regisss/math_qa huggingface dataset:
Problem: the curved surface area of a cylindrical pillar is 264 sq . m and its volume is 924 cub . m . find the ratio of its diameter to its height
Options: a ) 7 : 9
b ) 7 : 3
c ) 7 : 7
d ) 7 : 6
e ) 7 : 1
Rationale: explanation : { \ color { black } \ frac { \ prod r ^ { 2 } h } { 2 \ prod rh } = \ frac { 924 } { 264 } } { \ color { black } \ rightarrow r = \ frac { 924 } { 264 } \ times 2 = 7 m } { \ color { black } and \ ; \ ; 2 \ prod rh = 264 \ rightarrow h = ( 264 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } \ times \ frac { 1 } { 7 } ) = 6 m } { \ color { black } \ therefore } required rato = { \ color { black } \ frac { 2 r } { h } } = { \ color { black } \ frac { 14 } { 6 } = 7 : 3 } answer : b ) 7 : 3
Answer: b
Problem: a can run 128 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 16 metre , e ) 28 metre
Rationale: clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 128 / 32 = 4 m / s distance covered by b in 4 seconds = speed ã — time = 4 ã — 4 = 16 metre i . e . , a beat b by 16 metre answer is d
Answer: d
Problem: jacob is now 13 years younger than michael . if 9 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 8 , b ) 7 , c ) 15 , d ) 21 , e ) 25
Rationale: "jacob = x years , michael = x + 13 years 9 years from now , 2 ( x + 9 ) = x + 22 2 x + 18 = x + 22 x = 4 x + 4 = 8 years answer a"
Answer: a
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 86.49 , the number of the member is the group is :
Options: a ) 93 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 86.49 x 100 ) paise = 8649 paise numbers of members = 8649 squareroot = 93 answer a"
Answer: a
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 84,000 through the lagaan from the village of mettur . mettur , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mettur over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.35424 , c ) 0.10982 , d ) 0.20933 , e ) 0.10984
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 384000 x \ therefore required percentage = \ inline \ frac { 800 x } { 384000 } \ times 100 = 0.20833 a"
Answer: a
Problem: in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 4 . if the probability that a number 12 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 7 / 12
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 4 = 1 p ( set 2 ) = 7 / 12 answer ( e )"
Answer: e
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 15,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 850 , c ) $ 800 , d ) $ 750 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 15,000 * 5 % = 750 . thus , d is the answer ."
Answer: d
Problem: the average of 65 numbers is 40 . if two numbers , 83 and 30 are discarded , then the average of the remaining numbers is nearly
Options: a ) 28.32 , b ) 39 , c ) 38.78 , d ) 29 , e ) 39.47
Rationale: explanation : total sum of 63 numbers = ( 65 * 40 ) - ( 83 + 30 ) = 2600 - 113 = 2487 average = 2487 / 63 = 39.47 answer : e
Answer: e
Problem: a + b + c + d = d + e + f + g = g + h + i = 17 given a = 4 . find value of g and h ?
Options: a ) 29 , b ) 39 , c ) 19 , d ) 49 , e ) 59
Rationale: a + b + c + d = 17 4 + 2 + 6 + 5 = 17 d = 5 d + e + f + g = 17 5 + 3 + 8 + 1 = 17 g = 1 g + h + i = 17 1 + 9 + 7 = 17 g = 1 , h = 9 . answer : c
Answer: c
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 111.30 , what was the total value of the item ?
Options: a ) $ 2380 , b ) $ 2590 , c ) $ 2760 , d ) $ 2940 , e ) $ 3150
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 111.30 x = 2590 the answer is b ."
Answer: b
Problem: find the smallest number which should be multiplied with 13225 to make it a perfect square .
