Cheukting/mathqa huggingface dataset:
Question (general): in an it company , there are a total of 60 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 15 , b ) 50 , c ) 55 , d ) 35 , e ) 65
Rationale: "you could pick 10 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 15 . a"
Answer: a
Question (physics): machine a takes 20 hours to complete a certain job and starts that job at 6 am . after four hour of working alone , machine a is joined by machine b and together they complete the job at 1 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 9.99 , b ) 3,615 , c ) 3.62 , d ) 4.62 , e ) 6.14
Rationale: "let us assume total job = 100 units a finishes 100 units in 20 hrs ( given ) hence a ( working rate ) = 5 units / hr now given that a works for 4 hr ( so 20 units done ) then a and b finish total work in 7 hours . hence a and b finish 80 units in 3 hours . of these 3 x 5 = 15 units were done by a . hence b did 65 units in 3 hours . hence b ( working rate ) = 65 / 3 units / hr hence b takes 100 x 3 / 65 = 4.62 hours to complete the job . answer d ."
Answer: d
Question (physics): two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 15 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 8 hr , c ) 8.57 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 15 = 7 / 60 hence , tank will be filled in 60 / 7 = 8.57 hour option ( c )"
Answer: c
Question (physics): to fill a tank , 100 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four - fifth of its present ?
Options: a ) 100 , b ) 125 , c ) 150 , d ) 175 , e ) 200
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 100 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 100 x ) / ( 4 x / 5 ) = ( 100 x ) x 5 / 4 x = 500 / 4 = 125 answer is b ."
Answer: b
Question (physics): in what time will a railway train 65 m long moving at the rate of 32 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 65 / 32 * 18 / 5 = 7 sec answer : e"
Answer: e
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.8 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1518.8 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.8 * 2 ) 2 * 2.8 = > 759.4 759.4 * 2 = rs . 1518.8 answer : a"
Answer: a
Question (other): the rational number for recurring decimal 0.125125 . . . . is :
Options: a ) 125 / 990 , b ) 125 / 999 , c ) 125 / 900 , d ) 12 / 999 , e ) 12 / 990
Rationale: 0.125125 . . . = 0.125 = 125 / 999 answer is b .
Answer: b
Question (general): if n is a natural number , then ( 7 ( n 2 ) + 7 n ) is always divisible by :
Options: a ) 3 and 7 , b ) 14 only , c ) 7 only , d ) 7 and 14 , e ) none
Rationale: "solution ( 7 n 2 + 7 n ) = 7 n ( n + 1 ) , which is always divisible by 7 and 14 both , since n ( n + 1 ) is always even . answer d"
Answer: d
Question (general): how many of the positive divisors of 360 are also multiples of 4 not including 360 ?
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 16
Rationale: "360 = 2 ^ 5 * 3 * 5 = ( 4 ) * 2 * 3 ^ 2 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 1 , 2 , and 1 . there are ( 1 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 360 . the answer is b ."
Answer: b
Question (gain): 3 candidates in an election and received 1136 , 8236 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55.4 % , c ) 57 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 8236 + 11628 ) = 21000 so , required percentage = 11628 / 21000 * 100 = 55.4 % b"
Answer: b
Question (physics): if 12 men or 20 women can do a piece of work in 81 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 60 days , e ) 40 days
Rationale: "d 60 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 81 days . so , 27 women can do it in ( 20 * 81 ) / 27 = 60 days ."
Answer: d
Question (gain): increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by
Options: a ) 32.25 % , b ) 31.00 % , c ) 30.25 % , d ) 30.00 % , e ) 22.50 %
Rationale: "you can do this by approximation , or with straight math by calculating 100 * 1.15 ^ 2 . or step by step : if you increase 100 by 15 % you ' ll get 115 , then if you increase 115 = 100 + 15 by 15 % again , 100 will gain 15 again and 15 will gain its 15 % which is 2.25 , so total gain is 15 + 2.25 = 17.25 - - > 115 + 17.25 = 132.25 . answer : a ."
