Cheukting/mathqa huggingface dataset:
Question (physics): a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed q of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = q ans = c
Answer: c
Question (gain): if 15 % of 30 % of 50 % of a number is 117 , then what is the number ?
Options: a ) 5200 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 117 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 117 = > a = 10 * 20 * 10 * 2 = 5200 . answer : a"
Answer: a
Question (gain): machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 20 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 8 minutes ?
Options: a ) 100 , b ) 90 , c ) 80 , d ) 30 , e ) 50
Rationale: "machine b produces 100 part in 20 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 20 / 2 = 10 minutes . now , machine a produces 100 parts in 10 minutes which is 100 / 10 = 10 parts / minute . 10 parts x a total of 8 minutes = 80 c"
Answer: c
Question (gain): during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 10 + 0.9 * 10 = 19 gallons , so the overall discount she got was 1 / 20 = 5 % . isabella purchased 25 gallons of gas . she paid for 10 + 0.9 * 15 = 23.5 gallons , so the overall discount she got was 1.5 / 25 = 6 % . 6 is 6 / 5 * 100 = 120 % of 5 . answer : d ."
Answer: d
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 2
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 6 - 4 ) / ( 10 - 6 ) = 2 / 4 = 1 / 2 so they should be mixed in the ratio 1 : 2 answer - e"
Answer: e
Question (general): how many numbers between 190 and 580 are divisible by 45 and 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a
Answer: a
Question (gain): if the cost price of 50 articles is equal to the selling price of 28 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 65 , c ) 78.57 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 28 articles . let cost price of one article = rs . 1 selling price of 28 articles = rs . 50 but cost price of 28 articles = rs . 28 therefore , the trader made profit . \ percentage of profit = 22 / 28 * 100 = 78.57 % answer : c"
Answer: c
Question (geometry): a block of wood has dimensions 10 cm x 10 cm x 100 cm . the block is painted red and then cut evenly at the 50 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 4.5 % , b ) 8.3 % , c ) 10.2 % , d ) 12.5 % , e ) 15.3 %
Rationale: "the area of each half is 100 + 4 ( 500 ) + 100 = 2200 the area that is not painted is 100 . the fraction that is not painted is 100 / 2200 = 1 / 22 = 4.5 % the answer is a ."
Answer: a
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) none of them
Rationale: "let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 75 < = > 5 x - 25 = 75 < = > x = 20 . therefore , length of the rectangle = 20 cm . answer is d"
Answer: d
Question (other): out of 420 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 ) 130 , d ) 180 , e ) 220
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 420 - 50 = 370 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 370 = 130 . answer is c"
Answer: c
Question (general): in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 5 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers :
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "m / nm > 5 x / 24 x m = 8 8 / nm > 5 x / 24 x 8 / nm - 5 x / 24 x > 0 ( 192 x - 5 x * nm ) / ( 24 x * nm ) > 0 192 x - 5 x * nm > 0 5 x * nm < 192 x nm < 192 x / 5 x nm < 38.4 maximum number of non managers = 38 answer : c"
Answer: c
Question (general): the average runs scored by a batsman in 15 matches is 30 . in the next 20 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Options: a ) 31.56 , b ) 25.65 , c ) 21.43 , d ) 28.36 , e ) 27.96
Rationale: total score of the batsman in 15 matches = 450 . total score of the batsman in the next 20 matches = 300 . total score of the batsman in the 35 matches = 750 . average score of the batsman = 750 / 35 = 21.43 . answer : c
Answer: c
Question (physics): a goes to place x and b goes to place y . after a travelled 180 km more than b they together meet at a point between xy . they together had their lunch for half an hour . after that a took 2 hrs to reach x and b took 4.5 hrs to reach y . find distance between x and y ?
Options: a ) 900 km , b ) 540 km , c ) 720 km , d ) 820 km , e ) 920 km
Rationale: let speed of a be - - - - - - - sa let speed of b be - - - - - - - - sb let the distance covered by b while going to position xy be - - - - - - - - - - - x so distance covered by a in same time while going to xy is - - - - - - - - - - 180 + x ( it ' s given in the question ) so total distance b / w x and y is = x + ( x + 180 ) while going to position xy : - time taken by a = time taken by b ( x + 180 ) / sa = x / sb sa / sb = ( x + 180 ) / x - - - - - - - - - - - - - - - - - - - - - 1 after lunch : - a . c . t ( according to question ) sa = x / 2 sb = ( x + 180 ) / 4.5 dividing sa / sb = ( x * 4.5 ) / ( ( x + 180 ) * 2 ) - - - - - - - - - - - - - - - - - - - - 2 equating equations 1 and 2 9 / 4 = ( x + 180 ) ^ 2 / x ^ 2 now taking square root on both sides we get 3 / 2 = ( x + 180 ) / x x = 360 therefore distance between x and y = x + ( x + 180 ) = 900 km answer : a
Answer: a
Question (physics): a train 140 m long is running at 60 kmph . in how much time will it pass a platform 260 m long ?
