regisss/math_qa huggingface dataset:
Problem: the difference between a two digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: sol . since the number is greater than the number obtained on reversing the digits , so the ten ' s is greater than the unit ' s digit . let the ten ' s and units digit be 2 x and x respectively . then , ( 10 × 2 x + x ) - ( 10 x + 2 x ) = 36 ⇔ 9 x = 36 ⇔ x = 4 . ∴ required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer b
Answer: b
Problem: 40 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 41
Rationale: "explanation : 40 + 5 * 12 / ( 180 / 3 ) = 40 + 5 * 12 / ( 60 ) = 40 + ( 5 * 12 ) / 60 = 40 + 1 = 41 . answer : e"
Answer: e
Problem: on dividing 13787 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 155 , c ) 852 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13787 - 14 ) / 89 = 155 answer ( b )"
Answer: b
Problem: in a mixture 60 litres , the ra ɵ o of milk and water 2 : 1 . if the this ra ɵ o is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these
Rationale: explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters answer : d
Answer: d
Problem: a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part
Options: a ) 17 inches , b ) 20 inches , c ) 15 inches , d ) 18 inches , e ) 19 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : b"
Answer: b
Problem: ramu bought an old car for rs . 42000 . he spent rs . 12000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 12 % , b ) 16 % , c ) 20.18 % , d ) 82 % , e ) 23 %
Rationale: "total cp = rs . 42000 + rs . 12000 = rs . 54000 and sp = rs . 64900 profit ( % ) = ( 64900 - 54000 ) / 54000 * 100 = 20.18 % answer : c"
Answer: c
Problem: there are 79 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 49 , e ) 32
Rationale: lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 79 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 79 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 49 answer : d
Answer: d
Problem: a man traveled a total distance of 900 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 240 , b ) 280 , c ) 320 , d ) 360 , e ) 400
Rationale: "total distance traveled = 900 km . distance traveled by plane = 300 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 300 = 900 5 x / 3 = 600 x = 360 km the answer is d ."
Answer: d
Problem: the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 51 : 53
Rationale: "let c . p . of the article be rs . x . then , required ratio = 102 % of x / 106 % of x = 102 / 106 = 51 / 53 = 51 : 53 answer : e"
Answer: e
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: what is the sum of all even numbers from 1 to 601 ?
Options: a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111
Rationale: "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c"
Answer: c
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 200 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 200 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 18 ( 44 - 12 ) must be those with four screens or more b is the answer"
Answer: b
Problem: in a certain pond , 70 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,750 , d ) 2,500 , e ) 10,000
Rationale: "this is a rather straight forward ratio problem . 1 . 70 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 70 / x thus , x = 1750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . c"
Answer: c
Problem: there are 990 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 165
Rationale: "female = x male = 990 - x x / 2 + 990 - x / 4 = 1 / 3 * ( 990 ) = 330 x = 330 x / 2 = 165 is supposed to be the answer m is missing something correct option e"
Answer: e
Problem: 5 years ago amith was 3 times as old as his daughter and 10 years hence , he will be two times as old as his daughter . then amith ’ s current age is ,
Options: a ) 10 , b ) 50 , c ) 40 , d ) 20 , e ) 60
Rationale: d 20 amith ’ s age = a and daughter ’ s age = b then , a – 5 = 3 ( b – 5 ) = > a – 3 b + 10 = 0 … … ( 1 ) and , a + 10 = 2 ( a + 10 ) = > a – 2 b – 10 = 0 … … ( 2 ) solving the 2 eqns , we will get a = 50 , b = 20 . therefore , amith ’ s age is 50 and his daughter ’ s age is 20
Answer: d
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 7 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1280 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 7 ) = $ 280 total revenue : 1000 + 280 = $ 1280 the answer is b ."
