Cheukting/mathqa huggingface dataset:
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 10.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be d .
Answer: d
Question (general): if jake loses 5 pounds , he will weigh thrice as much as his sister . together they now weigh 285 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 215
Rationale: "this problem can be solved as a simple word problem in which we must convert words to math . before we create our equations , we want to define some variables . j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 5 = 3 s j = 3 s + 5 ( equation 1 ) next , we are told that “ together they now weigh 275 pounds . ” we can also put this into an equation . j + s = 285 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 3 s + 5 = 285 - s 4 s = 280 s = 70 j + 70 = 285 j = 215 answer : e"
Answer: e
Question (physics): 6 computers , each working at the same constant rate , together can process a certain amount of data in 9 days . how many additional computers , each working at the same constant rate , will be needed to process the same amount of data in 6 days ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 9 , e ) 12
Rationale: explanation : if six computers require 9 days to process the data , thats a total of 54 computer - days the product of 6 and 9 . if you change the number of computers or the number of days , 54 will have to remain the product , whether that means 54 days of one computer or one day with 54 computers . in 6 days , the number of computers is : 6 c = 54 c = 9 9 computers is 3 more than the 6 that it took to do the job in 9 days , so the correct choice is ( a ) .
Answer: a
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 4 cm . find the whole surface of the cylinder ?
Options: a ) 484 , b ) 771 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 4 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 11 ) = 484 answer : a"
Answer: a
Question (general): mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.96 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.00 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.958 0.708 0.958 1.208 1.458 1.708 1.958 total = $ 8.00 so this must be the answer . b"
Answer: b
Question (general): determine the value of ( 27 / 31 * 31 / 27 ) * 3
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) none
Rationale: "solution : both fractions should be reduced before performing arithmetic operations . we get ( 27 / 31 * 31 / 27 ) 3 = 1 * 3 = 3 answer d"
Answer: d
Question (physics): a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt
Options: a ) 680 , b ) 378 , c ) 267 , d ) 299 , e ) 271
Rationale: "explanation : area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a ) 680 rs"
Answer: a
Question (physics): in a dairy farm , 16 cows eat 16 bags of husk in 16 days . in how many days one cow will eat one bag of husk ?
Options: a ) 16 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: explanation : one bag of husk = 16 cows per day ⇒ 16 × 1 × 16 = 1 × 16 × x for one cow = 16 days answer : a
Answer: a
Question (physics): in 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each , how many pumps will raise 2030 tons of water in 12 days of 11 hrs each ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 22
Rationale: explanation : pumps work time 12 1218 99 x 2030 132 = > 1218 / ( 912 * 99 ) = 2020 / ( x × 132 ) = > x = 15 pumps answer : option b
Answer: b
Question (general): if the probability of rain on any given day in chicago during the summer is 20 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 inclusive ?
Options: a ) 2 / 25 , b ) 3 / 125 , c ) 7 / 125 , d ) 12 / 625 , e ) 16 / 625
Rationale: "one possible case is : rainy - rainy - rainy - not rainy . the probability of this case is 1 / 5 * 1 / 5 * 1 / 5 * 4 / 5 = 4 / 625 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 4 / 625 = 16 / 625 the answer is e ."
Answer: e
Question (general): find the product of the local value and absolute value of 2 in 564823
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 18000
Rationale: "explanation : place value = local value face value = absolute value the place value of 2 in 564823 is 2 x 10 = 20 the face value of 2 in 564823 is nothing but 2 . = > 20 x 2 = 40 answer : option a"
Answer: a
Question (gain): the present population of a town is 60,000 . the population increases annually at 10 % . find the population after 3 years .
Options: a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these
Rationale: "explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79,860 answer : b"
Answer: b
Question (general): 32.32 / 2000 is equal to :
Options: a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.01616 , e ) 0.12725
Rationale: "25.25 / 2000 = 2525 / 200000 = 0.01616 answer : d"
Answer: d
Question (general): george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 22.5 , e ) 12
Rationale: let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 5 % of 200 = 10 for taxi fare , so he is left with 190 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 90 ( 190 - 100 ) no of oranges he can buy = 90 / 4 = > 22,5 so , george can buy 20 oranges . d
Answer: d
Question (physics): if 4 spiders make 4 webs in 4 days , then 1 spider will make 1 web in how many days ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 4 , e ) 6
Rationale: "explanation : let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 4 | | : : 4 : 1 webs 4 : 1 | = > 1 * 4 * x = 4 * 1 * 4 = > x = 4 answer : d"
Answer: d
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 36 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 65.80 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 36 % of 1100 ) + ( 32 % of 900 ) = 396 + 288 = 684 failed = 2000 - 684 = 1316 failed % = [ ( 1316 / 2000 ) x 100 ] % = 65.8 % . answer : b"
Answer: b
Question (physics): john left home and drove at the rate of 50 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 50 * 2 + 3 * 55 = 265 miles . answer d"
Answer: d
Question (physics): a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 88 kg , e ) 96 kg
Rationale: "volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced x density of water = ( 0.06 x 1000 ) kg = 60 kg . answer : option b"
Answer: b
Question (geometry): one of the longest sides of the triangle is 20 m , the other side is 10 m . area of the triangle is 80 m ^ 2 . what is the another side of the triangle ?
