Cheukting/mathqa huggingface dataset:
Question (physics): the ratio between the length and the breadth of a rectangular park is 1 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 4 min , then the area of the park ( in sq . m ) is ?
Options: a ) 800 m , b ) 12000 m , c ) 36000 m , d ) 80000 m , e ) 30000 m
Rationale: "perimeter = distance covered in 4 min . = ( 12000 x 4 ) / 60 m = 800 m . let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 800 or x = 100 . length = 100 m and breadth = 300 m . area = ( 100 x 300 ) m 2 = 30000 m e"
Answer: e
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 4 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 34 , e ) 41
Rationale: let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 4 = > 2 b - b - 4 = 30 b = 34 so the present age of b is 34 years answer : d
Answer: d
Question (general): the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 23 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.4 , b ) 984.4 , c ) 877.4 , d ) 637.4 , e ) 667.4
Rationale: let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 23 = 2 r a = 12 / 5 r and r = 69 a = 165.6 required total cost = 4 * 165.6 + 3 * 69 + 5 * 23 = 662.4 + 207 + 115 = $ 984.40 b
Answer: b
Question (general): if x is equal to the sum of the integers from 50 to 60 , inclusive , and y is the number of even integers from 50 to 60 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 491 , e ) 611
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 50 + ( 11 - 1 ) * 1 } = 11 * 55 = 605 = x number of even number = ( 60 - 50 ) / 2 + 1 = 6 = y x + y = 605 + 6 = 611 e"
Answer: e
Question (general): a number x is 7 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 85.7 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 7 . then y = 1 is less than x = 7 by ( 7 - 1 ) / 7 * 100 = 6 / 7 * 100 = 85.7 % . answer : b ."
Answer: b
Question (gain): an alloy weighing 48 ounces is 25 % gold . how many ounces of pure gold must be added to create an alloy that is 40 % gold ?
Options: a ) 15 , b ) 20 , c ) 12 , d ) 14 , e ) 7
Rationale: an alloy of 48 oz which is 25 % gold means there is 12 oz of gold . to get to an alloy that is 40 % gold , let ' s use this expression : ( 12 + x ) / ( 48 + x ) = 0.40 with x representing the amount of pure gold that must be added to get to 40 % . the expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40 % or 0.4 . you will see that 12 is the correct answer , as 24 / 60 = 0.4 choose c
Answer: c
Question (gain): a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 420 . find the sum ?
Options: a ) s . 5000 , b ) s . 7000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 420 = > 30 x / 100 - 24 x / 100 = 420 = > 6 x / 100 = 420 = > x = 7000 . answer : b"
Answer: b
Question (general): if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is
Options: a ) 343 , b ) 393 , c ) 363 , d ) 391 , e ) 409
Rationale: n = smallest number n + 6 = largest number ( n + n + 6 ) / 2 = 20 = > ( 2 n + 6 ) / 2 = 20 = > n + 3 = 20 = > n = 17 so product of n and n + 6 = ( 17 ) ( 23 ) = 391 answer - d
Answer: d
Question (physics): a train , 120 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 255 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 120 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 120 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 120 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 120 + x = > 45 ã — 10 ã — 10 / 12 = 120 + x = > 15 ã — 10 ã — 10 / 4 = 120 + x = > 15 ã — 25 = 120 + x = 375 = > x = 375 - 120 = 255 answer : option b"
Answer: b
Question (other): find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 6 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 6 = 2 / 1 = 2 : 3 answer is e"
Answer: e
Question (geometry): the number 90 can be written as the sum of the squares of 4 different positive integers . what is the sum of these 4 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "4 ^ 2 + 3 ^ 2 + 8 ^ 2 + 1 ^ 2 = 90 - - > 1 + 3 + 8 + 4 = 16 . b"
Answer: b
Question (physics): a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts overtaking the john ( he is riding on the horse ) before it starts overtaking the mike ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time ( in secs ) after the train has crossed the mike do the john meets to mike ?
