Cheukting/mathqa huggingface dataset:
Question (general): how many integerskgreater than 100 and less than 800 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 ) 90
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 six pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 6 * 10 = 60 hence b ."
Answer: b
Question (other): local kennel has cats and dogs in the ratio of 5 : 10 . if there are 40 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 80 , b ) 70 , c ) 60 , d ) 50 , e ) 45
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 5 : 10 or cats 5 dogs 10 we can write number of cats as 5 x and number of dogs as 10 x and we know that 10 x - 5 x = 40 ( therefore 5 x = 40 = > x = 8 ) then # of dogs = 10 x 8 = 80 answer is a"
Answer: a
Question (general): for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 45 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer b ( a + b ) ( a - b ) = 45 3 cases for ( a + b ) , ( a - b ) 45 , 1 15 , 3 9 , 5 answer b"
Answer: b
Question (general): if the number 892 , 142,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 142,24 x sum of digits at odd places = 8 + 2 + 4 + 2 + x = 16 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 4 = 16 ( ii ) ( i ) - ( ii ) = 16 + x - 16 = x - 0 hence x should be = 0 to make this a multiple of 11 ( 0 ) option d"
Answer: d
Question (general): a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio w of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore w , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Question (general): of the families in city x in 1992 , 60 percent owned a personal computer . the number of families in city x owning a computer in 1993 was 50 percent greater than it was in 1992 , and the total number of families in city x was 3 percent greater in 1993 than it was in 1992 . what percent of the families in city x owned a personal computer in 1993 ?
Options: a ) 68.99 % , b ) 66.55 % , c ) 91.23 % , d ) 77.77 % , e ) 87.37 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60 number of families owning computer in 1998 = 60 * 150 / 100 = 90 number of families in 1998 = 103 the percentage = 90 / 103 * 100 = 87.37 % . answer : e"
Answer: e
Question (general): find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.00 ) / ( √ 0.49 ) is
Options: a ) 2.65 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.00 ) / ( √ 0.49 ) 11 / 9 + 10 / 7 = > 2.65 answer is a
Answer: a
Question (general): louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ?
Options: a ) 333 , b ) 383 , c ) 402 , d ) 433 , e ) 483
Rationale: after 1 st month : ( 1000 ) ( 1.1 ) - x = 1100 - x after 2 nd month : ( 1100 - x ) ( 1.1 ) - x = 1210 - 2.21 x after 3 rd month : ( 1210 - 2.21 x ) ( 1.1 ) - x = 1331 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 1331 - 3.31 x = 0 x = 1331 / 3.31 = 402.11 the answer is c
Answer: c
Question (physics): if the perimeter of a rectangular garden is 600 m , its length when its breadth is 200 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 100 m , e ) 128 m
Rationale: "2 ( l + 200 ) = 600 = > l = 100 m answer : d"
Answer: d
Question (gain): rs 3000 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 400 , b ) s 280 , c ) s 300 , d ) s 350 , e ) s 310
Rationale: explanation : average rate = ( 144 / 3000 ) * 100 = 4.8 ratio = 2 : 18 so , first part = ( 2 / 20 ) * 3000 = rs 300 . answer : c
Answer: c
Question (geometry): the area of a square is equal to three times the area of a rectangle of dimensions 3 cm * 9 cm . what is the perimeter of the square ?
Options: a ) 30 , b ) 36 , c ) 46 , d ) 66 , e ) 76
Rationale: "area of the square = s * s = 3 ( 3 * 9 ) = > s = 9 cm perimeter of the square = 4 * 9 = 36 cm . answer : option b"
Answer: b
Question (physics): a machine , working at a constant rate , manufactures 18 dies in 25 minutes . how many dies does it make in 1 hr 15 min ?