Answer: a
Question (gain): a merchant purchased a jacket for $ 48 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 16
Rationale: "actual cost = $ 48 sp = actual cost + mark up = actual cost + 40 % sp = 48 * 100 / 60 on sale sp = 80 / 100 ( 48 * 100 / 60 ) = 64 gross profit = $ 16 answer is e"
Answer: e
Question (physics): pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed o ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this o we get x = 8 . b .
Answer: b
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 6 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 90
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 6 * 180 / 12 = 90 ounces of water e"
Answer: e
Question (probability): the probability that a number selected at random from the first 100 natural numbers is a composite number is ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 5 / 2
Rationale: "explanation : the number of exhaustive events = 100 c ₁ = 100 . we have 25 primes from 1 to 100 . number of favourable cases are 75 . required probability = 75 / 50 = 3 / 2 . answer is d"
Answer: d
Question (geometry): a circular logo is enlarged to fit the lid of a jar . the new diameter is 60 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50
b ) 80
c ) 100
d ) 143.36
e ) 250
Rationale: let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 6.24 , so radius is 3.12 new area = 9.7344 π increase in area is 5.7344 π % increase in area = 5.7344 / 4 * 100 so , % increase is 143.36 % answer will be ( d )
Answer: d
Question (physics): if 4 men working 10 hours a day earn rs . 1000 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1350 , c ) rs 1620 , d ) rs 1680 , e ) none of these
Rationale: explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1000 : x hence 4 * 10 * x = 9 * 6 * 1000 or x = 9 * 6 * 1000 / 4 * 10 = 1350 answer : b
Answer: b
Question (general): the ages of two person differ by 20 years . if 10 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 35 , 15 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 10 ) = ( x + 20 - 10 ) = > 4 x = 60 = > x = 15 their present ages are 35 years and 15 year . answer : d"
Answer: d
Question (general): a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000
Answer: b
Question (gain): in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate ?
Options: a ) 358000 , b ) 368000 , c ) 357000 , d ) 358000 , e ) 367000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 answer : c"
Answer: c
Question (general): if 7 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 4 , c ) - 3 , d ) 1 , e ) - 10
Rationale: "the phrase “ 7 is one solution of the equation ” means that one value of x is 7 . thus , we first must plug 7 for x into the given equation to determine the value of k . so we have 7 ^ 2 + ( 3 ) ( 7 ) + k = 10 49 + 21 + k = 10 70 + k = 10 k = - 60 next we plug - 60 into the given equation for k and then solve for x . x ^ 2 + 3 x – 60 = 10 x ^ 2 + 3 x – 70 = 0 ( x + 10 ) ( x - 7 ) = 0 x = - 10 or x = 7 thus , - 10 is the other solution . answer e ."
Answer: e
Question (other): if both 112 and 33 are factors of the number a * 43 * 62 * 1311 , then what is the smallest possible value of a ?
Options: a ) 121 , b ) 3267 , c ) 363 , d ) 33 , e ) none of the above
Rationale: explanatory answer step 1 : prime factorize the given expression a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311 step 2 : find factors missing after excluding ' a ' to make the number divisible by both 112 and 33 112 is a factor of the given number . if we do not include ' a ' , 11 is not a prime factor of the given number . if 112 is a factor of the number , 112 should have been in ' a ' 33 is a factor of the given number . if we do not include ' a ' , the number has only 32 in it . therefore , if 33 has to be a factor of the given number ' a ' has to contain 31 in it . therefore , ' a ' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors . the smallest value that ` ` a ' ' can take is 363 . choice c is the correct answer .
Answer: c
Question (geometry): two isosceles triangles have equal vertical angles and their areas are in the ratio 9 : 25 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 3 / 5
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 9 / 25 - - > height / height = 3 / 5 . answer : e ."
Answer: e
Question (general): a straight line in the xy - plane has y - intercept of 20 . on this line the x - coordinate of the point is 150 and y - coordinate is 600 then what is the slope of the line ?
