regisss/math_qa huggingface dataset:
Problem: a man rows his boat 70 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 5 kmph , d ) 8 kmph , e ) 7 kmph
Rationale: "speed downstream = d / t = 75 / ( 2 1 / 2 ) = 28 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 28 - 18 ) / 2 = 5 kmph answer : c"
Answer: c
Problem: a train passes a station platform in 48 sec and a man standing on the platform in 40 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 80 , b ) 120 , c ) 60 , d ) 90 , e ) 50
Rationale: "speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 40 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 48 = 10 = > x = 80 m . answer : a"
Answer: a
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 12 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 32 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.88 * 150 x = 132 x hence total profit = 32 % option b"
Answer: b
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18600 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6000 , d ) 6200 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18600 = 6200 answer : d"
Answer: d
Problem: a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : ( 300 / 35 ) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d
Answer: d
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 6 ¤ √ 6 =
Options: a ) 0 , b ) 5 , c ) 10 , d ) 24 , e ) 20
Rationale: "x = √ 6 and y also = √ 6 applying the function ( √ 6 + √ 6 ) ^ 2 - ( √ 6 - √ 6 ) ^ 2 = ( 2 √ 6 ) ^ 2 - 0 = 4 x 6 = 24 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 6 and y = √ 6 you get the answer 24 . answer d"
Answer: d
Problem: an investment yields an interest payment of $ 240 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 32,000
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 240 = > p = ( 240 * 4 * 10 ^ 2 ) / 3 = 80 * 4 * 10 ^ 2 = 320 * 10 ^ 2 = 32000 answer e"
Answer: e
Problem: the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle ?
Options: a ) 22 , b ) 37 , c ) 87 , d ) 84 , e ) 82
Rationale: "let inner radius be r metres . then , 2 r = 440 ; r = = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer : d"
Answer: d
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 25 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 331.2 km , d ) 550 km , e ) 600 km
Rationale: "sol . average speed of a tractor = 23 km / h the speed of a bus in an hour = 23 × 2 = 46 km the speed of a car in an hour = 9 / 5 * 46 = 82.8 km so , the distance covered by car in 4 h is 82.8 × 4 = 331.2 km ans . ( c )"
Answer: c
Problem: there are 56 lights which are functional and each is controlled by a separate on / off switch . two children x and y start playing with the switches . x starts by pressing every third switch till he reaches the end . y , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 18 , b ) 19 , c ) 17 , d ) 15 , e ) 16
Rationale: editing my solution : number of switches = 56 number of switches turned on by x : 3 , 6 , . . . 54 = 18 number of switches turned on by y : 5 , 10 , . . . . 55 = 11 few switches are turned on by x and later turned off by y : lcm ( 35 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both x and y as they are turned off . number of switches that are turned on = ( 18 - 6 ) + ( 11 - 6 ) = 17 answer : c
Answer: c
Problem: how many multiples of 5 are there between 5 to 95 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: "as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the unit ’ s place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 . answer c"
Answer: c
Problem: the difference between the local value and face value of 7 in the numeral 657903 is :
Options: a ) 0 , b ) 7896 , c ) 6993 , d ) 903 , e ) 803
Rationale: ( local value ) - ( face value ) = ( 7000 - 7 ) = 6993 . answer : c
Answer: c
Problem: find the value of b from ( 15 ) ^ 2 x 9 ^ 2 ã · 356 = b .
Options: a ) 53.2 , b ) 52.2 , c ) 51.2 , d ) 8.2 , e ) 54.2
Rationale: given exp . = ( 15 ) ^ 2 x 9 ^ 2 ã · 356 = b = 225 x 81 ã · 356 = 51.2 c
Answer: c
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 4 : 5 , b ) 9 : 10 , c ) 14 : 15 , d ) 19 : 20 , e ) 24 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 ( 3 x + 2 x ) = 2 ( y + y ) 5 x = 2 y ( 5 / 2 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : ( 25 / 4 ) * x ^ 2 = 24 : 25 the answer is e ."
Answer: e
Problem: how many cuboids of length 5 m , width 2 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 18 answer is e ."