Options: a ) 2 sqrt ( 61 )
b ) 2 sqrt ( 62 )
c ) 2 sqrt ( 63 )
d ) 2 sqrt ( 64 )
e ) 2 sqrt ( 65 )
Rationale: base of triangle is 20 and area is 80 therefore height = 2 * 80 / 20 = 8 . now one side of triangle is of 10 . so we can get the point were the base is divided by applying pythagoras therm so division pt = sqrt ( 10 ^ 2 - 8 ^ 2 ) = sqrt ( 36 ) = 6 threfore other half is 14 . now second side = sqrt ( 14 ^ 2 + 8 ^ 2 ) = sqrt ( 260 ) = 2 sqrt ( 65 ) answer : e
Answer: e
Question (general): anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ?
Options: a ) $ 8 , b ) $ 12 , c ) $ 6 , d ) $ 21 , e ) $ 10
Rationale: 5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a
Answer: a
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 70 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 160 - - 2 subtracting 1 from 2 we have c - a = 70 ; answer : b"
Answer: b
Question (general): a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.56 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "800 * 8.2 6560.0 gm 6.56 kg answer : a"
Answer: a
Question (probability): if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 4 flips and not on the last flip ?
Options: a ) 1 / 8 , b ) 1 / 32 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 16
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Answer: b
Question (physics): the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 990 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 990 d = 90 the answer is e ."
Answer: e
Question (other): income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 14000 , then find his savings ?
Options: a ) 3600 , b ) 2800 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 14000 = > x = 2800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 2800 . answer : b"
Answer: b
Question (general): two employees x and y are paid a total of rs . 750 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.90 , b ) s . 250.90 , c ) s . 290.90 , d ) s . 300.90 , e ) s . 340.90
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 750 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 750 ⇒ y [ 12 / 10 + 1 ] = 750 ⇒ 22 y / 10 = 750 ⇒ 22 y = 7500 ⇒ y = 7500 / 22 = rs . 340.90 e )"
Answer: e
Question (gain): the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 19 . find the sum :
Options: a ) 4500 , b ) 7600 , c ) 5000 , d ) 6000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 19 , the sum = 400 × 19 = 7600 answer b"
Answer: b
Question (general): 1398 x 1398 = ?
Options: a ) 1624404 , b ) 1851404 , c ) 1951404 , d ) 1954404 , e ) none of these
Rationale: "explanation : 1398 x 1398 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = 14002 - ( 2 × 1400 × 2 ) + 22 = 1960000 - 5600 + 4 = 1954404 . answer : option d"
Answer: d
Question (gain): machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 60 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 10 , e ) 16
Rationale: "machine b produces 100 part in 60 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 60 / 2 = 30 minutes . now , machine a produces 100 parts in 30 minutes which is 100 / 30 = 10 / 3 parts / minute . 10 / 3 parts x a total of 6 minutes = 20 a"
Answer: a
Question (geometry): if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 3 , e ) 18
Rationale: "let length of rectangle = l 3 ^ 2 = l * 4 = > l = 9 / 4 = 3 answer d"
Answer: d
Question (general): if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : b .
Answer: b
Question (general): set j consists of 5 consecutive even numbers . if the smallest term in the set is - 2 , what is the range of the positive integers in set j ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: since there are only 5 integers , another approach is the just list all 5 . we get : - 2 , 0,2 , 4 , 6 range of positive integers = 6 - 2 = 4 answer : c
Answer: c
Question (other): what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 450 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 450 = 3 ^ 900 * 2 ^ 900 the answer is e ."
Answer: e
Question (general): the sum of all the integers g such that - 26 < g < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 g = - 49 . d is the answer ."
Answer: d
Question (gain): a sum of money at simple interest amounts to $ 680 in 3 years and to $ 710 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 590 , d ) $ 549 , e ) $ 675
Rationale: "c $ 590 s . i . for 1 year = $ ( 710 - 680 ) = $ 30 . s . i . for 3 years = $ ( 30 x 3 ) = $ 90 . principal = $ ( 680 - 90 ) = $ 590 ."