Options: a ) 25 , b ) 5 , c ) 1 , d ) 23 , e ) 6
Rationale: "13225 = 5 * 5 * 23 * 23 required smallest number = 1 1 is the smallest number which should be multiplied with 13225 to make it a perfect square . answer : c"
Answer: c
Problem: 3 candidates in an election and received 2500 , 5000 and 20000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 72.72 % , b ) 50 % , c ) 57.57 % , d ) 60 % , e ) 65 %
Rationale: "total number of votes polled = ( 2500 + 5000 + 20000 ) = 27500 so , required percentage = 20000 / 27500 * 100 = 72.72 % a"
Answer: a
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 25 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: "so 24 days answer c = 24"
Answer: c
Problem: a 30 % alcohol mixture is added to a 50 % alcohol mixture to form a 10 litre mixture of 45 % alcohol . how much of the 30 % mixture was used ?
Options: a ) 1.5 liters , b ) 2.5 liters , c ) 3.5 liters , d ) 4.5 liters , e ) 5.5 liters
Rationale: solution a = 50 % solution solution b = 30 % solution 30 % - 45 % = 15 % solution b 50 % - 45 % = 5 % solution a so the ratio is 3 : 1 for 30 % : 50 % solutions 3 / 4 * 10 liter = 7.5 for 30 % solution and 2.5 for 50 % solution . . answer : b
Answer: b
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 11.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 176 , c ) $ 282 , d ) $ 302 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 11 = 16 * 11 = 176 $ total charge = 126 + 176 = 302 $ answer d"
Answer: d
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 1 screws and 5 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 1 s and 5 n = 1 s + 5 * 1 s = 6 s . . ratio = 15 s / 6 s = 15 / 6 = 5 / 2 b"
Answer: b
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is - 3 , what is the value of x ?
Options: a ) - 4 , b ) - 1 and - 3 , c ) 2 , d ) 4 , e ) can not be determined .
Rationale: a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 3 - - > x ^ 2 + 4 x = - 3 i . e x ^ 2 + 4 x + 3 = 0 is the quadratic equation which needs to be solved . ( x + 1 ) ( x + 3 ) = 0 hence x = - 1 . x = - 3 imo b
Answer: b
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 44 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 42
Rationale: "amount earned by james = 40 * x + 4 * 2 x = 48 x therefore , amount earned by james = 48 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 48 x ] ] so x * ( 1.5 y - 45 + 30 ) = 48 x or x * ( 1.5 y - 15 ) = 48 x so 1.5 y - 15 = 48 so 1.5 y = 63 so y = 42 answer is e"
Answer: e
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 5766 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 1287 , c ) 125 , d ) 155 , e ) 271
Rationale: "3 x * 2 x = 5766 = > x = 31 2 ( 93 + 62 ) = 310 m 310 * 1 / 2 = rs . 155 answer : d"
Answer: d
Problem: find the smallest number of 6 digits which is exactly divisible by 111
Options: a ) 100011 , b ) 111111 , c ) 101111 , d ) 1011111 , e ) 211111
Rationale: "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer a 100011"
Answer: a
Problem: when the positive integer k is divided by the positive integer n , the remainder is 13 . if k / n = 81.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : b"
Answer: b
Problem: kareem is 3 times as old as his son . after 10 years , the sum of their ages will be 76 years . find their present ages .
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: sol . let the present age of kareem ’ s son be x years . then , kareem ’ s age = 3 x years after 10 years , kareem ’ s age = 3 x + 10 years and kareem ’ s son ’ s age = x + 10 years ∴ ( 3 x + 10 ) + ( x + 10 ) = 76 = > 4 x = 56 = > x = 14 ∴ kareem ’ s present age = 3 x = 3 × 14 = 42 years kareem ’ s son ’ s age = x = 14 years . answer b
Answer: b
Problem: what is the greatest value of x such that 4 ^ x is a factor of 21 ! ?
Options: a ) 5 , b ) 6 , c ) 3 , d ) 2 , e ) 4
Rationale: pretty simple , really . if m = 6 , then 4 m = 24 , which is 12 x 2 , both of which are included in 21 ! since 6 is the largest number here , its the answer . answer is b
Answer: b
Problem: if 8 spiders make 8 webs in 8 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 8 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 8 webs 8 : 1 1 x 8 x x = 8 x 1 x 8 = > x = 8 answer is d"
Answer: d
Problem: what is the sum of the integers from - 160 to 162 , inclusive ?