Options: a ) 55 , b ) 53 , c ) 54 , d ) 52 , e ) 50
Rationale: "change 1 hr 15 min to 75 min . for this , we need to set up a simple proportion of dies per time 18 / 25 = s / 75 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 25 in the two denominators . 18 / 1 = s / 3 s = 3 * 18 s = 54 the machine would be 54 dies in 1 hr 15 min . answer : c"
Answer: c
Question (physics): a room 5.44 m long and 3.74 m broad is to be paved with square tiles . the least number of square tiles required to cover the floor is :
Options: a ) 176
b ) 192
c ) 184
d ) 162
e ) 172
Rationale: area of the room = 544 * 374 sq . cm size of largest square tile = hcf of 544 cm & 374 cm area of 1 tile = 34 * 34 sq . cm therefore , number of tiles = ( 544 * 374 / 34 * 34 ) = 176 answer : a
Answer: a
Question (general): find the maximum value of n such that 50 ! is perfectly divisible by 2520 ^ n
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: 2520 = 2 ^ 3 * 3 ^ 2 * 5 * 7 here , 7 is the highest prime , so find the no . of 7 ' s in 50 ! only no . of 7 ' s in 50 ! = [ 50 / 7 ] + [ 50 / 7 ^ 2 ] = 7 + 1 = 8 answer : b
Answer: b
Question (geometry): in two triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 the ratio of their bases is
Options: a ) 16 : 9
b ) 9 : 16
c ) 9 : 12
d ) 16 : 12
e ) 4 : 12
Rationale: explanation : given a 1 / a 2 = 4 / 3 , h 1 / h 2 = 3 / 4 also , we know that a 1 / a 2 = ( 1 / 2 × b 1 × h 1 ) / ( 1 / 2 × b 2 × h 2 ) on substituting in above equation , we get b 1 / b 2 = 16 / 9 therefore b 1 : b 2 = 16 : 9 answer : option a
Answer: a
Question (general): a number exceeds by 30 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 48
Rationale: "x – 3 / 8 x = 30 x = 48 answer : e"
Answer: e
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 520 . if one of the numbers is 480 , then the other is :
Options: a ) 13 , b ) 18 , c ) 21 , d ) 24 , e ) 38
Rationale: "other number = ( 12 x 520 ) / 480 = 13 . answer : a"
Answer: a
Question (geometry): the radius of a cylinder is 12 m , height 21 m . the lateral surface area of the cylinder is :
Options: a ) 1584
b ) 1854
c ) 1458
d ) 1485
e ) none of them
Rationale: lateral surface area = 2 π rh = 2 × 22 / 7 × 12 × 21 = 44 × 36 = 1584 m ( power 2 ) answer is a .
Answer: a
Question (gain): in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1500 , e ) 1800
Rationale: "let v be the total number of votes . 0.2 v = 240 v = 1200 the answer is c ."
Answer: c
Question (other): how many of the positive factors of 19 are not factors of 29 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 19 - 1 , 19 factors of 29 - 1 , 29 comparing both , we have three factors of 19 which are not factors of 29 - 19 , the answer is b"
Answer: b
Question (gain): a retailer buys a radio for rs 225 . his overhead expenses are rs 30 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 17.6 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 30 ) = 255 sell price = 300 gain = ( 45 / 255 ) * 100 = 17.6 % . answer : d"
Answer: d
Question (general): the number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 54 , d ) 81 , e ) 162
Rationale: "explanations 1 ) this tells us that the number of boxes is evenly divisible by both 6 and 27 ; in other words , it ’ s a common multiple of 6 and 27 . the question says : what ’ s the smallest value it could have ? in other words , what ’ s the lcm of 6 and 27 ? ( this question is one example of a real - world set - up where the question is actually asking for the lcm . ) step ( a ) : 6 = 2 * 3 27 = 3 * 3 * 3 step ( b ) : 6 = 2 * 3 27 = 3 * 3 * 3 gcf = 3 step ( c ) : 6 = 3 * 2 27 = 3 * 9 step ( d ) lcm = 3 * 2 * 9 = 54 thus , 54 is the lcm of 6 and 27 . answer : c ."
Answer: c
Question (gain): if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 210 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 290 , b ) 320 , c ) 350 , d ) 380 , e ) 410
Rationale: let x be the minimum number of questionnaires to be mailed . 0.6 x = 210 x = 350 the answer is c .
