regisss/math_qa huggingface dataset:
Problem: in a renowned city , the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 86,400 , e ) 259,200
Rationale: "every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d"
Answer: d
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 24,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 180 %
Rationale: "the percent increase is ( 24947 - 8902 ) / 8902 = 16045 / 8902 = 1.80 so the approximate answer is e"
Answer: e
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 70 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 1000 π , b ) 400 π , c ) 280 π , d ) 200 π , e ) 20 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 70 π ) = 280 π the answer is c ."
Answer: c
Problem: find the cost of fencing around a circular field of diameter 30 m at the rate of rs . 5 a meter ?
Options: a ) 288 , b ) 132 , c ) 772 , d ) 592 , e ) 471.25
Rationale: "2 * 22 / 7 * 15 = 94.25 94.25 * 5 = rs . 471.25 answer : e"
Answer: e
Problem: if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 2 ) # - 3 =
Options: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 2 , d ) - 1 / 12 , e ) - 4 / 3
Rationale: ( - 1 ) ^ 2 / 2 = 1 / 2 ( - 1 / 2 ) ^ 2 / - 3 = - 1 / 12 so d is my answer
Answer: d
Problem: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 15 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 26 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 15 : 39 : : 12 : x working hours / day 6 : 5 15 x 6 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 15 x 6 ) x = 26 . answer : d"
Answer: d
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 5 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 5 , b ) - 1 , c ) 0 , d ) 1 , e ) 5
Rationale: "when x = 1 and when x = - 5 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 5 ) f ( 0 ) = - 5 the answer is a ."
Answer: a
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 600 ft , d ) 900 ft , e ) 1000 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 40 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 15 . sub x = 15 either in ( x + 5 ) * 30 or in x * 40 to get the distance , which is 600 . so the correct choice is c ."
Answer: c
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 6480 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4.5 = 6480 . answer : d"
Answer: d
Problem: a and b invests rs . 10000 each , a investing for 8 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 5000 , find their shares ?
Options: a ) 2000,8000 , b ) 2000,4000 , c ) 2000,3000 , d ) 1000,3000 , e ) 4000,3000
Rationale: "the ratio of their profits a : b = 8 : 12 = 2 : 3 share of a in the total profit = 2 / 5 * 5000 = rs . 2000 share of b in the total profit = 3 / 5 * 5000 = rs . 3000 answer : c"
Answer: c
Problem: a circular path of 12 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 50 p per m 2 ?
Options: a ) rs . 49 , b ) rs . 40 , c ) rs . 81.72 , d ) rs . 42 , e ) rs . 43
Rationale: "explanation : π ( 14 ^ 2 - 12 ^ 2 ) = 22 / 7 * 52 = 163.43 163.43 * 1 / 2 = rs . 81.72 answer : option c"
Answer: c
Problem: last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 8 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 132 % , b ) 147 % , c ) 158 % , d ) 176 % , e ) 188 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.08 * 1.1 x = 0.088 x 0.088 x / 0.06 x = 88 / 60 = 1.47 = 147 % the answer is b ."
Answer: b
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 10 cm and breadth is increased by 10 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 25 cm , b ) 35 cm , c ) 30 cm , d ) 45 cm , e ) 55 cm
Rationale: "let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x ^ 2 sq . cm . new length = ( 2 x − 10 ) cm new breadth = ( x + 10 ) cm new area = ( 2 x − 10 ) ( x + 10 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 10 ) ( x + 10 ) = 2 x ^ 2 + 75 ⇒ 2 x ^ 2 + 20 x − 10 x − 100 = 2 x ^ 2 + 75 ⇒ 10 x − 100 = 75 ⇒ 10 x = 75 + 100 = 175 ⇒ x = 175 / 10 = 17.5 cm length = 2 x = 2 × 17.5 = 35 cm answer : b"
Answer: b
Problem: factory x ' s bulbs work for over 5000 hours in 78 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 65 % of cases . it is known that factory x supplies 90 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 76.4 % , b ) 76.7 % , c ) 77.4 % , d ) 75 % , e ) 73.9 %
Rationale: "for x , 90 % of 78 % will work . for y , 10 % of 65 % will work . * 10 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.90 ( 0.78 ) = . 702 0.10 ( 0.65 ) = 0.065 the combined probability then is 70.2 + 6.5 = 76.7 % ans b"
Answer: b
Problem: 7 years ago , paula was 3 times as old as karl . in 2 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 26 , b ) 32 , c ) 38 , d ) 44 , e ) 50
Rationale: "p - 7 = 3 ( k - 7 ) and so p = 3 k - 14 p + 2 = 2 ( k + 2 ) ( 3 k - 14 ) + 2 = 2 k + 4 k = 16 p = 34 p + k = 50 the answer is 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 5 : 4 . the ratio of economy cars to sport utility vehicles is 3 : 2 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 5 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 4 - - > e : l = 5 : 4 = 15 : 12 . the ratio of economy cars to sport utility vehicles is 3 : 2 - - > e : s = 3 : 2 = 15 : 10 . thus , l : s = 12 : 10 = 6 : 5 . answer : c ."