Options: a ) 325 , b ) 327 , c ) 323 , d ) 330 , e ) 350
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 162 , a = - 160 , d = 1 hence , 162 = - 160 + ( n - 1 ) or n = 323 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 323 * ( - 160 + 162 ) / 2 sn = 323 * 2 / 2 = 323 answer : c"
Answer: c
Problem: chloe has $ 27 dollars to go to the fair . she is bringing 2 other friends along . admission to the fair is $ 3 . each ride costs $ 1.70 . how many rides can she and her friends go on and how much money will be left over ?
Options: a ) they can go on 15 rides and $ 1.50 will be left over .
b ) they can go on 3 rides and $ 2.70 will be left over .
c ) they can go on 7 rides and $ 0 will be left over .
d ) they can go on 6 rides and $ 0 will be left over .
e ) they can go on 5 rides and $ 1.50 will be left over .
Rationale: admission to the fair is $ 3 per person . if she wants her and her friends to go , the cost will be $ 9 . 27 - 9 is 18 . to go on a ride is $ 5.10 . 5.10 x 3 is 15.30 . 18 - 15.30 is 2.70 . they can go on 3 rides and $ 2.70 will be left over . the correct answer is b .
Answer: b
Problem: if the selling price of 50 articles is equal to the cost price of 30 articles , then the loss or gain percent is :
Options: a ) 10 % , b ) 40 % , c ) 30 % , d ) 25 % , e ) 35 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 30 . loss % = 20 / 50 * 100 = 40 % answer : b"
Answer: b
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600
Rationale: we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 200 then y = 600 answer : e
Answer: e
Problem: what will be the compound interest on a sum of rs . 26,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10123.20 , d ) s . 10123.28 , e ) s . 10528.12
Rationale: "amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 36528.12 c . i . = ( 36528.12 - 26000 ) = rs . 10528.12 answer : e"
Answer: e
Problem: the star running back on our football team got most of his total yardage running . the rest was catching passes . he caught passes for 60 yards . his total yardage was 150 yards . the running back for the other team got 200 yards . how many yards did the star running back on our football team get running ?
Options: a ) 50 yards , b ) 60 yards , c ) 70 yards , d ) 80 yards , e ) 90 yards
Rationale: . the other team is extra information . 150 – 60 = 90 he got 90 yards running . correct answer e
Answer: e
Problem: in what ratio must rice of rs . 30 per kg be mixed with rice of rs . 56 per kg so that cost of mixture is rs . 35 per kg ?
Options: a ) 28 : 15 , b ) 6 : 7 , c ) 7 : 6 , d ) 5 : 21 , e ) 21 : 5
Rationale: "( 35 - 56 ) / ( 30 - 35 ) = 6 / 2 = 21 : 5 answer : e"
Answer: e
Problem: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 30 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1305 , b ) 1375 , c ) 1345 , d ) 1415 , e ) 1455
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 30 % of the gaskets to x = 18 gaskets = 25 * 10 + 20 * 8 = 250 + 160 = 410 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 55 % to z = 33 gaskets = 25 * 10 = 250 + 20 * 23 = 710 thus , total money earned 410 + 225 + 710 = 1345 answer is c"
Answer: c
Problem: two cars start from the opposite places of a main road , 113 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : d ) 28 km
Answer: d
Problem: a straight line in the xy - plane has a slope of 4 and a y - intercept of 4 . on this line , what is the x - coordinate of the point whose y - coordinate is 800 ?
Options: a ) 233 , b ) 299 , c ) 333 , d ) 199 , e ) 339
Rationale: eq of line = y = mx + c m = 4 , c = 4 y = 4 x + 4 , substitute y by 800 as given in question . 800 = 4 x + 4 , x = 199 . correct option is d
Answer: d
Problem: a shop owner sells 25 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 25 m cloth ) – ( c . p . of 25 m cloth ) selling price of 15 m cloth = selling price of 25 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 15 m cloth = rs . 1500 and s . p . of 15 m cloth = rs . rs . 2500 profit % = 10 / 15 × 100 = 66.67 % profit of 66.67 % was made by the merchant . d"
Answer: d
Problem: what number has a 150 : 1 ratio to the number 2 ?