Options: a ) 3576 s , b ) 3589 s , c ) 3596 s , d ) 3598 s , e ) 3576 s
Rationale: "let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e"
Answer: e
Question (physics): two trains 100 m and 60 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 5.76 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 100 + 60 = 160 m . required time = 160 * 9 / 250 = 5.76 = 5.76 sec . answer : b"
Answer: b
Question (general): the price of lunch for 15 people was $ 207.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.00 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "if the amount spent excluding the gratuity was x , then x ( 1.15 ) = 207 = > x = 207 / 1.15 = 180 then the average price per person = 180 / 15 = 12 option ( b )"
Answer: b
Question (gain): find the missing figures : 0.50 % of ? = 0.12
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let 0.50 % of x = 0.12 . then , 0.50 * x / 100 = 0.12 x = [ ( 0.12 * 100 ) / 0.50 ] = 24 . answer is e ."
Answer: e
Question (general): a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 15
Rationale: "220 + 43 = 263 / 17 = 8 ( remainder ) b"
Answer: b
Question (general): shipment - - - - - - no . of defective chips / shipment - - - total chips in shipment s 2 - - - - - - - - - - - - - - 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - 6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18000 s 4 - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts s 1 , s 2 , s 3 and s 4 comined as shown in the table above . what is the expected number q of defective chips in a shipment of 60000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 25
Rationale: i agree with your solution = 20 . but the question is : there are different combination to get 60000 chips . for example : 1 * s 3 + 2 * s 4 + 2 * s 2 . in this way , we ship 60000 chips with only 6 + 4 * 2 + 2 * 2 = 18 defective chips , better than the average of 20 . the question is to find the expected number q of defective chips , i guess it assume the minimum # , therefore it might not be 20 .
Answer: b
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then 8 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 8 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 8 * 3 * 1 ) / 3 = 24 / 3 = 8 b"
Answer: b
Question (general): the maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "number of pens = 640 number of pencils = 520 required number of students = h . c . f . of 640 and 520 = 40 answer is a"
Answer: a
Question (gain): a certain airline ' s fleet consisted of 80 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let x be the number of years . 4 x > 80 - 3 x 7 x > 80 x > 11 + 3 / 7 the answer is d ."
Answer: d
Question (other): if the numbers 1 to 96 are written on 96 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 96 , d ) 1 , e ) 2
Rationale: there are 25 primes , 70 composite numbers from 1 to 96 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 96 . answer : c
Answer: c
Question (physics): sandy walked 25 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 25 meters . she then turned to her right and walked 12 meters . what distance is she from the starting point and in which direction ?
Options: a ) 32 meters east , b ) 32 meters north , c ) 32 meters west , d ) 42 meters east , e ) 52 meters west
Rationale: "the net distance is 20 + 12 = 32 meters to the east . the answer is a ."
Answer: a
Question (physics): the length of the bridge , which a train 120 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 239 , b ) 277 , c ) 255 , d ) 88 , e ) 232
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 = = > 2 ( 120 + x ) = 750 = = > x = 255 m . answer : c"
Answer: c
Question (gain): how many liters of water must be evaporated from 50 liters of a 1 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 35 , b ) 40 , c ) 42 , d ) 45 , e ) 48
Rationale: 1 % of a 50 liter solution is 0.5 l which is 10 % of the solution at the end . the solution at the end must be 5 l . we need to evaporate 45 liters . the answer is d .
Answer: d
Question (gain): raman mixed 27 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 190 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 27 ( 150 ) + 36 ( 125 ) ] / ( 27 + 36 ) = rs . 135.71 sp = cp [ ( 100 + profit % ) / 100 ] = 135.71 * [ ( 100 + 40 ) / 100 ] = rs . 190 . answer : c"
Answer: c
Question (general): the average of 50 numbers id 56 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 51.35 , e ) 56.25
Rationale: explanation : total of 50 numbers = ( 50 × 56 ) = 2800 total of 48 numbers = ( 2800 - ( 45 + 55 ) ] = 2700 required average = 2700 / 48 = 56.25 answer : e
Answer: e
Question (general): a set consists of 12 numbers , all are even or multiple of 5 . if 7 numbers are even and 14 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 9
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 7 + 14 - { both } + 0 ; { both } = 9 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : e ."