Answer: c
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 65 % . staff are allowed a further 60 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.15 d , b ) 0.16 d , c ) 0.65 d , d ) 0.14 d , e ) 0.05 d
Rationale: "effective discount = a + b + ab / 100 = - 65 - 60 + ( - 65 ) ( - 60 ) / 100 = - 86 sale price = d * ( 1 - 86 / 100 ) sale price = . 14 * d answer ( d )"
Answer: d
Problem: the difference of two numbers is 11 . one third of their sum is 7 . what are the two numbers ?
Options: a ) 21,10 , b ) 16,5 , c ) 3,14 , d ) 11,10 , e ) 7,14
Rationale: "let the two numbers be x and y . equation ( i ) : x - y = 11 equation ( ii ) : ( x + y ) / 3 = 7 solve system of equations : x + y = 21 x - y = 11 ( add equations together ) - - - 2 x = 32 - - - x = 16 16 - y = 11 - - - y = 5 since x = 16 and y = 5 , answer b ( 16,5 ) is correct ."
Answer: b
Problem: 75 % of 480 = ( ? ) x 15 ?
Options: a ) 32 , b ) 18 , c ) 360 , d ) none of these , e ) can not be determined
Rationale: "answer let 75 % of 480 = a x 15 . ⇒ ( 75 x 480 ) / 100 = 15 a ∴ a = ( 75 x 480 ) / ( 100 x 15 ) = 24 correct option : d"
Answer: d
Problem: if a truck is traveling at a constant rate of 54 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 40
Rationale: "speed = 54 km / hr = > 54,000 m / hr in one minute = > 54000 / 60 = 900 meters in one sec = > 900 / 60 = 15 meters time = total distance need to be covered / avg . speed = > 600 / 15 = 40 and hence the answer : e"
Answer: e
Problem: what number times ( 1 ⁄ 7 ) ^ 2 will give the value of 7 ^ 3 ?
Options: a ) 7 , b ) 49 , c ) 343 , d ) 2401 , e ) 16,807
Rationale: "x * ( 1 / 7 ) ^ 2 = 7 ^ 3 x = 7 ^ 2 * 7 ^ 3 = 7 ^ 5 = 16,807 the answer is e ."
Answer: e
Problem: the ratio 2 : 10 expressed as percent equals to
Options: a ) 50 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 90 %
Rationale: "explanation : actually it means 2 is what percent of 10 , which can be calculated as , ( 2 / 10 ) * 100 = 2 * 10 = 20 answer : option d"
Answer: d
Problem: a watch was sold at a loss of 21 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 560 , b ) 882 , c ) 799 , d ) 778 , e ) 901
Rationale: "79 % 104 % - - - - - - - - 25 % - - - - 140 100 % - - - - ? = > rs . 560 answer : a"
Answer: a
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 8 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 4 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: originally there were 3 k cooks and 8 k waiters . the new ratio is 1 : 4 which equals 3 : 12 . 12 k = 8 k + 12 k = 3 there are 9 cooks . the answer is c .
Answer: c
Problem: a bag contains 5 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 3 / 7 , b ) 6 / 11 , c ) 12 / 21 , d ) 19 / 39 , e ) 29 / 49
Rationale: "the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 38 / 78 = 19 / 39 the answer is d ."