Answer: e
Problem: an engineer undertakes a project to build a road 10 km long in 60 days and employs 30 men for the purpose . after 20 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 20 , b ) 15 , c ) 30 , d ) 45 , e ) 60
Rationale: "30 workers working already let x be the total men required to finish the task in next 40 days 2 km done hence remaining is 8 km also , work has to be completed in next 40 days ( 60 - 20 = 40 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 20 ) / ( 2 * 40 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : c"
Answer: c
Problem: a retailer bought a machine at a wholesale price of $ 81 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 108 , c ) 120 , d ) 135 , e ) 160
Rationale: "my solution : wholesale price = 81 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 81 + 1 / 5 ( 81 ) x = 108 ; answer : b"
Answer: b
Problem: 1.5 , 2.3 , 3.1 , 3.9 , . . ?
Options: a ) 0.6 , b ) 0.8 , c ) 0.4 , d ) 0.24 , e ) 0.15
Rationale: "1.5 + 0.8 = 2.3 2.3 + 0.8 = 3.1 3.1 + 0.8 = 3.9 3.9 + 0.8 = 4.7 answer : b"
Answer: b
Problem: at steel factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at steel factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Problem: a circular swimming pool is surrounded by a concrete wall 4 ft wide . if the area of the concrete wall surrounding the pool is 11 / 25 that of the pool , then the radius of the pool is ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 387 , e ) 19
Rationale: "let the radius of the pool be rft radius of the pool including the wall = ( r + 4 ) ft area of the concrete wall = { \ color { black } \ pi \ left [ ( r + 4 ) ^ { 2 } - r ^ { 2 } \ right ] } = { \ color { black } \ pi \ left [ ( r + 4 + r ) ( r + 4 - r ) \ right ] = 8 \ pi ( r + 2 ) } sq feet { \ color { black } \ rightarrow 8 \ pi ( r + 2 ) = \ frac { 11 } { 25 } \ pi r ^ { 2 } \ rightarrow 11 r ^ { 2 } = 200 ( r + 2 ) } radius of the pool r = 20 ft answer : b ) 20 ft"
Answer: b
Problem: 36 men can complete a piece of work in 18 days . in how many days will 81 men complete the same work ?
Options: a ) 8 , b ) 77 , c ) 88 , d ) 29 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 81 : 36 : : 18 : x x = 8 answer : a ) 8 days"
Answer: a
Problem: simplify : 0.2 * 0.4 + 0.6 * 0.8
Options: a ) 0.52 , b ) 0.42 , c ) 0.48 , d ) 0.64 , e ) 0.56
Rationale: "given exp . = 0.2 * 0.4 + ( 0.6 * 0.8 ) = 0.08 + 0.48 = 0.56 answer is e ."
Answer: e
Problem: what is 0.05 percent of 12,356 ?
Options: a ) 0.6178 , b ) 61.78 , c ) 6.178 , d ) 0.06178 , e ) 0.006178
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.05 ( 1 / 100 ) 12,356 . the answer is 6.178 . hence , the correct answer is c .
Answer: c
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container s ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio e of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore e , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Problem: an article is bought for rs . 800 and sold for rs . 1200 , find the loss percent ?
Options: a ) 55 % , b ) 25.25 % , c ) 33.33 % , d ) 45 % , e ) 50 %
Rationale: "800 - - - - 400 400 - - - - ? = > 50 % answer : e"
Answer: e
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.5 = $ 255 answer a"
Answer: a
Problem: diana works 10 hours per day on monday , wednesday and friday , and 15 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 1800 per week . how much does she earn in dollars per hour ?