Answer: e
Question (general): sum of the squares of 3 no . is 149 and the sum of their products taken two at a time is 70 . find the sum ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 13 , e ) 18
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 149 + 2 * 70 a + b + c = â ˆ š 289 = 17 answer a"
Answer: a
Question (general): if x and y are positive integers and x = 5 y + 2 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 2 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 7 7 / 5 = 1 remainder 2 final answer : c"
Answer: c
Question (general): if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 5 * 7 * 9 = 68 then find , 7 * 9 * 11 = ?
Options: a ) 106 , b ) 49 , c ) 68 , d ) 38 , e ) 55
Rationale: a 106 ( 11 * 9 ) + 7 = 106
Answer: a
Question (physics): a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days answer : c"
Answer: c
Question (physics): points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 4 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 4 ( ac = 4 ) d - 8 ( bd = 6 ) cd is 8 - 4 = 4 . ans d"
Answer: d
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 844 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 728 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 844 - 815 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 815 - 87 ) = rs . 728 . answer : option d"
Answer: d
Question (gain): a side of beef lost 40 percent of its weight in processing . if the side of beef weighed 240 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 400 , c ) 737 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 60 / 100 ) * x = 240 = > x = ( 240 * 100 ) / 60 = 400 answer b"
Answer: b
Question (physics): 36 men can complete a piece of work in 18 days . in how days will 27 men can complete the work ?
Options: a ) 18 , b ) 20 , c ) 17 , d ) 24 , e ) 21
Rationale: "let the required number of days be x less men , more days ( indirect proportion ) 27 : 36 : : 18 : x 27 x = 36 * 18 x = ( 36 * 18 ) / 27 x = 24 days option is d"
Answer: d
Question (gain): a trader bought a car at 50 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 71 %
Rationale: "original price = 100 cp = 95 s = 95 * ( 180 / 100 ) = 112 100 - 171 = 71 % answer : e"
Answer: e
Question (physics): renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 4.8 , b ) 1.2 , c ) 4.4 , d ) 4.6 , e ) 4.7
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 8 = 5 / 24 suma can do it alone in 4.8 days . answer : a"
Answer: a
Question (general): what is the sum of the odd integers from 35 to 65 , inclusive ?
Options: a ) 800 , b ) 550 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 50 . sum = mean ( # of elements ) there are 16 odd numbers between 35 - 65 inclusive . 16 * 50 = 800 a"
Answer: a
Question (physics): excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 20 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( 18 / 54 ) x 60 = 20 min answer : a"
Answer: a
Question (physics): a worker can load one truck in 6 hours . a second worker can load the same truck in 5 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.7 , b ) 2.9 , c ) 3.1 , d ) 3.3 , e ) 3.5
Rationale: "the workers fill the truck at a rate of 1 / 6 + 1 / 5 = 11 / 30 of the truck per hour . then the time to fill one truck is 30 / 11 which is about 2.7 hours . the answer is a ."
Answer: a
Question (general): which is equal to 11 ?
Options: a ) 1.1 , b ) - 11 , c ) 11 / 11 , d ) 11 / 1 , e ) 1 / 11
Rationale: "11 / 1 is equal to 11 . answer : d"
Answer: d
Question (physics): the speed of a train is 102 kmph . what is the distance covered by it in 30 minutes ?
Options: a ) 50 kmph , b ) 51 kmph , c ) 41 kmph , d ) 61 kmph , e ) 21 kmph
Rationale: "102 * 30 / 60 = 51 kmph answer : b"
Answer: b
Question (geometry): a rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown . ab = 8 cm and bc = 4 cm . the perimeter of the figure abcpqra ( in cm ) is :
Options: a ) 24
b ) 28
c ) 36
d ) 48
e ) none of these
Rationale: solution required perimeter = ( ab + bc + cp + pq + qr + ra ) = ab + bc + ( cp + qr ) + ( pq + ra ) = ab + bc + ab + bc = 2 ( ab + bc ) = [ 2 ( 8 + 4 ) ] cm = 24 cm . answer a
Answer: a
Question (physics): 20 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 20 * 10 / 40 = 5 answer is e"
Answer: e
Question (general): if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 110 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,210
Rationale: "10 / 100 p = 110 > > p = 110 * 100 / 10 = 1100 1100 - 110 = 990 answer : b"
Answer: b
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 9 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 9 , b ) - 1 , c ) 0 , d ) 1 , e ) 9
Rationale: "when x = 1 and when x = - 9 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 9 ) f ( 0 ) = - 9 the answer is a ."