Answer: d
Problem: if 60 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 36 60 / 100 * 3 / 5 * x = 36 x = ( 36 * 25 / 9 ) = 100 required number = 100 . correct option : b"
Answer: b
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 15 % , c ) 12 % , d ) 22 % , e ) 19 %
Rationale: "s . i . for 3 years = ( 12005 - 9800 ) = rs . 2205 s . i . for 5 years = rs . 2205 / 3 * 5 = rs . 3675 . principal = ( 9800 - 3675 ) = rs . 6125 hence , rate = ( 100 * 3675 ) / ( 6125 * 5 ) = 12 % answer : c"
Answer: c
Problem: two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 200 in interest bringing his total balance to $ 1,200 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 1,000 ?
Options: a ) 19 % , b ) 30 % , c ) 42 % , d ) 45 % , e ) 25 %
Rationale: "investment 1000 dollars 1 st year total gained = 200 total amount end of first year = 1200 second year account increased by 20 % = 1200 * 0.2 = 240 therefore total amount by second year end = 1420 so total percentage increase in money = ( 1420 - 1000 ) * 100 / 1000 = 42 % correct answer c = 42 %"
Answer: c
Problem: in a college , 1 percent of students hate math , 2 percent of students hate english , 1 percent hate french and 4 percent hate german . can you find out the percentage of students who hate all 4 subjects ?
Options: a ) 8 % , b ) 5 % , c ) 7 % , d ) 12 % , e ) 19 %
Rationale: a 8 % of student hate all four subjects .
Answer: a
Problem: walking at 6 / 7 th of his usual speed , a man is 25 mins too late . his usual time is
Options: a ) 7.5 hrs , b ) 1.5 hrs , c ) 2.5 hrs , d ) 1.67 hrs , e ) 2.67 hrs
Rationale: "as the distance is same s * t = 6 / 7 s * ( t + 25 ) solving this we get t = 150 sec 150 / 60 = 2.5 hrs answer : c"
Answer: c
Problem: amit and ananthu can do a work in 15 days and 30 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 30 ananthu can do work in = 4 / 5 * 30 = 24 days so total days = 24 + 3 = 27 days answer : e"
Answer: e
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 39 , find the value of ab .
Options: a ) 15 , b ) 8 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 39 - 9 = 30 ab = 15 . answer is a ."
Answer: a
Problem: a cylinder of height h is 2 / 3 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 2 / 3 new cylinder 3 / 5 so 3 / 5 / 2 / 3 = 3 / 5 * 3 / 2 = 0.90 or 90 % . answer e"
Answer: e
Problem: a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , what is the ratio between a and b ?
Options: a ) 2 : 3 , b ) 3 : 2 , c ) 4 : 5 , d ) 5 : 3 , e ) can not be determined
Rationale: "( 4 / 15 ) a = ( 2 / 5 ) b a = ( ( 2 / 15 ) * ( 15 / 4 ) ) b a = ( 3 / 2 ) b a / b = 3 / 2 a : b = 3 : 2 option b"
Answer: b
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 sq . cm , what is the width of the rectangle ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 294 3 w ^ 2 / 2 = 294 w ^ 2 = 196 w = 14 the answer is c ."
Answer: c
Problem: express a speed of 108 kmph in meters per second ?
Options: a ) 30 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "108 * 5 / 18 = 30 mps answer : a"
Answer: a
Problem: the ratio of the two natural numbers is 6 : 5 . if a certain number is subtracted to both the numbers , the ratio becomes 5 : 4 . if the larger number exceeds the smaller number by 5 , find the number subtracted ?
Options: a ) 8 , b ) 5 , c ) 15 , d ) 22 , e ) 6
Rationale: let the two numbers be 6 x and 5 x . let the numbers subtracted to both so that their ratio becomes 5 : 4 be k . ( 6 x - k ) / ( 5 x - k ) = 5 / 4 = > 24 x - 4 k = 25 x - 5 k = > k = x . 6 x - 5 x = 5 = > x = 5 k = x = 5 . answer : b
Answer: b
Problem: 200 is what percent of 50 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 400 %
Rationale: "200 = x * 50 / 100 x = 400 % ans ; e"
Answer: e
Problem: a big container is 30 % full with water . if 54 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 120 liters
Rationale: "a big container is 30 % full with water and after 54 liters of water is added , the container becomes 75 % full . hence these 54 liters account for 45 % of the container , which means that the capacity of it is 54 / 0.45 = 120 liters . or : if the capacity of the container is x liters then : 0.3 x + 54 = 0.75 x - - > x = 120 liters . answer : e"
Answer: e
Problem: at what rate percent per annum will the simple interest on a sum of money be 6 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 12 %
Rationale: "let sum = x . then , s . i . = 6 x / 5 , time = 10 years . rate = ( 100 * 6 x ) / ( x * 5 * 10 ) = 12 % answer : e"
Answer: e
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 5 x + 7 .