Options: a ) 130 , b ) 300 , c ) 200 , d ) 30 , e ) 75
Rationale: "150 : 1 = x : 2 x = 150 * 2 x = 300 answer : b"
Answer: b
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 50 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 50 % . 5 x = 200 = > x = 400 answer a"
Answer: a
Problem: a sum fetched a total simple interest of rs . 6016.75 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs . 16241.875 , b ) rs . 15041.85 , c ) rs . 15401.875 , d ) rs . 15041.875 , e ) none of these
Rationale: "explanation : principal = rs 100 x 6016.75 / 8 x 5 = rs . 601675 / 40 = rs . 15041.875 answer : option d"
Answer: d
Problem: x starts a business with rs . 45000 . y joins in the business after 2 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 9 : 5 , c ) 1 : 5 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 10 = 45 ã — 12 : 30 ã — 10 = 3 ã — 12 : 2 ã — 10 = 9 : 5 answer : option b"
Answer: b
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 165 m long ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 42
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 165 = 525 m required time = 525 * 2 / 25 = 42 sec answer : e"
Answer: e
Problem: two pipes can fill a tank in 8 minutes and 5 minutes . an outlet pipe can empty the tank in 12 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 10 minutes , e ) 14 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 8 + 1 / 5 - 1 / 12 = ( 15 + 24 - 10 ) / 120 = 29 / 120 so , the tank becomes full in 14 minutes . answer : e"
Answer: e
Problem: the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 8325 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 7239.13 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 6728
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8325 ( 100 / 115 ) = rs . 7239.13 . answer : b"
Answer: b
Problem: a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 km / h and the speed of the boat in still water is 14 km / h , what is the distance between a and b ?
Options: a ) 200 km , b ) 180 km , c ) 160 km , d ) 220 km , e ) none of these
Rationale: "speed of boat for downstream = 14 + 4 = 18 km / hr speed of boat for upstream = 14 – 4 = 10 km / hr distance = x x / 18 + ( x / 2 ) / 10 = 19 x = 180 km answer : b"
Answer: b
Problem: if 73 ! has 16 zeroes at the end , how many zeroes will 80 ! have at the end ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: prime factoring : you need a 2 and a 5 to make a 10 ( a ` ` zero ' ' ) , and there are tons of 2 ' s so let ' s skip these and focus on the ( rarer ) 5 s : 80 ! = 1 * 2 * 3 * 4 * 5 * 6 . . . * 78 * 79 * 80 since there are 80 consecutive numbers , there are 16 multiples of 5 in there , but if we ' re prime factoring , we need to remember that some multiples of 5 actually contain more than just one 5 . which ? 25 comes to mind - - it ' s got two of them ! so all the multiples of 25 actually contain two 5 ' s ( ie : 50 and 75 ) so , to recap , we have 16 of them , plus 3 more ( the additional 5 ' s in 25 , 50 , and 75 ) , so that makes 19 , and since we have more than enough 2 ' s , we know our number will have exactly 19 zeros at the end . answer : d
Answer: d
Problem: in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."
Answer: a
Problem: 6 bells commence tolling together and toll at the intervals of 24 , 68 , 1012 seconds resp . in 60 minutes how many times they will toll together .
