gain): fresh grapes contain 75 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 25 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 75 = 25 % of whole weight ) , so 25 * 0.75 = x * 0.25 - - > x = 75 . answer : a ."
Answer: a
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 81000 , b ) 22887 , c ) 26877 , d ) 26771 , e ) 17121
Rationale: 64000 * 9 / 8 * 9 / 8 = 81000 answer : a
Answer: a
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 188 m , c ) 120 m , d ) 160 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 8 = 160 m . answer : d"
Answer: d
Question (gain): victor gets 95 % marks in examinations . if these are 285 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 288 , e ) 300
Rationale: let the maximum marks be m then 95 % of m = 285 ⇒ 95 / 100 × m = 285 ⇒ m = ( 285 × 100 ) / 95 ⇒ m = 28500 / 95 ⇒ m = 300 therefore , maximum marks in the examinations are 300 . answer : e
Answer: e
Question (gain): last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.9 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 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.9 ( x ) + 0.5 ( 1 - x ) = 0.75 0.4 x = 0.75 - 0.5 x = 0.25 / 0.4 x = 5 / 8 therefore the answer is c : 5 / 8 ."
Answer: c
Question (geometry): find the circumference and area of radius 7 cm .
Options: a ) 151 cm ² , b ) 152 cm ² , c ) 154 cm ² , d ) 155 cm ² , e ) 157 cm ²
Rationale: "circumference of circle = 2 π r = 2 × 22 / 7 × 7 = 44 cm area of circle = π r ² = 22 / 7 × 7 × 7 cm ² = 154 cm ² answer : c"
Answer: c
Question (general): a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 375 and $ 150 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the smallest amount that the company can spend is the lcm of 375 and 150 , which is 750 for each , which is total 1500 . the number of 1 st type of computers which costing $ 375 = 750 / 375 = 2 . the number of 2 nd type of computers which costing $ 150 = 750 / 150 = 5 . total = 2 + 5 = 7 answer is e .
Answer: e
Question (general): how many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ten pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 10 * 10 = 100 hence e"
Answer: e
Question (general): a batch of cookies was divided amomg 3 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 5 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 21 / 31 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 3 b = 1 / 5 we can solve for g which is 7 / 10 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 7 / 10 + 1 / 3 ) = 7 / 10 x = 21 / 31 answer : a"
Answer: a
Question (general): a grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 360 , b ) 252 , c ) 280 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 30 * 42 * 60 dimensions of the soap = 5 * 6 * 7 we get = 6 x 6 x 10 = 360 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( a )"
Answer: a
Question (general): if ( a - b - c + d = 13 ) and ( a + b - c - d = 5 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 , e ) 64
Rationale: a - b - c + d = 13 - - equation 1 a + b - c - d = 5 - - equation 2 adding 1 and 2 , we get 2 a - 2 c = 18 = > a - c = 9 - - equation 3 using equation 3 in 2 , we get b - d = 5 - 9 = - 4 = > ( b - d ) ^ 2 = 16 answer d
Answer: d
Question (physics): a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm 3 , then the weight of the pipe is
Options: a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) none of these
Rationale: "explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = [ ( 22 / 7 ) × ( 42 - 32 ) × 21 ] cm 3 = 462 cm 3 weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b"
Answer: b
Question (physics): a train 225 m in length crosses a telegraph post in 15 seconds . the speed of the train is ?
Options: a ) 37 kmph , b ) 34 kmph , c ) 32 kmph , d ) 38 kmph , e ) 76 kmph
Rationale: "s = 225 / 25 * 18 / 5 = 32 kmph answer : c"
Answer: c
Question (general): find the value of 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) 2400
Rationale: "answer 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3 x 4 x 4 x 50 = 2400 correct option : e"
Answer: e
Question (other): sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.5 per pound , and german chocolate cost $ 2.8 per pound . if the total the she spent on chocolate was $ 28 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "if there were all the expensive ones , 3.5 . . . . there would be 28 / 3.5 or 8 of them but since 2.8 $ ones are also there , answer has to be > 8 . . if all were 2.8 $ ones , there will be 28 / 2.8 or 10 . . . so only 9 is left answer a . ."
Answer: a
Question (physics): the length of the bridge , which a train 110 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 10 m , b ) 16 m , c ) 245 m , d ) 265 m , e ) 27 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 25 / 2 = > 2 ( 110 + x ) = 750 = > x = 265 m . answer : d"
Answer: d
Question (physics): if 16 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 225 , c ) 287 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 16 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 16 * 30 / 24 * 80 x = 225 answer : b"
Answer: b
Question (gain): a shop sells 1 chocolate at the rate rupee 1 each . you can exchange 3 warppers for one chocolate . if you have rs . 15 , what is the maximum number of chocolates you can get ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: rs . 15 = 15 chocolates 15 wrappers = 5 chocolates 5 wrappers = 1 chocolate ( u have 2 wrappers with you . . ) count this wrapper with already existing wrappers = 15 + 5 + 1 + 1 = 22 chocolates . . answer : b
Answer: b
Question (general): jim is now twice as old as fred , who is 9 years older than sam . 6 years ago , jim was 5 times as old as sam . how old is jim now ?
Options: a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58
Rationale: j = 2 f = 2 ( s + 9 ) = 2 s + 18 j - 6 = 5 * ( s - 6 ) ( 2 s + 18 ) - 6 = 5 s - 30 s = 14 and so j = 46 the answer is b .
Answer: b
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 204 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 300 , d ) 500 , e ) 821
Rationale: p - 204 = ( p * 4 * 8 ) / 100 p = 300 answer : c
Answer: c
Question (geometry): in the coordinate plane , a circle centered on point ( 3 , - 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
Options: a ) 29 π , b ) 18 π , c ) 25 π , d ) 37 π , e ) 41 π
Rationale: "r ^ 2 = ( 3 - 1 ) ^ 2 + ( - 4 - 1 ) ^ 2 = 4 + 25 = 29 area of circle = π r ^ 2 = 29 π answer : a"
Answer: a
Question (other): the l . c . m . of 2 numbers is 48 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 48 x = 8 the numbers are = 16 and 24 required sum = 16 + 24 = 40 answer is b"
Answer: b
Question (gain): the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 42.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 39.1 , e ) 33.8
Rationale: "$ 69 - $ 42 = 27 $ ( 27 / 69 ) * 100 = 39.13 % answer : d"
Answer: d
Question (general): how many positive integers less than 100 have a remainder of 2 when divided by 13 ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "take the multiples of 13 and add 2 0 x 13 + 2 = 2 . . . . 13 x 7 + 2 = 93 there are 14 numbers answer c"
Answer: c
Question (physics): convert 60 miles into yards ?
Options: a ) 105600 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 60 miles = 60 * 1760 = 105600 yards answer is a"
Answer: a
Question (general): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 10.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 10.2 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: i tried using time / rate approach : - initial price difference = 10.80 - 3.20 = 7.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 7.6 = t ( 5.4 x ) - > t = ( 7.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 7.6 / 5.4 = 10.2 answer b .
Answer: b