Options: a ) 6.125 , b ) 8.125 , c ) 10.125 , d ) 12.125 , e ) 14.125
Rationale: this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 5 x + 7 = ( - 2 x + 7 ) ( x + 1 ) the roots are 7 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.25 the maximum value is - 2 ( 1.25 ) ^ 2 + 5 ( 1.25 ) + 7 = 10.125 the answer is c .
Answer: c
Problem: the perimeter of one face of a cube is 40 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 1000 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 40 / 4 = 10 cm volume = a * a * a = 10 * 10 * 10 = 1000 cm cube option d"
Answer: d
Problem: a starts business with rs . 3500 and after 10 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 31500 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 10 = 2 months . so there profit ratio = ( 3500 ã — 12 ) : ( 2 x ) = 2 : 3 â ‡ ’ x = 31500 answer : d"
Answer: d
Problem: if the personal income tax rate is lowered from 45 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 48000 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 3150 , d ) $ 7200 , e ) $ 10000
Rationale: saving = ( 45 - 30 ) % of 48000 = 7200 . answer : d
Answer: d
Problem: a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 85 , c ) rs . 88 , d ) rs . 100 , e ) none of these
Rationale: sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 12 = rs . 88 . answer : c
Answer: c
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 10 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 10 / 2.5 ) = 4 hrs answer : d"
Answer: d
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 16 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 27 , c ) 28 , d ) 20 , e ) 24
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 16 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 16 = 15 m / s speed of each train = v = 15 / 2 = 7.5 m / s = 7.5 × 36 / 10 km / hr = 27 km / hr answer : option b"
Answer: b
Problem: how much is 80 % of 60 is greater than 4 / 5 of 25 ?
Options: a ) 15 , b ) 28 , c ) 16 , d ) 12 , e ) 73
Rationale: "( 80 / 100 ) * 60 â € “ ( 4 / 5 ) * 25 48 - 20 = 28 answer : b"
Answer: b
Problem: a 6 litre sol is 30 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3 , e ) e . 2.4
Rationale: 30 % of 6 = 1.8 50 % of 6 = 3 shortage is 1.2 so we need to have 1.2 / 50 % to get 50 % alcohol content . = 2.4 e
Answer: e
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 470 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 550 , d ) 560 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 470 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 770 a + b + c = 70 per hour so for eight hrs = 70 * 8 = 560 = answer = d"
Answer: d
Problem: can you find a 7 digit number which describes itself . the first digit is the number of zeros in the number . the second digit is the number of ones in the number , etc . for example , in the number 21200 , there are 2 zeros , 1 one , 2 twos , 0 threes and 0 fours .
Options: a ) 4211000 , b ) 1211000 , c ) 5211000 , d ) 2211000 , e ) 3211000
Rationale: e 3211000
Answer: e
Problem: what decimal fraction is 50 ml of a litre ?
Options: a ) . 5 , b ) . 05 , c ) . 05 , d ) 0.05 , e ) none of these
Rationale: "answer required fraction = 50 / 1000 = 5 / 100 = . 05 correct option : b"
Answer: b
Problem: gary ’ s gas station serves an average of 13 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,088 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 13 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 13 + 10 ) = 16 * 68 = 1088 answer : a"
Answer: a
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is
Options: a ) 8.5 km / hr , b ) 9 km / hr , c ) 10 km / hr , d ) 12.5 km / hr , e ) none
Rationale: sol . man ' s rate in still in water = ( 15 - 2.5 ) km / hr = 12.5 km / hr . man ' s rate against the current = ( 12.5 - 2.5 ) km / hr = 10 km / hr . answer c
Answer: c
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 8.5 sec , d ) 2.2 sec , e ) 4.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 100 / 40 = 2.5 sec . answer : a"
Answer: a
Problem: if r is a positive integer , and r / 15 = 8.2 , what is the remainder when r is divided by 15 ?