Answer: c
Question (general): a lemonade stand sold only small and large cups of lemonade on tuesday . 4 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) ( a ) 7 / 16 , b ) ( b ) 7 / 15 , c ) ( c ) 10 / 21 , d ) ( d ) 7 / 31 , e ) ( e ) 1 / 2
Rationale: "a simpler way i guess would be to think that in total 5 cups were sold . out of which 4 are small and 1 is large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 4 * 6 = 24 and 1 * 7 = 7 . total revenue was 24 + 7 = 31 and large cup sales as found above is 7 therefore answer is 7 / 31 d"
Answer: d
Question (gain): 96 % of the population of a city is 23040 . find the total population of the city ?
Options: a ) 30000 , b ) 28000 , c ) 24000 , d ) 25000 , e ) 25500
Rationale: "population consider as x x * ( 96 / 100 ) = 23040 x = 240 * 100 = = > 24000 answer c"
Answer: c
Question (general): the average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 58 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: since the average has increased by 2.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 2.5 58 + 25 = 83 kg ans : ' b '
Answer: b
Question (general): if 6 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 10 , b ) 11 , c ) 7 , d ) 12 , e ) 9
Rationale: 6 ( log 2 ^ 2 * 5 ^ 2 ) = x 6 log ( 5 * 2 ) ^ 2 = x 6 * 2 log ( 5 * 2 ) = x 12 log 10 = x log 10 base 10 = 1 so 12 * 1 = x x = 12 answer : d
Answer: d
Question (general): in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 10 , − 7 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 10 / 20 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Question (gain): the price of a t . v . set worth rs . 40000 is to be paid in 20 installments of rs . 2500 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 27098 , d ) 37500 , e ) 2799
Rationale: "money paid in cash = rs . 2500 balance payment = ( 40000 - 2500 ) = rs . 37500 . answer : d"
Answer: d
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 250 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 × $ 0.5 = $ 250 the answer is a ."
Answer: a
Question (gain): boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) rs . 320 , b ) rs . 450 , c ) rs . 550 , d ) rs . 640 , e ) rs . 680
Rationale: "find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) × c . p . 100 selling price = ( 100 + 10 ) × 500 100 selling price = ( 110 ) × 500 100 therefore , selling price = rs . 550 c"
Answer: c
Question (gain): in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 20 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 30 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 20 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 20 % of people have their job of choice , then 80 % of people do not have their job of choice . 25 % of 80 % = 20 % . we can also see that 10 % of the people have their job of choice and a diploma ( 20 % - 10 % = 10 % ) . 10 % + 20 % = 30 % . therefore 30 % of the people in country z have a diploma . ans a"
Answer: a
Question (general): a batsman makes a score of 84 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 36 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 84 = 17 x therefore x = 36 answer : c"
Answer: c
Question (gain): of the 120 passengers on flight 750 , 40 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 40 , b ) 48 , c ) 50 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 4 * 120 = 48 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 48 - 8 = 40 answer a"
Answer: a
Question (general): the maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is
Options: a ) 41 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 451 and 410 . â € ¹ = â € º 41 . answer a"
Answer: a
Question (general): find the average of all the numbers between 4 and 32 which are divisible by 5 .
Options: a ) 17.5 , b ) 20 , c ) 24 , d ) 30 , e ) 32
Rationale: "solution average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 6 ) = 105 / 6 = 17.5 . answer a"
Answer: a
Question (geometry): a cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm . the radius of the cone will be :
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) none
Rationale: sol . let the radius of the cone be r cm . then , 1 / 3 ∏ * r ² * 6 = ∏ * 8 * 8 * 2 ⇔ r ² = [ 8 * 8 * 2 * 3 / 6 ] = 64 ⇔ r = 8 cm . answer a
Answer: a
Question (general): if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 18 . then 4 n < 18 and n < 4.5 the largest possible integer is n = 4 . the answer is d ."