Answer: b
Problem: a retailer buys a radio for rs 232 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 21.4 % , d ) 52 % , e ) none of these
Rationale: explanation : cost price = ( 232 + 15 ) = 247 sell price = 300 gain = ( 53 / 247 ) * 100 = 21.4 % . answer : c
Answer: c
Problem: a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction q of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction q = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Problem: aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 3 , b ) 6 , c ) 2 , d ) 5 , e ) 8
Rationale: "xyt / ( x + y ) x = 3 , y = 6 , t = 3 3 * 6 * 3 / 3 + 6 = 54 / 9 = 6 answer : b"
Answer: b
Problem: a man engaged a servant on the condition that he would pay him rs . 710 and a uniform after a year service . he served only for 8 months and got rs . 460 and a uniform . find the price of the uniform ?
Options: a ) rs . 40 , b ) rs . 30 , c ) rs . 25 , d ) rs . 20 , e ) rs . 45
Rationale: "8 / 12 = 2 / 3 * 710 = 473.33 460.00 - - - - - - - - - - - - - - - 13.33 1 / 3 uniform 13.33 1 - - - - - - - - - - - - - - - ? = > rs . 40 answer : a"
Answer: a
Problem: the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 73 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 600 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 125 + 73 33 x / 100 = 198 x = 600 answer is d"
Answer: d
Problem: a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is
Options: a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 180 ⇔ x = 15 . hence , the first number is 45 . answer b"
Answer: b
Problem: mike , jim and bob are all professional fisherman . mike can catch 30 fish in one hour , jim can catch twice as much and bob can catch 50 % more than jim . if the 3 started to fish together and after 40 minutes mike and bob left , how many fish did the 3 fishermen catch in one hour ?
Options: a ) 110 , b ) 120 , c ) 140 , d ) 130 , e ) 112
Rationale: all of them catch fishes in relation to number 30 . . . . 2 / 3 * 30 + 2 * 30 + 2 * 1.5 * 30 * 2 / 3 = 140 answer is c
Answer: c
Problem: in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and john will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d ."
Answer: d
Problem: it was calculated that 75 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 10 days . , b ) 20 days . , c ) 25 days . , d ) 12.5 days . , e ) 15 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 10 * 75 ) the total no . of days required to complete the work = ( 75 * 10 ) / 50 = 15 answer : e"
Answer: e
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 7 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 14 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10
Rationale: suppose the water in each jug is l liters cx x ( 1 / 7 ) = l cx = 7 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 7 l = 1 / 14 answer will be b
Answer: b
Problem: a grocery store bought some mangoes at a rate of 4 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 1 : 2 , e ) 1 : 2
Rationale: "the cost price of a mango = 1 / 4 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 4 = 1 / 12 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 3 - 1 / 6 = 1 / 6 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 12 * 6 / 1 = 1 / 2 = 1 : 2 e"
Answer: e
Problem: if the weight of 13 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.18 kg , e ) none
Rationale: answer ∵ weight of 13 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 13 kg ∴ weight of 6 m long rod = 13.4 x 6 / 13 = 6.18 kg option : d
Answer: d
Problem: if each side of a rectangle is increased by 50 % with the length being double the width , find the percentage change in its area ?
Options: a ) 284 % , b ) 276 % , c ) 265.25 % , d ) 284.5 % , e ) 275 %
Rationale: "area = 2 a x a new length = 250 a / 100 = 5 a / 2 new width = 150 a / 100 = 3 a / 2 new area = ( 5 a x 3 a ) / ( 2 x 2 ) = ( 15 a ² / 4 ) increased area = = ( 15 a ² / 4 ) - a ² increase % = [ ( 11 a ² / 4 ) x ( 1 / a ² ) x 100 ] % = 275 % answer : e"
Answer: e
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre
Options: a ) 22488 , b ) 16500 , c ) 27889 , d ) 23778 , e ) 29982
Rationale: "explanation : area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b ) rs . 16500"
Answer: b
Problem: if the area of a circle decreases by 25 % , then the radius of a circle decreases by
Options: a ) 13 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 25 ) % = ( 100 − 10 √ 75 ) % = 100 - 87 = 13 % answer a"
Answer: a
Problem: alfred buys an old scooter for $ 4700 and spends $ 1000 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 1.75 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 1000 = $ 5700 s . p . = $ 5800 gain = 5800 - 5700 = $ 100 gain % = 100 / 5700 * 100 = 1.75 % answer is c"
Answer: c
Problem: find the average of all the numbers between 11 and 36 which are divisible by 5 .