Options: a ) a . 1 , b ) b . 2 , c ) c . 3 , d ) d . 4 , e ) e . 8
Rationale: if r were a multiple of 15 , the quotient r / 15 would be an integer . the fact that it ' s a decimal tells us that 15 goes into r eight whole times and some decimal part of a time . this decimal part , 0.2 is the remainder divided by the divisor . let b be the remainder . b / 15 = 0.2 = 1 / 5 b = ( 15 ) * ( 1 / 5 ) = 3 answer = ( c )
Answer: c
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 15 , 12 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 15 , b ) 1 / 2 , c ) 15 / 22 , d ) 25 / 12 , e ) 11 / 4
Rationale: "the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 12 + 1 / 18 = 5 / 36 the time it takes y and z is 36 / 5 the ratio of times is 15 / ( 36 / 5 ) = 5 * 15 / 36 = 25 / 12 the answer is d ."
Answer: d
Problem: what is the 20 - fifth decimal to the right in the fraction 10 / 11 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 10 / 11 = 0.9090909090 . . . the odd - numbered decimal places are 9 . the answer is e .
Answer: e
Problem: one cutting machine cuts 100 metal bars in 30 minutes . another machine does the same job in 30 seconds . what time will it take if both machines are put on the same work ?
Options: a ) 25.0 seconds , b ) 29.5 seconds , c ) 30.0 seconds , d ) 30.5 seconds , e ) 30.7 seconds
Rationale: by guess it is clear that the time taken will be less than 30 seconds and very near to it . therefore , answer 29.5 seconds will be correct . answer - b
Answer: b
Problem: what is the average ( arithmetic mean ) of the numbers 16 , 17 , 17 , 18 , 19 , 19 and 20 ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 19
Rationale: "{ 16 , 17 , 17 , 18 , 19 , 19 , 20 } = { 18 - 2,18 - 1,18 - 1 , 18 , 18 + 1 , 18 + 1,18 + 2 } - - > the average = 18 . answer : a ."
Answer: a
Problem: the sum of 5 th and 21 th term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0
Options: a ) 11 , b ) 10 , c ) 12 , d ) 13 , e ) 14
Rationale: "t 5 + t 21 = t 8 + t 15 + t 13 = > a + 4 d + a + 20 d = a + 7 d + a + 14 d + a + 12 d = > a + 9 d = 0 = > t 10 = 0 i . e . 10 th term is zero . answer : b"
Answer: b
Problem: what is 0.01 percent of 15,356 ?
Options: a ) 0.15356 , b ) 1.5356 , c ) 15.356 , d ) 0.015356 , e ) 0.0015356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.01 ( 1 / 100 ) 15,356 . the answer is 1.5356 . hence , the correct answer is b .
Answer: b
Problem: evaluate : 12 + sqrt ( - 5 + 7 ã — 8 ã · 4 ) = ?
Options: a ) 90 , b ) 91 , c ) 92 , d ) 93 , e ) 94
Rationale: "according to order of operations , inner brackets first where 7 x 8 ã · 4 is first calculated since it has a multiplication and a division . 7 x 8 ã · 4 = 56 ã · 4 = 14 hence 12 + sqrt ( - 5 + 7 ã — 8 ã · 4 ) = 12 + sqrt ( - 5 + 14 ) = 12 + sqrt ( 9 ) = 12 + 81 = 93 correct answer d ) 93"
Answer: d
Problem: in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards n will he need to gain this sunday if he wants to keep his season average above 100 yards ?
Options: a ) 101 , b ) 116 , c ) 130 , d ) n = 131 , e ) n = 141
Rationale: sorry the answer n = 131 is d .
Answer: d
Problem: ab + cd = jjj , where ab and cd are two - digit numbers and jjj is a 3 digit number ; a , b , c , and d are distinct positive integers . in the addition problem above , what is the value of c ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) can not be determined
Rationale: ab and cd are two digit integers , their sum can give us only one three digit integer of a kind of jjj it ' s 111 . so , a = 1 . 1 b + cd = 111 now , c can not be less than 9 , because no to digit integer with first digit 1 ( mean that it ' s < 20 ) can be added to two digit integer less than 90 to have the sum 111 ( if cd < 90 meaning c < 9 cd + 1 b < 111 ) - - > c = 9 answer : d .