Options: a ) 15 seconds , b ) 24 seconds , c ) 28 seconds , d ) 30 seconds , e ) 35 seconds
Rationale: "distance travelled = 140 + 260 m = 400 m speed = 60 * 5 / 8 = 50 / 3 m time = 400 * 3 / 50 = 24 second answer : b"
Answer: b
Question (physics): with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity r of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Question (other): if the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 15 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 2 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 2 : 15 answer c"
Answer: c
Question (general): a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 25 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 180,000 , d ) $ 200,000 , e ) $ 192,500
Rationale: "30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 25 * 5 = 37500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 37500 + 100000 + 40000 + 15000 = 192500 hence , answer is e"
Answer: e
Question (physics): a 290 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 290 / 9 = 500 / 9 x = 210 ans is 210 m answer : a"
Answer: a
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 4 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 25 , e ) 10.93
Rationale: "a : b = 2 : 4 b : c = 2 : 5 a : b : c = 4 : 8 : 20 8 / 32 * 100 = 25 answer : d"
Answer: d
Question (general): if f ( x ) = 6 x ^ 4 - 4 x ^ 3 - 3 x ^ 2 + 6 x , then f ( - 1 ) =
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "f ( - 1 ) = 6 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 3 ( - 1 ) ^ 2 + 6 ( - 1 ) = 6 + 4 - 3 - 6 = 1 the answer is d ."
Answer: d
Question (physics): a train 820 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 540 , c ) 480 , d ) 520 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 820 + x ) / 60 = 65 / 3 x = 480 m . answer : option c"
Answer: c
Question (general): if 5 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 3.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 8.00 , e ) $ 20.00
Rationale: "d for me 4 people with 3 $ each - > maximum = 8"
Answer: d
Question (gain): a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 8 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 1600 , b ) 1500 , c ) 1200 , d ) 1388 , e ) 1211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 8 = > x = 1600 answer : a ) rs 1600"
Answer: a
Question (general): jacob is now 12 years younger than michael . if 11 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 15 , d ) 5 , e ) 25
Rationale: jacob = x years , mike = x + 12 years 11 years from now , 2 ( x + 11 ) = x + 23 2 x + 22 = x + 23 x = 1 x + 4 = 5 years answer d
Answer: d
Question (other): the marks obtained by vijay and amith are in the ratio 2 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 3 : 1 , c ) 6 : 5 , d ) 3 : 2 , e ) 3 : 5
Rationale: "2 : 5 3 : 2 - - - - - - - 6 : 15 : 10 6 : 10 3 : 5 answer : e"
Answer: e
Question (general): a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent e of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which e is 40 % of 80 hence , d is the answer"
Answer: d
Question (physics): the area of a rectangular field is 144 m 2 . if the length had been 6 metres more , the area would have been 54 m 2 more . the original length of the field is
Options: a ) 22 metres
b ) 18 metres
c ) 16 metres
d ) 24 metres
e ) none of these
Rationale: let the length and breadth of the original rectangular field be x m and y m respectively . area of the original field = x × y = 144 m 2 ∴ x = 144 ⁄ y . . . . . ( i ) if the length had been 6 m more , then area will be ( x + 6 ) y = 144 + 54 ⇒ ( x + 6 ) y = 198 … ( ii ) putting the value of x from eq ( i ) in eq ( ii ) , we get ( 144 ⁄ y + 6 ) y = 198 ⇒ 144 + 6 y = 198 ⇒ 6 y = 54 ⇒ y = 9 m putting the value of y in eq ( i ) we get x = 16 m answer c
Answer: c
Question (general): find a sum for 1 st 6 prime number ' s ?
Options: a ) 41 , b ) 28 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option a"
Answer: a
Question (general): chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 4 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 19
Rationale: "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 4 4 lbs of nuts = $ 16 total value of mixture = 16 + 3 = 19 fraction of the value of raisin = 3 / 19 ans : e"
Answer: e
Question (general): 45 x ? = 45 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 9 , e ) 11
Rationale: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 45 x 9 ) / 45 = 9 correct option : d"
Answer: d
Question (general): the average of first five multiples of 3 is ?
Options: a ) 2 , b ) 9 , c ) 8 , d ) 6 , e ) 3
Rationale: "average = 3 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 45 / 5 = 9 . answer : b"
Answer: b
Question (physics): p , q and r together earn rs . 1980 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 30 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1980 / 9 = 220 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 220 = 30 = > amount earned by r in 1 day = 30 answer : option a"
Answer: a
Question (gain): the cost price of a radio is rs . 1390 and it was sold for rs . 890 , find the loss % ?