Options: a ) 15 , b ) 16 , c ) 30 , d ) 31 , e ) none of these
Rationale: explanation : lcm of 2 - 4 - 6 - 8 - 10 - 12 is 120 seconds , that is 2 minutes . now 60 / 2 = 30 adding one bell at the starting it will 30 + 1 = 31 answer : option d
Answer: d
Problem: in a full deck of 52 cards , there are 13 spades . a game is played whereby a card from is chosen at random from the deck . if the card is a spade , a winner is declared . if the card is not a spade , it is returned to the deck , the deck is reshuffled and another card is drawn . this process is repeated until a spade is drawn . what is the probability that one will pick the first spade on the second draw or later ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 4 , e ) 7 / 8
Rationale: favorable case = the spade is picked in the third draw or later unfavorable case = the spade is picked in either first draw or in second draw probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case : probability of spade picked in first draw = 13 / 52 = 1 / 4 i . e . , favorable probability = 1 - ( 1 / 4 ) = 3 / 4 answer option : d
Answer: d
Problem: of 600 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 75
Rationale: say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 600 = 1.25 b + b - 0.25 b - - > b = 300 , a = 1.25 b = 375 and { both } = 0.25 b = 75 . the number of students who read only book a is { a } - { both } = 375 - 75 = 300 ; the number of students who read only book b is { b } - { both } = 300 - 75 = 225 ; the difference is 300 - 225 = 75 . answer : e .
Answer: e
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4340 , r will receive
Options: a ) 600 , b ) 700 , c ) 840 , d ) 900 , e ) none of these
Rationale: explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4340 * ( 6 / 31 ) = 140 * 6 = 840 . answer : option c
Answer: c
Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are red balls ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 5 / 12 , d ) 5 / 24 , e ) 7 / 24
Rationale: "the number of ways of choosing 3 balls from the jar is 10 c 3 = 120 . the number of ways of choosing 3 red balls is 6 c 3 = 20 . p ( 3 red balls ) = 20 / 120 = 1 / 6 . the answer is b ."
Answer: b
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 100 ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 25 , e ) 26
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 100 4 n < 93 n < 23 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 23 ) combining the two - 1.5 < n < 23.25 n = 1 to 23 ( 23 integers ) and n = - 1 and 0 so 25 integers . d is the answer"
Answer: d
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 25 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 50 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 30 hence , the correct answer is c"
Answer: c
Problem: if the population of a certain country increases at the rate of one person every 25 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 144 , d ) 180 , e ) 160
Rationale: "answer = 2.4 * 60 = 144 answer is c"
Answer: c
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 912 , d ) 1200 , e ) 775
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 300 62 % - - - - - - - - ? = > 775 answer : e"
Answer: e
Problem: 10 percent of ram ' s monthly salary is equal to 8 percent of shyam ' s monthly salary . shyam ' s monthly salary is twice abhinav ' s monthly salary . if abhinav ' s annual salary is rs . 1.92 lakhs , find ram ' s monthly salary ?
Options: a ) rs . 18000 , b ) rs . 20000 , c ) rs . 25600 , d ) rs . 32000 , e ) none of these
Rationale: let the monthly salaries of ram and shyam be rs . r and rs . s respectively . 10 / 100 r = 8 / 100 s r = 4 / 5 s monthly salary of abhinav = ( 1.92 lakhs ) / 12 = rs . 0.16 lakhs s = 2 ( 0.16 lakhs ) = 0.32 lakhs r = 4 / 5 ( 0.32 lakhs ) = rs . 25600 answer : c
Answer: c
Problem: during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 10 candies . the store still makes a profit of 12 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . b"
Answer: b
Problem: if the selling price of 50 articles is equal to the cost price of 25 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 50 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 25 . loss % = 25 / 50 * 100 = 50 % answer e"
Answer: e
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm ?
Options: a ) 288 , b ) 276 , c ) 285 , d ) 299 , e ) 261
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c"
Answer: c
Problem: when the bus started from the first bus stop , the number of male passengers to the number of female passengers was 1 : 3 . at the first stop , 16 passengers got down and 6 more female passengers got in . the ratio of the male to female passengers now became 1 : 2 . what was the total number of passengers in the bus when it started from the first stop ?