Answer: d
Question (physics): a runs twice as fast as b and gives b a start of 60 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 120 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: ratio of speeds of a and b is 2 : 1 b is 60 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 60 m is 60 / 1 = 60 m so the total time taken by a and b to reach = 2 * 60 = 120 m answer : a
Answer: a
Question (physics): how long does a train 100 m long running at the speed of 80 km / hr takes to cross a bridge 142 m length ?
Options: a ) 10.7 sec , b ) 10.9 sec , c ) 10.1 sec , d ) 15.1 sec , e ) 12.7 sec
Rationale: "speed = 80 * 5 / 18 = 22.2 m / sec total distance covered = 100 + 142 = 242 m . required time = 242 / 22.2 ' = 10.9 sec . answer : b"
Answer: b
Question (physics): a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 5 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 5 days , b can do 1 / 6 of the project . thus a and b must complete 5 / 6 of the project , which takes 10 days . the total number of days is 10 + 5 = 15 . the answer is b ."
Answer: b
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 580 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,000 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 580 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25000 answer : c"
Answer: c
Question (gain): a dessert recipe calls for 50 % melted chocolate and 50 % raspberry puree to make a particular sauce . a chef accidentally makes 15 cups of the sauce with 30 % melted chocolate and 70 % raspberry puree instead . how many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50 % of each ?
Options: a ) 1.5 , b ) 2.14 , c ) 3 , d ) 4.5 , e ) 5
Rationale: "yes , we assume that the mix is homogeneous . otherwise , we will not be able to solve the question . you have 15 cups of sauce with 30 % chocolate . you also have unlimited amount of pure chocolate sauce . now you need to mix these two in such a way that you get total 15 cups of sauce with 50 % chocolate . using scale method : w 1 / w 2 = ( 100 - 50 ) / ( 50 - 30 ) = 5 / 2 w 1 - amount of 30 % chocolate sauce w 2 - amount of pure chocolate sauce so for every 5 / 2 cups of 30 % chocolate sauce , we need 2 cup of pure chocolate sauce . this will give us 7 cups of 50 % chocolate sauce . but we need 15 cups of 50 % chocolate sauce . so we need to mix 5 * 15 / 7 = 12.5 cups of 40 % chocolate sauce with 1 * 15 / 7 = 2.14 cups of pure chocolate sauce . answer ( b )"
Answer: b
Question (general): the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 35 cents less than the price of commodity y ?
Options: a ) 2006 , b ) 2007 , c ) 2008 , d ) 2009 , e ) 2010
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 35 cents less than commodity y . $ 1.75 / 25 cents = 7 years the answer is 2001 + 7 years = 2008 . the answer is c ."
Answer: c
Question (other): if log 1087.5 = 1.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 1.9421 + 1 ) = 10 ( 2.9421 ) = 29.421 x = antilog ( 29.421 ) therefore , number of digits in x = 30 . answer : a"
Answer: a
Question (physics): a river 4 m deep and 65 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 25000 , b ) 26000 , c ) 27000 , d ) 28000 , e ) 29000
Rationale: "rate of water flow - 6 kmph - - 6000 / 60 - - 100 m / min depth of river - - 4 m width of river - - 65 m vol of water per min - - 100 * 4 * 65 - - - 26000 answer b"
Answer: b
Question (physics): in a garden , there are 10 rows and 17 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 34 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 17 plants . there are 15 gapes between the two corner trees ( 16 x 2 ) metres and 1 metre on each side is left . therefore length = ( 32 + 2 ) m = 34 m . answer : c"
Answer: c
Question (gain): a person spent rs . 6,040 from his salary on food and 8,000 on house rent . after that he was left with 70 % of his monthly salary . what is his monthly salary ?
Options: a ) 46,800 , b ) 66,800 , c ) 56,800 , d ) 26,800 , e ) 76,800
Rationale: "total money spent on food and house rent = 6,040 + 8,000 = 14,040 which is 100 - 70 = 30 % of his monthly salary ∴ his salary = 14040 x 100 / 30 = 46800 answer : a"
Answer: a