Answer: d
Problem: 8 friends went to a hotel and decided to pay the bill amount equally . but 7 of them could pay rs . 80 each as a result 8 th has to pay rs . 70 extra than his share . find the amount paid by him .
Options: a ) 140 , b ) 121 , c ) 110 , d ) 160 , e ) none
Rationale: "explanation : average amount paid by 7 persons = rs . 80 increase in average due to rs . 70 paid extra by the 8 th men = rs . 70 / 7 = rs . 10 therefore , average expenditure of 8 friends = rs . 80 + rs . 10 = rs . 90 therefore , amount paid by the 11 th men = rs . 90 + rs . 70 = rs . 160 correct option : d"
Answer: d
Problem: if 4 men can colour 48 m long cloth in 2 days , then 8 men can colour 36 m long cloth in
Options: a ) 0.75 day , b ) 2 days , c ) 1.2 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 × 8 = 0.75 day . a"
Answer: a
Problem: a person lent a certain sum of money at 6 % per annum at simple interest and in 8 years the interest amounted to $ 572 less than the sum lent . what was the sum lent ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 1300 , e ) 1400
Rationale: "p - 572 = ( p * 6 * 8 ) / 100 p = 1100 the answer is b ."
Answer: b
Problem: a circular ground whose diameter is 35 metres , has a 1.4 metre - broad garden around inside of it . what is the area of the garden in square metres ?
Options: a ) 301.5 , b ) 484.12 , c ) 401.84 , d ) 301.0 , e ) 301.84
Rationale: "req . area = ï € [ ( 35 ) 2 â € “ ( 33.6 ) 2 ] = 22 â  „ 7 ã — ( 68.6 ã — 1.4 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 68.6 ã — 0.2 = 301.84 sq m . answer e"
Answer: e
Problem: the edges of three metal cubes are 4 cm , 5 cm , and 6 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 6.6 , b ) 6.8 , c ) 7.0 , d ) 7.2 , e ) 7.4
Rationale: "the total volume is 4 ^ 3 + 5 ^ 3 + 6 ^ 3 = 405 the edge of the new cube is the cube root of 405 which is about 7.4 cm . the answer is e ."
Answer: e
Problem: mr . hernandez , who was a resident of state x for only 8 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 10 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 1500 , b ) $ 1720 , c ) $ 1600 , d ) $ 1300 , e ) $ 1160
Rationale: "total tax for the year = 22,500 x 10 % = 2250 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 8 / 12 ) = 1500 answer a"
Answer: a
Problem: walking at 3 / 4 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 36 , b ) 48 , c ) 60 , d ) 62 , e ) 66
Rationale: let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 12 ) t / 4 = 9 t = 36 the answer is a .
Answer: a
Problem: if a : b = 4 : 1 , then find ( a - 3 b ) / ( 2 a - b ) ?
Options: a ) 6 / 7 , b ) 1 / 7 , c ) 5 / 7 , d ) 3 / 2 , e ) 4 / 7
Rationale: answer : option b a / b = 4 / 1 = > a = 4 b ( a - 3 b ) / ( 2 a - b ) = ( 4 b - 3 b ) / ( 8 b - b ) = b / 7 b = > 1 / 7
Answer: b
Problem: log 3 n + log 12 n what is 3 digit number n that will be whole number
Options: a ) 6291 , b ) 7292 , c ) 1728 , d ) 1929 , e ) 1727
Rationale: "no of values n can take is 1 12 ^ 3 = 1728 answer : c"
Answer: c
Problem: the average weight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 23 , b ) 43 , c ) 21 , d ) 31 , e ) 43
Rationale: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d
Answer: d
Problem: the price of a shirt is increased by 15 % and then reduced by 15 % . the final price of the shirt is ?