Options: a ) 64 , b ) 48 , c ) 54 , d ) 46 , e ) can not be determined
Rationale: let , initially the number of males and females in the bus be ’ x ’ and ’ 3 x ’ respectively . at the first stop , suppose ’ m ’ males and ’ f ’ females left the bus . therefore at the first stop the number of males is ’ x - m ’ and the number of females is ’ ( 3 x - f ) + 6 ’ therefore ( x - m ) / [ ( 3 x - f ) + 6 ] = 1 / 2 = > 2 x - 2 m = 3 x - f + 6 also m + f = 16 x = 26 - f as we have 3 variable and 2 equations , a definite value can not be determined . answer : e
Answer: e
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 15 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 85 % ( 100 - 15 ) . therefore 0.5 x amount of flower - nectar = 0.85 x amount of honey = 0.85 x 1 kg therefore amount of flower - nectar needed = ( 0.85 / 0.51 ) kg = 1.7 kgs answer : c"
Answer: c
Problem: a batsman scored 90 runs which included 2 boundaries and 7 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 30 % , b ) 40 % , c ) 44.44 % , d ) 60 % , e ) 80 %
Rationale: "explanation : number of runs made by running = 90 - ( 2 x 4 + 7 x 6 ) = 90 - ( 50 ) = 40 now , we need to calculate 40 is what percent of 90 . = > 40 / 90 * 100 = 44.44 % option c"
Answer: c
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability w that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability w = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b
Answer: b
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and further to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 6.67 % , d ) 6.25 % , e ) 8.33 %
Rationale: answer initial amount invested = $ x amount at the end of year 3 = $ 300 amount at the end of year 8 ( another 5 years ) = $ 400 therefore , the interest earned for the 5 year period between the 3 rd year and 8 th year = $ 400 - $ 300 = $ 100 as the simple interest earned for a period of 5 years is $ 100 , interest earned per year = $ 20 . therefore , interest earned for 3 years = 3 * 20 = $ 60 . hence , initial amount invested x = amount after 3 years - interest for 3 years = 300 - 60 = $ 240 . rate of interest = ( interest per year / principal ) * 100 = 20 / 240 * 100 = 8.33 % choice is ( e )
Answer: e
Problem: 28 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 42 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 28 ã — 13.5 = 378 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 378 â  „ 9 = 42 answer b"
Answer: b
Problem: the average ( arithmetic mean ) of 4 different positive integers is 16 . if the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer , what is the least possible value of the fourth integer ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: let the second integer be x and the fourth be a . then [ 3 x + x + ( x + 2 ) + a ] / 4 = 16 = > 5 x + 2 + a = 64 = > 5 x + a = 62 = > a = 62 - 5 x from the above equation we can see that a is minimum when x is maximum , provided both are positive the maximum value that x can take in the above equation while still keeping a positive is x = 12 this gives us a = 62 - 60 = 2 therefore the minimum value that the fourth integer can have is 2 . option d .
Answer: d
Problem: 36 welders work at a constant rate they complete an order in 3 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 3 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: "1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 3 = 108 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 3 of the job . so 24 workers have to finish only 2 / 3 of the job . 5 . total time taken by 24 workers can be got from formula used at ( 2 ) . i . e . , 24 * total time taken = 108 . total time taken by 6 workers to finish the complete job is 108 / 24 = 4.5 days . 6 . time taken by 24 workers to finish 2 / 3 of the job is 2 / 3 * 4.5 = 3 days . the answer is choice a"
Answer: a
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 200 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 50 , d ) 180 , e ) 240
Rationale: "area = length x breadth 200 = 40 x breadth so , breadth = 5 units fencing required is - breadth + breadth + length 5 + 5 + 40 = > 50 feet answer must be ( c ) 50"
Answer: c
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 120 marks , the no of questions he attempts correctly is :
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 120 = > 5 x = 180 = > x = 36 answer : b"
Answer: b
Problem: a certain car increased its average speed by 4 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 20 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 20 + 4 + 5 = 29 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 29 * 1 / 12 = 2.5 miles . answer : d ."
Answer: d
Problem: an engineer undertakes a project to build a road 10 km long in 15 days and employs 30 men for the purpose . after 5 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 ) 15 , b ) 20 , c ) 25 , d ) 28 , e ) 30
Rationale: "30 workers working already let x be the total men required to finish the task in next 10 days 2 km done hence remaining is 8 km also , work has to be completed in next 10 days ( 15 - 10 = 5 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 5 ) / ( 2 * 10 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : e"
Answer: e
Problem: chandigarh express of 100 m runs at a speed of 60 km / hr . what will be the time taken to cross a platform of 150 meters long ?