Options: a ) 20 , b ) 22 , c ) 30 , d ) 24 , e ) 25
Rationale: so , she works 30 hours in 3 days so , she works 30 hours in 2 days so in a week she works 60 hours ( 30 + 30 ) and earns $ 1800 so , hourly wage is 1800 / 60 = > 30 hence answer will be ( c ) 30
Answer: c
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 8 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 520 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 8 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 = 8 × 65 = 520 miles correct answer is c ) 520 miles"
Answer: c
Problem: the mean of 50 observations was 36 . it was found later that an observation 30 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.02 , b ) 36.14 , c ) 36.12 , d ) 36.11 , e ) 36.8
Rationale: explanation : correct sum = ( 36 * 50 + 30 - 23 ) = 1825 . correct mean = = 1807 / 50 = 36.14 answer : b ) 36.14
Answer: b
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 200 more than a :
Options: a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 5800
Rationale: explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 200 total earning = \ inline \ frac { 58 xy } { 100 } = 5800 answer : e ) rs . 5800
Answer: e
Problem: the average of first 14 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "sum of 14 even numbers = 14 * 15 = 210 average = 210 / 14 = 15 answer : e"
Answer: e
Problem: a certain rectangular crate measures 12 feet by 16 feet by 18 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4
b ) 5
c ) 6
d ) 8
e ) 10
Rationale: for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 18 x 16 i . e . of radius 16 / 2 = 8 d
Answer: d
Problem: for what values of k will the pair of equations 4 ( 3 x + 4 y ) = 48 and kx + 12 y = 30 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: we have 2 equations 1 . 4 ( 3 x + 4 y ) = 48 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b
Answer: b
Problem: the sector of a circle has radius of 21 cm and central angle 120 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 11.5 cm , c ) 91.8 cm , d ) 86 cm , e ) 99.5 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 120 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 44 + 42 = 86 cm answer : d"
Answer: d
Problem: how many different positive integers are factors of 40 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 6 , e ) 4
Rationale: 2 * 20 4 * 10 8 * 5 answer : d
Answer: d
Problem: a couple married in 1980 had two children , one in 1982 and the other in 1984 . their combined ages will equal the years of the marriage in ?
Options: a ) 1986 , b ) 1985 , c ) 1987 , d ) 1988 , e ) 1989
Rationale: sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a
Answer: a
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 19 per cubic meter ?
Options: a ) 2998 , b ) 1881 , c ) 2890 , d ) 1485 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 19 = 1881 answer : b"
Answer: b
Problem: at an election 2 candidates are participated and a candidate got 45 % of votes and defeated by 9000 . and 83 votes are invalid . find the total polled votes ?
Options: a ) 84512 , b ) 78452 , c ) 65893 , d ) 90083 , e ) 74502
Rationale: winner votes = 100 - 45 = 55 polled votes = [ ( 100 * 9000 ) / 2 * 55 - 100 ] + 83 = 90083 answer is d
Answer: d
Problem: after working for 6 days , david was joined by moore . together they completed the remaining job in 3 days . how many days will it take both of them to complete the entire job , given that it would have taken david 12 days to complete the job alone ?
Options: a ) 7 , b ) 4 , c ) 6 , d ) 2 , e ) 7
Rationale: explanation : david and moore complete half work in 3 days = > they can complete whole work in 6 days answer : option c
Answer: c
Problem: how long does a train 110 m long running at the speed of 54 km / hr takes to cross a bridge 132 m length ?
Options: a ) 12.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.13 sec , e ) 14.9 sec
Rationale: "speed = 54 * 5 / 18 = 15 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 15 = 16.13 sec . answer : d"
Answer: d
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 35 % ?
Options: a ) 228 , b ) 480 , c ) 267 , d ) 416 , e ) 276
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : d"
Answer: d
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 55 + 20 ) kg = 75 kg the answer is a ."
Answer: a
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 910 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 140 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 910 x = 30 required perimeter = 2 ( 30 + 40 ) = 140 d"
Answer: d
Problem: what is the least number which should be added to 5432 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 16 , b ) 22 , c ) 28 , d ) 34 , e ) 40
Rationale: l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 5432 by 60 , the remainder is 32 . the number to be added = 60 - 32 = 28 . the answer is c .
Answer: c
Problem: two airplanes take off from one airfield at noon . one flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 406 , d ) 483 , e ) 566
Rationale: "c in two hours : the plane flying east will be 406 miles away from airport . the other plane will be 566 miles away from airport . 566 / 406 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 406 miles apart . c"
Answer: c
Problem: a man can swim in still water at 6 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 3 , b ) 7.5 , c ) 2.25 , d ) 2 , e ) 4
Rationale: "m = 6 s = x ds = 6 + x us = 6 - x 6 + x = ( 6 - x ) 2 6 + x = 12 - 2 x 3 x = 6 x = 2 answer : d"
Answer: d
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 4 years ?
Options: a ) 20300 , b ) 20400 , c ) 20730 , d ) 20500 , e ) 20600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 120 / 100 ã — 120 / 100 ã — 120 / 100 ã — 120 / 100 = 20730 c"
Answer: c
Problem: a certain roller coaster has 4 cars , and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 4 times , what is the probability that the passenger will ride in each of the 4 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 3 / 32 , e ) 1
Rationale: "if he is to ride 4 times and since he can choose any of the 4 cars each time , total number of ways is = 4 * 4 * 4 * 4 = 256 now the number of ways if he is to choose a different car each time is = 4 * 3 * 2 * 1 = 24 so the probability is = 24 / 256 = 6 / 64 = 3 / 32 = 3 / 32 answer : d"
Answer: d
Problem: what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle .
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 1 , d ) data inadequate , e ) none of these
Rationale: "area of δ ebc = 1 ⁄ 2 × bc × ef = 1 ⁄ 2 × bc × ab [ since , ef = ab ] area of δ ebc = 1 ⁄ 2 × area of δ abcd \ required ratio = 2 : 1 . answer b"
Answer: b
Problem: the average age of a , b and c is 25 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 17 , b ) 35 , c ) 20 , d ) 32 , e ) 21
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 25 ã — 3 â € “ 29 ã — 2 = 75 â € “ 58 = 17 years a"
Answer: a
Problem: a man walking at the rate of 6 km per hour crosses a square field diagonally in 9 seconds the area of the field is
Options: a ) 110 sq . m
b ) 111.5 aq . m
c ) 112.5 sq . m
d ) 114 sq . m
e ) none of these
Rationale: explanation : distance covered in 9 seconds = ( 6 × 1000 / 3600 ) × 9 = 15 m diagonal of square field = 15 m side of square = a then diagonal of that square = √ 2 a hence area of the square = a 2 = ( 152 ) / 2 = 112.5 sq . m answer : option c
Answer: c
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 175 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 455 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 175 x = 35 total number of students = 13 x = 13 * 35 = 455 answer is c"
Answer: c
Problem: i spend 40 hours a week ( 5 days ) at work and like to organize my time so that i spend an equal number of hours on the two tasks i currently have . currently , i am spending 5 hours a day on task 1 and 3 on task 2 . how many hours a week less do i need to spend on task 1 in order to evenly distribute my time ?
Options: a ) 5 , b ) 3 , c ) 7 , d ) 1 , e ) 6
Rationale: 5 x 5 = 25 25 - 5 = 20 the answer is a .
Answer: a
Problem: what is the greatest of 3 consecutive integers whose sum is 27 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 11
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 27 ; = > 3 n = 27 ; = > n = 9 the greatest of the three numbers is therefore 9 + 2 = 11 answer : e"
Answer: e
Problem: the area of a triangle is with base 4 m and height 5 m ?
Options: a ) 11
b ) 10
c ) 99
d ) 17
e ) 12
Rationale: 1 / 2 * 4 * 5 = 10 m 2 answer : b
Answer: b
Problem: a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of and then $ 10 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 26 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: ( 10 / 108 ) / ( 5 / 20 ) = 20 / 27 = 74 % it means that 10 / 108 represents only 74 % . therefore a decrease of 26 % . answer b
Answer: b
Problem: peter brought a scooter for a certain sum of money . he spent 10 % of the cost on repairs and sold the scooter for a profit of $ 1100 . how much did he spend on repairs if he made a profit of 20 % ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: e 500 let the c . p . be $ x . then , 20 % of x = 1100 20 / 100 * x = 1100 = > x = 5500 c . p . = $ 5500 , expenditure on repairs = 10 % actual price = $ ( 100 * 5500 ) / 110 = $ 5000 expenditures on repairs = ( 5500 - 5000 ) = $ 500 .
Answer: e
Problem: 10 people can write 55 book in 12 days working 8 hour a day . then in how many day 198 can be written by 48 people ?
Options: a ) 9 , b ) 13 , c ) 21 , d ) 24 , e ) 23
Rationale: "work per day epr hour per person = 55 / ( 12 * 8 * 10 ) / / eq - 1 people = 48 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 198 / ( p * 8 * 48 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 9 answer : a"
Answer: a
Problem: the current of a stream runs at the rate of 4 kmph . a boat goes 12 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 17.33 , b ) b ) 2 , c ) c ) 18 , d ) d ) 16 , e ) e ) 13.21
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 12 / ( x + 4 ) + 12 / ( x - 4 ) = 2 x = 13.21 answer : e"
Answer: e
Problem: a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 45 km / hr , b ) 50 km / hr , c ) 77 km / hr , d ) 55 km / hr , e ) 56 km / hr
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = 20 m / sec . [ 20 * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 72 = = > x = 77 km / hr . answer : c"
Answer: c
Problem: to fill a tank , 200 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 - fifths of its present ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 200 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 200 x ) / ( 4 x / 5 ) = ( 200 x ) x 5 / 4 x = 1000 / 4 = 250 answer is e ."