Options: a ) $ 97.75 , b ) $ 90 , c ) $ 91.56 , d ) $ 95.62 , e ) $ 93.45
Rationale: let the original price be $ 100 new final price = 85 % of ( 115 % of $ 100 ) = 85 / 100 * 115 / 100 * 100 = $ 97.75 answer is a
Answer: a
Problem: if two integers x , y ( x > y ) are selected from - 3 to 4 ( inclusive ) , how many cases are there ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: there are 8 integers from - 3 to 4 inclusive . 8 c 2 = 28 . the answer is e .
Answer: e
Problem: in 100 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 10 , b ) 12 , c ) 30 , d ) 40 , e ) 20
Rationale: dist = ( 100 / 45 * 9 ) = 20 m answer e
Answer: e
Problem: the citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 ( in base 5 ) buildings numbered 1 to 1000 . how many 3 s are used in numbering these buildings ? express result in terms of base 10 .
Options: a ) 54
b ) 64
c ) 75
d ) 85
e ) 100
Rationale: no of 3 s b / w 1 - 99 is 20,100 - 199 is 20 and so on . so leavn d range b / w 300 - 399 total no of 3 s is ( 9 * 20 = ) 180 . no of 3 s b / w 300 - 399 is ( 20 + 100 = ) 120 . total no of 3 s b / w 1 - 1000 = 120 + 180 = 300 in base 10 300 = 3 * 5 ^ 2 = 75 . answer : c
Answer: c
Problem: of the people who responded to a market survey , 150 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 5 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 180 , c ) 240 , d ) 360 , e ) 480
Rationale: ratio = 5 : 1 = > 5 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 150 = > 5 x = 150 = > x = 30 hence total no . of respondents = 150 + 30 = 180 hence b is the answer .
Answer: b
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 9 and 10 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 230 , d ) 345 , e ) 395
Rationale: "clearly , the numbers are ( 23 x 9 ) and ( 23 x 10 ) . larger number = ( 23 x 10 ) = 230 . answer : option c"
Answer: c
Problem: a semicircle has a radius of 11 . what is the approximate perimeter of the semicircle ?
Options: a ) 45
b ) 51
c ) 57
d ) 63
e ) 69
Rationale: the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 11 + 2 * 11 which is about 57 . the answer is c .
Answer: c
Problem: a milk man has 15 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 20 % . answer : a"
Answer: a
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 37 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 37 : fully covered day 36 : half covered so 36 days answer : a"
Answer: a
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 64 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 5 : 8 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 64 = 5 : 8 answer : d"
Answer: d
Problem: the total circumference of two circles is 80 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 10.6 , d ) 9.7 , e ) 18.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 80 where 2 r = r thus : 2 π r + 4 π r = 80 6 π r = 80 r = approx 4.2 π r + 2 r π = 80 3 π r = 80 r = approx 8.4 r + r = approx 10.6 answer is c"
Answer: c
Problem: 20 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 26 , d ) 30 , e ) 45
Rationale: "let number is x . when 20 added to it , = ( x + 20 ) 2 multiplied to sum , = 2 * ( x + 20 ) now , = [ { 2 * ( x + 20 ) } / 2 ] and , = [ { 2 * ( x + 20 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 20 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 40 ) / 2 ) = 44 + 2 2 x + 40 = 46 * 2 x + 20 = 46 x = 46 - 20 x = 26 so , required number is : 26 . answer : c"
Answer: c
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction e of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is e = 2 / 14 = 1 / 7 . answer : e
Answer: e
Problem: a shopkeeper sold an article at $ 100 with 40 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 71 , e ) $ 69
Rationale: cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 140 = $ 71 ( approximately ) answer is d
Answer: d
Problem: a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 23760 , b ) 47520 , c ) 33000 , d ) 48600 , e ) 54000
Rationale: "whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12 c 2 = 66 ways . now 2 out of 12 means total of 6 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 6 * 5 * 4 * 3 * 2 * 1 = 720 here alt and alt are the same : so 720 / 2 = 360 ways . total ways of selecting = ( selecting 2 out of 12 ) * arranging those teams in shifts = 66 * 360 = 23760 ans : a"
Answer: a
Problem: instead of multiplying a number by 5 , the number is divided by 10 . what is the percentage of error obtained ?