Options: a ) 11.00 sec , b ) 12.50 sec , c ) 15.00 sec , d ) 15.23 sec , e ) 5.23 sec
Rationale: explanation : given : length of train = 100 m , speed of train = 60 km / hr , length of platform = 150 m 1 ) always remember first step is the conversion of units . convert 60 km / hr into m / s by multiplying it with ( 5 / 18 ) speed of the train = 60 x 5 / 18 = 16.66 m / s 2 ) distance covered by the train in passing the platform = ( length of train + length of platform ) = ( 100 + 150 ) = 250 m therefore , the time taken = distance / speed = 250 / 16.66 = 15 sec answer is c
Answer: c
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many p cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . p = 4 + 4 + 4 = 12 . answer a"
Answer: a
Problem: in a school 50 % of the students are younger than 10 , 1 / 20 are 10 years old and 1 / 10 are older than 10 but younger than 12 , the remaining 70 students are 12 years or older . how many students are 10 years old ?
Options: a ) 50 , b ) 60 , c ) 10 , d ) 20 , e ) 30
Rationale: let us write the fraction for each group of students group a : younger than 10 : 50 % = 50 / 100 = 1 / 2 group b : 10 years old : 1 / 20 group c : older that 10 but younger than 12 : 1 / 10 group d : 12 years or older : 70 students the fraction for group a , b and c together is given by 1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator = 13 / 20 , add numerators the fraction for group d is given by 20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students if x is the total number of students , then 7 / 20 of x = 70 or ( 7 / 20 ) * x = 70 solve for x x = 70 * ( 20 / 7 ) = 200 students who are 10 years old have a fraction of 1 / 20 of the total x and their number is equal to ( 1 / 20 ) of 200 = 10 students correct answer c
Answer: c
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 180 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 270 + l ) / 20 = l / 8 2160 + 8 l = 20 l l = 2160 / 12 = 180 m answer a"
Answer: a
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 7 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 240 , e ) 560
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 7 € 40 = 2 * 3 * 40 = 560 hence , answer is e"
Answer: e
Problem: if a farmer wants to plough a farm field on time , he must plough 90 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 1600 , b ) 2490 , c ) 3780 , d ) 4235 , e ) 6179
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 90 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 90 x = 85 ( x + 2 ) + 40 5 x = 210 x = 42 so the farmer planned to have the work done in 6 days , and the area of the farm field is 90 ( 42 ) = 3780 hectares correct answer c"
Answer: c
Problem: the workforce of company x is 60 % female . the company hired 30 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 240 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 30 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 30 ) 0.05 x = 16.5 x = 330 - this is quantity of employees before adding 30 men so after adding it will be 360 answer is d"
Answer: d
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 4,500 meters of fabric ?
Options: a ) $ 8,617 , b ) $ 8,710 , c ) $ 8,810 , d ) $ 8,835 , e ) $ 8,915
Rationale: for first 2000 metres he does not get any discount amount = 2 * 2000 = $ 4000 for next 1500 metres he gets 5 % discount amount = 2 * 1500 - ( 1 / 20 ) * 3000 = $ 2850 for the nest 1000 metres he gets 7 % discount amount = 2 * 1000 - 7 * 20 = $ 1860 total amount = $ 4000 + $ 2850 + $ 1860 = $ 8710 answer : b
Answer: b
Problem: 20 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 17.4 %
Rationale: "alcohol in the 20 litres of mix . = 20 % of 20 litres = ( 20 * 20 / 100 ) = 4 litres water in it = 20 - 3 = 17 litres new quantity of mix . = 20 + 3 = 23 litres quantity of alcohol in it = 4 litres percentage of alcohol in new mix . = 4 * 100 / 23 = 17.4 % answer is e"
Answer: e
Problem: the heights of a wall is 6 times its width and the length of the wall is 7 times its height . if volume of the wall be 16128 cu . m , its width is
Options: a ) 4 m , b ) 4.5 m , c ) 5 m , d ) 6 m , e ) none
Rationale: solution let the width of the wall be x metres . then , height = ( 6 x ) m and length = ( 42 x ) m . 42 x × x × 6 x = 16128 x 3 ‹ = › ( 16128 / 42 × 6 ) = 64 ‹ = › x = 4 . answer a
Answer: a
Problem: ( 9 ^ 5.6 x 9 ^ 10.3 ) ÷ 9 ^ 2.56256 = 9 ^ ?