Answer: c
Question (general): a student chose a number , multiplied it by 2 , then subtracted 180 from the result and got 104 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 142 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 180 = 104 2 x = 284 x = 142 correct answer d"
Answer: d
Question (physics): two brothers take the same route to school on their bicycles , one gets to school in 25 minutes and the second one gets to school in 36 minutes . the ratio of their speeds is
Options: a ) 4 : 5 , b ) 1 : 2 , c ) 6 : 7 , d ) 5 : 6 , e ) none
Rationale: solution let us name the brothers as a and b . = ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 36 = 5 : 6 answer d
Answer: d
Question (physics): the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 9 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 45 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 9 = 45 km imo , correct answer is ` ` c . ' '"
Answer: c
Question (general): in a certain warehouse , 50 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 72 , d ) 102 , e ) 144
Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 50 % of the packages weigh less than 75 pounds so , 50 % oft = number of packages that weigh less than 75 pounds 50 % of 240 = 120 , so 120 packages weigh less than 75 pounds of those 120 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 120 - 48 = 72 = c"
Answer: c
Question (physics): in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph . = 8 kmph . answer c"
Answer: c
Question (gain): the ratio of the cost price and the selling price is 4 : 5 . the profit percent is ?
Options: a ) 17 , b ) 56 , c ) 25 , d ) 28 , e ) 12
Rationale: "let c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % . answer : c"
Answer: c
Question (gain): if 45 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 65 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 86 % , b ) 87 % , c ) 88 % , d ) 89 % , e ) 90 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 100 + 0.50 x 78 + 0.05 x 63 = 87.15 the class average ( rounded ) is 87 % final answer b ) 87 %"
Answer: b
Question (gain): of the votes cast on a certain proposal , 62 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 280 , b ) 290 , c ) 300 , d ) 310 , e ) 320
Rationale: let x be the total number of votes cast . 0.6 x = 0.4 x + 62 0.2 x = 62 x = 310 the answer is d .
Answer: d
Question (general): how many of the integers between 20 and 80 are even ?
Options: a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 20 to 80 is 60 numbers half of them is even . . which is 30 answer : b"
Answer: b
Question (general): if a and b are positive integers , and a = 5 b + 20 , the greatest common divisor of a and b can not be
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: if b is 2 , 4 , 5 , or 10 , then gcd of a and b is 2 , 4 , 5 , and 10 respectively . so , by poe the answer must be d . still : if b is a multiple of 6 , then a is 20 greater than a multiple of 6 , so not a multiple of 6 , so both of them can not be divisive by 6 . answer : d .
Answer: d
Question (general): what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 ) / 44444444 ^ 2
Options: a ) 88888883 , b ) 88888827 , c ) 16992677 , d ) 88888237 , e ) 88888182
Rationale: "ans : a let x = 44444444 ( x + 1 ) × ( 2 x − 3 ) × ( x − 2 ) + ( x − 6 ) x 2 ( x + 1 ) × ( 2 x − 3 ) × ( x − 2 ) + ( x − 6 ) x 2 ( x 2 − x − 2 ) × ( 2 x − 3 ) + ( x − 6 ) x 2 ( x 2 − x − 2 ) × ( 2 x − 3 ) + ( x − 6 ) x 2 2 x 3 − 2 x 2 − 4 x − 3 x 2 + 3 x + 6 + x − 6 x 22 x 3 − 2 x 2 − 4 x − 3 x 2 + 3 x + 6 + x − 6 x 2 2 x 3 − 5 x 2 x 2 = 2 x − 52 x 3 − 5 x 2 x 2 = 2 x − 5 substituting the value of x in 2 x - 5 , we get 88888883 answer : a"
Answer: a
Question (general): find the greatest number which leaves the same remainder when it divides 21 , 57 and 105 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "105 - 57 = 48 57 - 21 = 36 105 - 21 = 84 the h . c . f of 36 , 48 and 84 is 12 . answer : c"
Answer: c
Question (general): at a summer camp with 2100 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 2100 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 62 , b ) 68 , c ) 66 , d ) 64 , e ) 66 2 / 3
Rationale: "total - 2100 participants campers are aged 8 to 12 = ( 1 / 2 ) * 2100 = 1050 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 1050 = 1400 percentage = ( 1400 / 2100 ) * 100 = 66 2 / 3 % answer : option e"
Answer: e
Question (physics): express 35 mps in kmph ?
Options: a ) 122 , b ) 188 , c ) 126 , d ) 140 , e ) 124
Rationale: "35 * 18 / 5 = 126 kmph answer : c"
Answer: c
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 999 , d ) s . 1665 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.5 = 1665 answer : d"
Answer: d
Question (general): what is the area inscribed by the lines y = 4 , x = 2 , y = 6 - 2 x on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 6 , e ) e ) 8
Rationale: "first , let ' s graph the lines y = 4 and x = 2 at this point , we need to find the points where the line y = 6 - 2 x intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = 6 - 2 x to get y = 6 - 2 ( 2 ) = 2 perfect , when x = 2 , y = 2 , so one point of intersection is ( 2,2 ) for the horizontal line , we know that y = 4 , so we ' ll plug y = 4 into the equation y = 6 - 2 x to get 4 = 6 - 2 x . solve to get : x = 1 so , when y = 4 , x = 1 , so one point of intersection is ( 1,4 ) now add these points to our graph and sketch the line y = 6 - 2 x at this point , we can see that we have the following triangle . the base has length 1 and the height is 2 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 1 ) ( 2 ) = 1 answer : a"
Answer: a