Options: a ) 96 % , b ) 98 % , c ) 95 % , d ) 97 % , e ) 96 %
Rationale: "let the number be x the right number is 5 x the wrong number is x / 10 error is ( 5 x - x / 10 ) = 49 x / 10 percentage of error is ( ( 49 x / 10 ) / 5 x ) * 100 = 98 % answer : b"
Answer: b
Problem: a car going at 30 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 60
Rationale: let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 30 m per hour = 1.5 hours distance travelled by car a = 30 * 1.5 = 45 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 45 / ( 4 / 3 ) = 60 miles per hour answer e
Answer: e
Problem: a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ?
Options: a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km
Rationale: "difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )"
Answer: b
Problem: if 325 / 999 = 0.125 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "0 . [ u ] 325 [ / u = 0.325325325 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 35 percent alcohol ?
Options: a ) 7 / 2 , b ) 300 / 13 , c ) 20 / 3 , d ) 8 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 35 % of ( 100 + x ) or 20 + x = ( 100 + x ) 7 / 20 400 + 20 x = 700 + 7 x 13 x = 300 x = 300 / 13 ans : b"
Answer: b
Problem: pipe p can fill a tank in 2 hours , pipe q in 4 hours and pipe r in 12 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 1.2 hours , c ) 3 hours , d ) 1.5 hours , e ) 2.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 2 + 1 / 4 + 1 / 12 ) = 5 / 6 all the three pipes together will fill the tank = 6 / 5 = 1.2 hours answer b"
Answer: b
Problem: 300 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 26 trees have 25 gaps between them , required distance ( 300 / 25 ) = 12 b
Answer: b
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a"
Answer: a
Problem: find the ratio in which rice at rs . 10.0 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 5 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 60 : 100 = 3 : 5 answer c"
Answer: c
Problem: in a 100 m race , sam beats john by 6 seconds . on the contrary , if sam allowed john to start 36 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 10.66 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 6 second but this difference is 0 if john allows sam to start the race from 36 m ahead . that means jhon was 36 m away from finishing line when they started together . so he will cover 36 m in 6 seconds . so his speed = 36 / 6 = 6 metre / second . so time taken = 100 / 6 = 16.66 seconds . so sam took = 10.66 seconds . correct answer = a"
Answer: a
Problem: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that balls drawn contain exactly two green balls ?
Options: a ) 9 / 16 , b ) 7 / 18 , c ) 12 / 55 , d ) 14 / 67 , e ) 19 / 87
Rationale: total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 4 c 2 * 8 c 1 = 6 * 8 = 48 probability = 48 / 220 = 12 / 55 answer is c
Answer: c
Problem: debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debanshu averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Problem: if d is the standard deviation a , b , and c , what is the standard deviation of a + 2 , b + 2 , c + 2 ?
Options: a ) 2 d , b ) d , c ) 2 d + 2 , d ) 8 d , e ) 2 d + 4
Rationale: concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 2 is added in each term of set { a , b , c } then the new set { a + 2 , b + 2 , c + 2 } will remain same as the previous standard deviation i . e . d answer : b
Answer: b
Problem: at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 75 billion of credit , or 1 / 2 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 412.16 , b ) 150 , c ) 400 , d ) 416.67 , e ) 420.34
Rationale: "system of equations a = ( 36 / 100 ) c ( 1 / 2 ) a = 75 - - > a = 150 substitution 150 = ( 36 / 100 ) c c = ( 100 / 36 ) 150 calculate 150 / 36 * 100 the correct answer is d - the correct answer will be slightly smaller than 513 . therefore , the correct answer is 475 ."
Answer: d
Problem: three table runners have a combined area of 204 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 204 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 204 - 24 - 140 all three = 20 answer : b"
Answer: b
Problem: nr books bought nr of people 6 3 7 1 8 5 9 2 what is the median of books bought per person ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 6 , d ) d ) 8 , e ) e ) 18
Rationale: 6 , 6,6 , 7,8 , 8,8 , 8,8 , 9,9 so you will observer that the median of the list is 8 . ans d
Answer: d
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 55 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 55 x = 22 the answer is b ."
Answer: b
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 34 ) ?
Options: a ) 2 , b ) 7 , c ) 13 , d ) 17 , e ) 19
Rationale: "f ( 34 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 * 32 * 34 the greatest prime factor in this list is 17 . the answer is d ."
Answer: d