Options: a ) 25 , b ) 77 , c ) 20 , d ) 28 , e ) 10
Rationale: "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer : a"
Answer: a
Problem: how many e ways can jason sit with his 5 friends in a row of 6 seats with an aisle on either side of the row , if jason insists on sitting next to one of the aisles ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 540 , e ) 720
Rationale: jason can select his seat in 2 ways ( two aisles ) his 1 st of 4 friends have 5 seats to select = > his 2 nd of remaining 3 friends will have 4 seat to chose from . . . and so on total ways e = > 2 * 5 * 4 * 3 * 2 * 1 = 240 . b
Answer: b
Problem: 56 : 65 : : 68 : ?
Options: a ) 49 , b ) 84 , c ) 86 , d ) 64 , e ) 56
Rationale: "ans 86 reverse of 68 answer : c"
Answer: c
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 148000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 25 , c ) 35 , d ) 40 , e ) 55
Rationale: "0.037 * 10 ^ 5 can be written as 3700 148000 * 10 ^ ( - 3 ) can be written as 148 required = 3700 / 148 = 25 answer : b"
Answer: b
Problem: the sum of ages of 5 children born 1.5 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 13
Rationale: "let the ages of children be x , ( x + 1.5 ) , ( x + 3 ) , ( x + 4.5 ) and ( x + 6 ) years . then , x + ( x + 1.5 ) + ( x + 3 ) + ( x + 4.5 ) + ( x + 6 ) = 50 5 x = 35 x = 7 . x + 6 = 7 + 6 = 13 answer : e"
Answer: e
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 100 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 55
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 100 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 10 ( 10 ) = 100 so we know that there are 10 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 100 = 110 20 + 90 = 110 30 + 80 = 110 etc . since there are 10 total terms , this pattern will create 5 ' pairs ' of 110 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 5 ) ( 110 ) / ( 10 ) = 55 answer : e"
Answer: e
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 7.5 , b ) 20 , c ) 30 , d ) 32 , e ) 40
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 5 ) = 1 / 20 the cistern will be filled in 20 / 1 hrs i . e . , 20 hrs . answer : b"
Answer: b
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 4 ?
Options: a ) 123,750 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 4 seeing the options after dividing and finding the reminder of 2 my answer was a"
Answer: a
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1200 votes . what is the total number of votes polled ?
Options: a ) 4500 , b ) 5200 , c ) 6900 , d ) 7520 , e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1200 20 x / 100 = 1200 x = 1200 * 100 / 20 = 6000 answer is e"
Answer: e
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Problem: tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: there are 6 ways to roll a seven : 1 and 6 , 6 and 1 , 2 and 5 , 5 and 2 , 3 and 4 , 4 and 3 . there are 6 * 6 = 36 ways to roll two six - sided dice . thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6 / 36 = 1 / 6 c
Answer: c
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90000 . the 75 associates have an average salary of $ 30000 . 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
Problem: a man can row upstream at 37 kmph and downstream at 53 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 45
Rationale: "us = 37 ds = 53 m = ( 53 + 37 ) / 2 = 45 answer : e"
Answer: e
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 4 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 10 : 12 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 4 - - > e : s = 5 : 4 = 15 : 12 . thus , l : s = 10 : 12 . answer : d ."
Answer: d
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,500 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 6,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 40 % , b ) 35 % , c ) 30 % , d ) 20 % , e ) 28 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 1500 : 6000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : d"
Answer: d
Problem: solve below question 2 x - 1 = 17
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 9
Rationale: 1 . add 1 to both sides : 2 x - 1 + 1 = 17 + 1 2 . simplify both sides : 2 x = 18 3 . divide both sides by 2 : 4 . simplify both sides : x = 9 e
Answer: e
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.54 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 36 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.54 - - > 15 p - 13.5 p = 54 - - > p = 36 . answer : c ."
Answer: c
Problem: 80 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.8 * 5 / 8 = 4 / 8 = 1 / 2 = 0.5 correct option : b"
Answer: b