Answer: e
Problem: if the cost price of 19 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 18.75 % loss , b ) 18.75 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 19 articles = rs . 19 . selling price of 16 articles = rs . 19 therefore , selling price of 19 articles is : - = > 19 / 16 ã — 19 = > 22.56 . therefore , profit = selling price - cost price . = > 22.56 â ˆ ’ 19 = 3.56 . hence , the percentage of profit = profit x 100 / c . p . = > 3.56 / 19 ã — 100 . = > 18.75 % profit . answer : b"
Answer: b
Problem: the mean of 40 observations was 100 . it was found later that an observation 50 was wrongly taken as 75 the corrected new mean is
Options: a ) 125.8 , b ) 102.8 , c ) 99.375 , d ) 100.52 , e ) 122
Rationale: "explanation : correct sum = ( 100 * 40 + 50 - 75 ) = 3975 . correct mean = = 3975 / 40 = 99.375 answer : c"
Answer: c
Problem: the entrance fee for a fair is $ 5 for persons under the age of 18 , and 20 % more for persons older . each ride at the fair costs $ 0.50 . if joe goes with her 6 years old twin brothers , and they each took 3 rides in total . how much money does joe end up spending at the fair ?
Options: a ) 16 , b ) 20.5 , c ) 17.5 , d ) 20 , e ) 4.5
Rationale: total entrance fee is ( 2 * $ 5 ) + ( 1.20 * 5 ) = $ 16 total rides fee is ( 0.50 * 3 ) * 3 = $ 4.50 total money spent is $ 20.50 answer is b
Answer: b
Problem: in the manufacture of a certain product , 7 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.35 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "0.07 * 0.05 = 0.0035 = 0.35 % the answer is b ."
Answer: b
Problem: a bag contains 6 red , 5 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 13 , b ) 3 / 17 , c ) 5 / 26 , d ) 5 / 21 , e ) 7 / 15
Rationale: "p ( both are red ) , = 6 c 213 c 2 = 6 c 213 c 2 = 5 / 26 c"
Answer: c
Problem: if 1488 / 1.24 = 1200 , then 148.8 / 12.4 is equal to ?
Options: a ) 17 , b ) 10 , c ) 14 , d ) 12 , e ) 11
Rationale: "answer given expression 148.8 / 12.4 = 1488 / 124 = 1488 / ( 1.24 x 100 ) = 1200 / 100 = 12 correct option : d"
Answer: d
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross - section is 10290 sq m , the depth of cannel is ?
Options: a ) 258 , b ) 260 , c ) 262 , d ) 264 , e ) 266
Rationale: 1 / 2 * d ( 6 + 4 ) = 10290 d = 258 answer : a
Answer: a
Problem: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.25 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 790
Rationale: let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.25 = > x = 790 e
Answer: e
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 4 be mixed with another mixture q of milk and water in the ratio 2 : 7 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 1
Rationale: ( 5 / 9 ) * p + ( 2 / 9 ) * q = ( 4 / 9 ) * p + ( 7 / 9 ) * q p = 5 q p / q = 5 / 1 the answer is e .
Answer: e
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 500 shares of the company ' s stock ?
Options: a ) $ 260 , b ) $ 96 , c ) $ 26 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 500 - - > $ 260 answer is a"
Answer: a
Problem: the positive integers s and t leave remainders of 2 and 3 , respectively , when divided by 6 . s > t . what is the remainder when s – t is divided by 6 ?
Options: a ) 3 , b ) 1 , c ) 4 , d ) 2 , e ) 5
Rationale: let ' s test out some values of p and q that satisfy the given information . s leaves are remainder of 2 when divided by 6 so , s could equal 8 t leaves are remainder of 3 when divided by 6 so , t could equal 3 what is the remainder when s – t is divided by 6 ? so , s - t = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : e
Answer: e
Problem: what is the remainder when 9 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
Answer: e
Problem: the sum of ages of 5 children born 2 years different each is 40 years . what is the age of the elder child ?