Options: a ) 11.34 , b ) 12.34 , c ) 13.34 , d ) 14.34 , e ) 15.34
Rationale: 5.6 + 10.3 = 15.9 i . e . . 15.9 - 2.56 = 13.34 so ur answer is 9 ^ 13.34 answer : c
Answer: c
Problem: 3850 * 99
Options: a ) 382550 , b ) 384560 , c ) 385690 , d ) 389650 , e ) 381150
Rationale: "explanation : 3850 * ( 100 - 1 ) = 385000 - 3850 = 381150 option e"
Answer: e
Problem: a milk man has 20 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 ) 22 , b ) 25 , c ) 27 , d ) 29 , e ) 11
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 = \ inline \ frac { 5 } { 20 } \ times 100 = 25 % % [ profit % = \ inline \ frac { profit } { cost \ : price } \ times 100 ] answer : b ) 25 %"
Answer: b
Problem: 10 + 45
Options: a ) 8 , b ) 55 , c ) 87 , d ) 90 , e ) 2
Rationale: b
Answer: b
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 8 full and other jar 1 / 6 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 2 , d ) 7 / 12 , e ) 1 / 4
Rationale: "same amount of water made bigger jar 1 / 8 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 8 + 1 / 8 = 1 / 4 full . answer : e ."
Answer: e
Problem: a certain bus driver is paid a regular rate of $ 20 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1000 in total compensation , how many total hours did he work that week ?
Options: a ) 46 , b ) 40 , c ) 44 , d ) 48 , e ) 49
Rationale: "for 40 hrs = 40 * 20 = 800 excess = 1000 - 800 = 200 for extra hours = . 75 ( 20 ) = 15 + 20 = 35 number of extra hrs = 200 / 35 = 5.71 = 6 approx . total hrs = 40 + 6 = 46 answer a 46"
Answer: a
Problem: a cistern normally takes 6 hours to be filled by a tap but because of a leak , 2 hours more . in how many hours will the leak empty a full cistern ?
Options: a ) 20 hours , b ) 24 hours , c ) 26 hours , d ) 18 hours , e ) none of these
Rationale: ∵ cistern fill in 6 hours . ∴ in 1 hour , filled part = 1 ⁄ 6 th now , due to leakage , filled part in 1 hour = 1 ⁄ 8 th part of the cistern emptied , due to leakage in 1 hour = 1 ⁄ 6 - 1 ⁄ 8 = 1 ⁄ 24 th ∴ the leakage will empty the full cistern in 24 hrs . answer b
Answer: b
Problem: what is the greatest integer m for which the number 20 ! / 10 ^ m is an integer ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 20 ! the multiples of 5 are : 5 , 10 , 15 , 20 . thus 5 ^ 4 will divide 20 ! but 5 ^ 5 will not . clearly 2 ^ 4 will divide 20 ! so m = 4 is the largest possible integer . the answer is b ."
Answer: b
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 4 ?
Options: a ) 5 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 4 + 1 ) / ( 4 - 1 ) = 5 / 3 = 5 / 3 answer : a"
Answer: a
Problem: doughnuts , cookies and muffins in a pastry shop are in the ratio of 5 : 3 : 1 . if there are 50 doughnuts , the number of muffins in the shop is : .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let doughnuts = 5 x , cookies = 3 x & muffins = 1 x . now , 5 x = 50 hence x = 10 . number of muffins = 1 x which is 10 . answer : c
Answer: c