Answer: a
Question (geometry): in a trapezium abcd , ab is parallel to dc , ab = 3 * dc , and the diagonals of the trapezium intersect at o . the ratio of the area of ∆ ocd to the area of ∆ oab is :
Options: a ) 1 : 9
b ) 1 : 3
c ) 3 : 1
d ) 1 : 10
e ) can not be determined
Rationale: triangles are similar , so ratio will be 1 : 9 a
Answer: a
Question (general): when 1 / 10 percent of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 694
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 6,000 ? 2 ) what is 1 / 10 of 6,000 ? to calculate 1 / 10 percent of 6,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 6,000 = 1 / 1,000 x 6,000 = 6 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 5,000 . to do this we simply multiply 1 / 10 by 6,000 . 1 / 10 x 6,000 = 600 the answer to part 1 is 6 , and the answer to part 2 is 600 . their difference is 600 – 6 = 694 . answer e ."
Answer: e
Question (general): if there are 200 questions in a 3 hr examination . among these questions are 10 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 17.14286 min , b ) 62 min , c ) 70.1346 min , d ) 74 min , e ) 76.1346 min
Rationale: x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 190 x + 10 * 2 x = 180 x = 180 / 210 x = 0.72 time taken for type a problem = 10 * 2 * 0.857143 = 17.14286 min answer : a
Answer: a
Question (physics): working individually , jane can bake cakes for 4 hours and roy can bake cakes in 5 hours . if jane and roy work together but independently at the task for 2 hours , at which point roy leaves , how many remaining hours will it take jane to complete the task alone ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 4 , d ) 1 / 4 , e ) 1 / 5
Rationale: in first 2 hrs roy will finish 2 / 5 = 2 / 5 of work and jane will finish 2 / 4 work so total 2 / 5 + 1 / 2 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now jane will take ( 1 / 10 ) * 4 = 2 / 5 hrs to finish it . so answer is b .
Answer: b
Question (general): the arithmetic mean of set x is zero . if y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of x consisting of all those elements in x which are more than two but less than 3 standard deviations away from the arithmetic mean of x , what could be equal to the standard deviation of x ?
Options: a ) 0.54 , b ) 0.77 , c ) 0.82 , d ) 0.97 , e ) 1.62
Rationale: this is a fairly straightforward question that can be solved quickly by just applying the options we are provided with mean , m = 0 and y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of s y consists of all those elements in x that are more than 2 but less than 3 xds away from the arithmetic mean of x if an element is 1 xd away from the mean , we can write it as either m + xd or m - xd similarly , if an element is 2 xds away from the mean , we can write it as either m + 2 * xd or m - 2 * xd so , if these elements lie within 2 and 3 xds of mean , m = 0 we can find which one of these values of xd satisfies each value within y only xd = 0.77 does answer : b
Answer: b
Question (general): what is the sum of odd integers from 25 to 85 , inclusive ?
Options: a ) 1,705 , b ) 1,500 , c ) 1,240 , d ) 1,120 , e ) 1,100
Rationale: number of odd integers = ( 85 - 25 ) / 2 + 1 = 60 / 2 + 1 = 31 sum of odd integers = ( 25 + 85 ) / 2 * 31 = 1705 answer a
Answer: a
Question (general): carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 25 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 25 = $ 248.75 . answer is b .
Answer: b
Question (general): evaluate the sum 1 - 2 + 3 - 4 + 5 - 6 + . . . + 997 - 998 + 999 - 1000
Options: a ) - 500 , b ) - 1000 , c ) - 999 , d ) - 1001 , e ) 500500
Rationale: one groups the first two terms and each successive two terms to obtain a sum of 500 expressions each of which is - 1 . the answer is - 500 correct answer a
Answer: a