Options: a ) 18 % , b ) 12 % , c ) 22 % , d ) 35 % , e ) 21 %
Rationale: "1390 - - - - 500 100 - - - - ? = > 35 % answer : d"
Answer: d
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 60 km / hr and 90 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 93 , c ) 24 , d ) 23 , e ) 12
Rationale: "relative speed = 60 + 90 = 150 km / hr . 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 125 = 24 sec . answer : c"
Answer: c
Question (geometry): a circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5 . the smaller side of the rectangle is :
Options: a ) 30 cm
b ) 60 cm
c ) 72 cm
d ) 132 cm .
e ) 142 cm .
Rationale: length of wire = circumference of circle of radius 42 cm = ( 2 * 22 / 7 * 42 ) = 264 cm . therefore , perimeter of rectangle = 264 cm . let , length = 6 x cm & breadth = 5 x cm . therefore , 2 ( 6 x + 5 x ) = 264 or x = 12 . therefore , smaller side = 60 cm answer : b
Answer: b
Question (general): if 6 years are subtracted from the present age of arun and the remainder is divided by 18 , then the present age of his grandson gokul is obtained . if gokul is 2 years younger to madan whose age is 5 years , then what is the age of arun ?
Options: a ) 48 , b ) 60 , c ) 84 , d ) 96 , e ) 69
Rationale: arun age x . ( x - 6 ) / 18 = y y is gokul age which is 3 x = 60 answer : b
Answer: b
Question (general): solve for the given equation 121 x 54 = ?
Options: a ) 68225 , b ) 75625 , c ) 76569 , d ) 45854 , e ) 45858
Rationale: explanation : this question can be solved by 2 approaches : = > direct multiplication = > numerical operations direct multiplication is quite time consuming and involves a lot of calculations . an easier approach is based on numerical operations . = > 121 x ( 10 / 2 ) 4 = 121 x 10000 / 16 = 75625 answer : b
Answer: b
Question (other): in a ratio which is equal to 7 : 9 , if the antecedent is 42 , then the consequent is ?
Options: a ) 72 , b ) 54 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 7 / 9 = 42 / x 7 x = 42 * 9 x = 54 consequent = 54 answer is b"
Answer: b
Question (general): john has 10 pairs of matched socks . if he loses 11 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 5 pairs ( 10 socks ) out of 10 pairs 1 sock from the 6 th pair . thus the no of matching socks pair remaining = 10 - 6 = 4 answer d"
Answer: d
Question (probability): a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 18 , b ) 21 , c ) 25 , d ) 30 , e ) 35
Rationale: the total number of ways to choose 4 managers is 7 c 4 = 35 we need to subtract the number of groups which include the two managers , which is 5 c 2 = 10 . 35 - 10 = 25 the answer is c .
Answer: c
Question (physics): convert 100 inches into centimeter ?
Options: a ) 112 cm , b ) 120 cm , c ) 150 cm , d ) 210 cm , e ) 254 cm
Rationale: "1 inch = 2.54 cm 100 inches = 100 * 2.54 = 254 cm answer is e"
Answer: e
Question (other): nitin ranks 23 th in a class of 60 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: explanation : number students behind the nitin in rank = ( 60 - 23 ) = 37 nitin is 38 nd from the last answer : b ) 38
Answer: b
Question (probability): in how many ways 4 boys and 1 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 24 , d ) 256 , e ) none
Rationale: solution : let the arrangement be , b b b b g 4 boys can be seated in 4 ! ways . girl can be seated in 1 ! ways . required number of ways , = 4 ! * 1 ! = 24 . answer : option c
Answer: c
Question (general): { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x 3 ) ( x + 14 ) ( 2 x + 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: x = - 4 prob = 1 / 12 answer - a
Answer: a
Question (general): the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 19 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) 40.1
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 19 = 401 hence , new average = 401 ⁄ 10 = 40.1 answer e"
Answer: e
Question (geometry): the side of a rhombus is 22 m and length of one of its diagonals is 16 m . the area of the rhombus is ?
Options: a ) 327.9 , b ) 325.9 , c ) 347.7 , d ) 357.9 , e ) 327.9
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 22 ; p = 16 a = 1 / 2 * 16 * √ 4 ( 22 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * √ 1936 - 256 = 1 / 2 * 16 * √ 1680 a = 327.9 answer : a"
Answer: a
Question (gain): sonika bought a v . c . r . at the list price of 18,600 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,088 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,600 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,600 = 8 ⁄ 100 × 18600 = 1488 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,600 + 1488 = 20,088 . answer a"
Answer: a
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 7 , 24 and 25 ?
Options: a ) 2.5 , b ) 6.5 , c ) 12.5 , d ) 14 , e ) 16
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 25 / 2 = 12.5 ans . c"
Answer: c