Options: a ) 3.9 , b ) 4.6 , c ) 5.2 , d ) 6 , e ) 8.1
Rationale: "eq of line = y = mx + c c = 20 x = 150 y = 150 m + 20 , substitute y by 600 as given in question . 600 = 150 m + 20 , m = 3.9 correct option is a"
Answer: a
Question (general): a case contains c cartons . each carton contains b boxes , and each box contains 400 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 400 bc , b ) 400 b / c , c ) 800 bc , d ) 800 b / c , e ) 800 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 400 clips / box = 800 bc paper clips the answer is c ."
Answer: c
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 238 , b ) 200 , c ) 287 , d ) 117 , e ) 198
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5300 [ 4 l - 40 ] = 5300 / 26.50 = 200 4 l = 240 l = 240 / 4 = 60 meters . answer : b"
Answer: b
Question (gain): mohit sold an article for $ 15000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 12500 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 15000 - 10 / 100 ( 15000 ) = 15000 - 1500 = $ 13500 = > 1.08 x = 13500 = > x = 12500 a"
Answer: a
Question (physics): calculate the time it will take for a train that is 250 meter long to pass a bridge of 150 meter length , if the speed of the train is 35 km / hour ?
Options: a ) 56 seconds , b ) 3515 seconds , c ) 41.15 seconds , d ) 30 seconds , e ) 36 seconds
Rationale: "speed = 35 km / hr = 35 * ( 5 / 18 ) m / sec = 9.72 m / sec total distance = 250 + 150 = 400 meter time = distance / speed = 400 * ( 1 / 9.72 ) = 41.15 seconds answer : c"
Answer: c
Question (gain): a number increased by 20 % gives 480 . the number is ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 480 ( 120 × 4 = 480 ) 100 % - - - - - - - > 400 ( 100 × 4 = 400 ) option ' c '
Answer: c
Question (general): if k ^ 3 is divisible by 1620 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "1620 = 2 ^ 2 * 3 ^ 4 * 5 therefore k must include at least 2 * 3 ^ 2 * 5 = 90 . the answer is d ."
Answer: d
Question (general): what least number should be added to 1052 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 6 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1052 / 23 ) gives remainder 17 17 + 6 = 23 , so we need to add 6 answer : option c"
Answer: c
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 16 % if no discount was offered ?
Options: a ) 17608 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 18560
Rationale: price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 16 % if no discount was offered = 16000 * 116 / 100 = rs . 18560 . answer : e
Answer: e
Question (general): in a simultaneous throw of a pair of dice , find the probability of getting a total more than 7
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
Rationale: "total number of cases = 6 * 6 = 36 favourable cases = [ ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,4 ) , ( 5,6 ) , ( 5,3 ) , ( 5,5 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) ] = 15 so probability = 15 / 36 = 5 / 12 answer is d"
Answer: d
Question (general): a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.6 , e ) 19.1
Rationale: "a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.00 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.0 + $ 15.6 = $ 18.6 . answer : d ."
Answer: d
Question (physics): the sum of 3 consecutive even numbers is 246 . what are the numbers ?
Options: a ) 80 , 8284 , b ) 65 , 6871 , c ) 45 , 4742 , d ) 100 , 10249 , e ) 87 , 8889
Rationale: first x make the first x second x + 2 even numbers , sowe add 2 to get the next third x + 4 add 2 more ( 4 total ) to get the third f + s + t = 246 summeansaddfirst ( f ) plussecond ( s ) plusthird ( t ) ( x ) + ( x + 2 ) + ( x + 4 ) = 246 replace each f , s , and t withwhatwe labeled them x + x + 2 + x + 4 = 246 here the parenthesis are not needed 3 x + 6 = 246 combine like terms x + x + x and 2 + 4 − 6 − 6 subtract 6 fromboth sides 3 x = 240 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 80 our solution for x first 80 replace x in the origional listwith 80 . second ( 80 ) + 2 = 82 the numbers are 80 , 82 , and 84 . third ( 80 ) + 4 = 84 correct answer a
Answer: a
Question (physics): if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 36 m long cloth in
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 6 = 1 day . a"
Answer: a
Question (geometry): the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 40 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75.00 %
b ) 56.80 %
c ) 110 %
d ) 150 %
e ) 180 %
Rationale: let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 40 percent to make square c length of each side of square c = 1.4 * 20 = 28 area of c = 28 ^ 2 = 784 difference in areas of c and cummulative areas of a and b = 784 - ( 400 + 100 ) = 284 percent is the area of square c greater than the sum of the areas of squares a and b = ( 284 / 500 ) * 100 % = 56.80 % answer b
Answer: b
Question (gain): a fruit seller had some apples . he sells 40 % apples and still he has 420 . originally he had how many apples ?