Options: a ) 12 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 40 5 x = 20 x = 4 . x + 8 = 4 + 8 = 12 answer : a"
Answer: a
Problem: find large number from below question the difference of two no . is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1234 , b ) 1456 , c ) 1256 , d ) 1456 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 4 % p . a . was rs . 326.40 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 4326.40 , b ) rs . 4236.40 , c ) rs . 4136.40 , d ) rs . 4316.40 , e ) rs . 4136.40
Rationale: "let the sum be rs . p p { [ 1 + 4 / 100 ] 2 - 1 } = 326.40 p ( 4 / 100 ) ( 2 + 4 / 100 ) = 326.40 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 326.40 / ( 0.04 ) ( 2.04 ) = 4000 amount = 4000 + 326.40 = 4326.40 answer : a"
Answer: a
Problem: if a square mirror has a 20 - inch diagonal , what is the approximate perimeter e of the mirror , in inches ?
Options: a ) 40
b ) 60
c ) 80
d ) 100
e ) 120
Rationale: if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter e must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b
Answer: b
Problem: james and david work at a grocery shop with 6 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
Options: a ) 1 / 20 , b ) 1 / 22 , c ) 1 / 23 , d ) 1 / 25 , e ) 1 / 15
Rationale: "probability that james and david will both be chosen out of 6 workers = ( 2 / 6 ) * ( 1 / 5 ) = 1 / 15 answer e"
Answer: e
Problem: 60 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 129 , e ) 281
Rationale: "( 60 / 100 ) * x + 120 = x 2 x = 600 x = 300 answer : a"
Answer: a
Problem: in a 60 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 29 , b ) 13 , c ) 25 , d ) 23 , e ) 21
Rationale: "solution simple out of 60 20 % are male i . e 12 and 25 % are female i . e 15 , so total homeowner is 27 . now min number homeowner is 12 and max is 27 so question ask us to find least and 13 has least value among all option . so ans is 13 . answer : b"
Answer: b
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is -
Options: a ) 8 / 13 , b ) 6 / 13 , c ) 3 / 13 , d ) 4 / 13 , e ) 1 / 13
Rationale: explanation : p ( s á ´ œ k ) = p ( s ) + p ( k ) - p ( s â ˆ © k ) , where s denotes spade and k denotes king . p ( s á ´ œ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : d
Answer: d
Problem: a man swims downstream 30 km and upstream 18 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 2 , e ) 4
Rationale: "30 - - - 6 ds = 5 ? - - - - 1 18 - - - - 6 us = 3 ? - - - - 1 m = ? m = ( 5 + 3 ) / 2 = 4 answer : e"
Answer: e
Problem: what is the least value of x . so that 23 x 59 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 9 = 19 + x least value of x may be 2 therefore 19 + 2 = 21 is divisible by 3 . answer : option a"
Answer: a
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 16 , what is the sum of the first 15 terms of the progression ?
Options: a ) 80 , b ) 100 , c ) 105 , d ) 120 , e ) 110
Rationale: "4 th term + 12 th term = 16 i . e . , ( a + 3 d ) + ( a + 11 d ) = 16 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 16 - - - - - - - - - - - - - - - from ( 1 ) = 120 answer : d"
Answer: d
Problem: the side of a square is increased by 25 % then how much % does its area increases ?
Options: a ) 56.28 , b ) 56.25 , c ) 56.2 , d ) 56.24 , e ) 56.21
Rationale: "a = 100 a 2 = 10000 a = 125 a 2 = 15625 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 5625 100 - - - - - - - ? = > 56.25 % answer : b"
Answer: b
Problem: if x = 1 - 2 t and y = 2 t - 2 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 3 / 4 , d ) 2 / 5 , e ) 0
Rationale: "we are given x = 1 – 2 t and y = 2 t – 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 2 t for x and 2 t – 2 for y in the equation x = y . this gives us : 1 – 2 t = 2 t – 2 3 = 4 t 3 / 4 = t the answer is c ."
Answer: c
Problem: pipes a and b can fill a tank in 6 and 4 hours . pipe c can empty it in 12 hours . if all pipes are opened together , then the tank will be filled in ?
Options: a ) 3 hr , b ) 2 hr , c ) 1 hr , d ) 9 / 7 hr , e ) 5 / 3 hr
Rationale: net part filled in 1 hour = 1 / 6 + 1 / 4 - 1 / 12 = 1 / 3 the tank will be full in 3 hr answer is a
Answer: a
Problem: hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
Options: a ) 720
b ) 900
c ) 1200
d ) 1800
e ) 2100
Rationale: 2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c
Answer: c
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2370 votes . how many votes were cast ?