Options: a ) 400 , b ) 500 , c ) 700 , d ) 450 , e ) 650
Rationale: suppose originally he had x apples then ( 100 - 40 ) % of x = 420 60 x / 100 = 420 x = 700 answer is c
Answer: c
Question (gain): a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 228 for it , the cost price of the cricket bat for a is :
Options: a ) 152 , b ) 120 , c ) 130 , d ) 160 , e ) 210
Rationale: "a 152 125 % of 120 % of a = 228 125 / 100 * 120 / 100 * a = 228 a = 228 * 2 / 3 = 152 ."
Answer: a
Question (gain): by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 300 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.5 % , b ) 1.9 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 300 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 300 ) / 100 + ( 1.8 * 700 ) / 100 = 15 gms % of liquid x in resultant mixture = ( 15 / 1000 ) * 100 = 1.5 % answer : 1.5 % answer : a"
Answer: a
Question (physics): two pipes a and b can fill a tank in 10 hour and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 2 hrs , b ) 6 hrs , c ) 5 hrs , d ) 4 hrs , e ) 1 hr
Rationale: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 15 part filled by a + b in 1 hour = 1 / 10 + 1 / 15 = 1 / 6 both the pipes will together will fill the tank in 6 hours . answer is b"
Answer: b
Question (general): if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 3 ) # 3 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 27 , d ) - 1 / 12 , e ) - 4 / 3
Rationale: "( - 1 ) ^ 2 / 3 = 1 / 3 ( 1 / 3 ) ^ 2 / 3 = 1 / 27 so c is my answer"
Answer: c
Question (general): how many integers between 362,855 and 852,755 have tens digit 1 and units digit 3 ?
Options: a ) 4,888 , b ) 4,898 , c ) 4,889 , d ) 4,869 , e ) 4,896
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 362,855 and 852,755 is 852,755 - 362,855 = 489,900 - one number per each hundred gives 133,900 / 100 = 4,889 numbers . answer : c ."
Answer: c
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 15 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 250 m , b ) 300 m , c ) 120 m , d ) 200 m , e ) 166 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 15 = 300 m . answer : b"
Answer: b
Question (geometry): two right circular cylinders of equal volumes have their heights in the ratio 1 : 2 . find the ratio of their radii .
Options: a ) √ 3 : 1
b ) √ 7 : 1
c ) √ 2 : 1
d ) 2 : 1
e ) 3 : 1
Rationale: explanation : let their heights be h and 2 h and radii be r and r respectively then . π r 2 h = π r 2 ( 2 h ) = > r 2 / r 2 = 2 h / h = 2 / 1 = > r / r = √ 2 / 1 = > r : r = √ 2 : 1 answer is c
Answer: c
Question (general): a certain country had a total annual expenditure of $ 4.8 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 4,8 x 10 ^ 11 ) / 240 000 000 = ( 4,8 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 2 x 10 ^ ( 11 - 8 ) = 2 x 10 ^ 3 = 2000 . answer is c ."
Answer: c
Question (general): a waitress ' s income consists of her salary and tips . during one week , her tips were 2 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9
Rationale: "her tips were 2 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 2 / 4 ) ( $ 4 ) = $ 2 so , her total income = $ 4 + $ 2 = $ 6 what fraction of her income for the week came from tips $ 2 / $ 6 = 1 / 3 = c"
Answer: c