Options: a ) 7500 , b ) 7900 , c ) 2665 , d ) 2888 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2370 100 % - - - - - - - - - ? = > 7900 answer : b"
Answer: b
Problem: sonika bought a v . c . r . at the list price of 18,500 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 19,980 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: sol . list price of v . c . r . = 18,500 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,500 = 8 ⁄ 100 × 18500 = 1480 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,500 + 1480 = 19,980 . answer a
Answer: a
Problem: a cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the west surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) none of these
Rationale: "solution area of the west surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 × 1.25 + 6 × 1.25 ) + 6 × 4 ] m 2 = 49 m 2 . answer a"
Answer: a
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 220 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,218
Rationale: "i can buy 9 250 - pack for rs 22.95 * 9 = $ 206.55 now , i can buy 5 20 - pack for 3.05 * 5 = $ 15.25 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2218 e"
Answer: e
Problem: if ( n + 2 ) ! / n ! = 90 , n = ?
Options: a ) 2 / 131 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 90 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 132 from here , we might just test the answer choices . since ( 10 ) ( 9 ) = 90 , we can see that n = 8 b"
Answer: b
Problem: abcd is a square . f and e are the midpoints of sides ad and cd , respectively . the area of triangle fed is 2 square inches . what is the area of square abcd ( in square inches ) ?
Options: a ) 4
b ) 8
c ) 16
d ) 32
e ) 64
Rationale: area of fed = 2 sq inches = 1 / 2 * de * fd = 1 / 2 * de ^ 2 because the sides of a square are equal , hence half of the sides will also be equal . de ^ 2 = 4 de = fd = 2 hence the side of the square = 4 area if the square = 4 * 4 = 16 correct option : c
Answer: c
Problem: the triplicate ratio of 1 : 7 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 343 , d ) 1 : 1 , e ) 1 : 2
Rationale: "1 ^ 3 : 7 ^ 3 = 1 : 343 answer : c"
Answer: c
Problem: what profit percent is made by selling an article at a certain price , if by selling at 3 / 4 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 29 % , c ) 7 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 3 / 4 sp 1 cp = 100 sp 2 = 80 3 / 4 sp 1 = 80 sp 1 = 107 100 - - - 107 = > 7 % answer : c"
Answer: c
Problem: 275.124 x 16.98 ã · 5.001 + 22.22 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 957.641 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 275.124 x 16.98 ã · 5.001 + 22.22 = ? â ‰ ˆ ( 275.124 x 17 / 5 ) + 22.22 â ‰ ˆ 935.421 + 22.22 â ‰ ˆ 957.641 answer : option c"
Answer: c
Problem: a clock store sold a certain clock to a collector for 30 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 60 percent of what the collector had paid . the shop then sold the clock again at a profit of 90 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 150 , for how much did the shop sell the clock the second time ?
Options: a ) $ 1010.46 , b ) $ 505.23 , c ) $ 2020.92 , d ) $ 800.46 , e ) $ 1515.69
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 30 % profit . this means the clocks ' selling price was c ( 1.3 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 60 % the price at which the collector bought it . thus , you get = 1.3 * 0.6 * c = 0.78 c furthermore , the store sells the clock for the second time for 90 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.9 = 1.9 * 0.78 c finally given that c - 0.78 c = 150 - - - - > c = 681.82 $ thus , the cost of the clock the second time around = 1.9 * 0.78 c = 1.9 * 0.78 * 681.82 = 1010.46 $ . hence a is the correct answer ."
Answer: a
Problem: a certain junior class has 1000 students and a certain senior class has 900 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 2 / 30000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 1000 first then we can only pick 1 other pair from the 800 so total will be 60 / 900 * 1000 simplify and you get 2 / 30000 answer is b"
Answer: b
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 3 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.86
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 3 / 100 ) = 350 â † ’ t = 4.86 answer e
Answer: e
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 400 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 ) 1.58 % , b ) 1.98 % , 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 400 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 400 ) / 100 + ( 1.8 * 700 ) / 100 = 15.8 gms % of liquid x in resultant mixture = ( 15.8 / 1000 ) * 100 = 1.58 % a"
Answer: a
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 21 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 21 - 9 = 12 ab = 6 . answer is d ."
Answer: d
Problem: out of 460 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 90
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 460 - 50 = 410 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 410 = 90 . answer is e"
Answer: e