Cheukting/mathqa huggingface dataset:
Question (general): some consecutive natural numbers , starting with 1 , are written on the board . now , one of the numbers was erased and the average of the remaining numbers is 800 / 39 . find the number which was erased .
Options: a ) 20 , b ) 87 , c ) 266 , d ) 288 , e ) 11
Rationale: we know that average of n consecutive numbes average = n × ( n + 1 ) 2 n = ( n + 1 ) 2 n × ( n + 1 ) 2 n = ( n + 1 ) 2 if the given n is sufficiently large , the average does not change much even though we exclude one or two numbers from it . so the approximate number of observations is almost double to the average ( remember : the average of consecutive numbers almost lies in the middle ) the approximate average is 800 / 39 = approx 20 . so the initial numbers may be nearer to 40 . in this question it is actually 40 as from the denominator of the new average 800 / 39 . the initial numbers are 40 . sum of 40 consecutive numbers = 40 × ( 40 + 1 ) 2 = 82040 × ( 40 + 1 ) 2 = 820 sum of 39 numbers = average x numbenumber of observations = 80039 × 3980039 × 39 = 800 so the number excluded = 820 - 800 = 20 answer : a
Answer: a
Question (geometry): find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm ?
Options: a ) 50 cm 2 , b ) 100 cm 2 , c ) 150 cm 2 , d ) 200 cm 2 , e ) 250 cm 2
Rationale: "1 / 2 * 10 ( 7 + 3 ) = 50 cm 2 answer : a"
Answer: a
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "area of first rectangle is 15 * 24 = 360 hence area of second would be 8 x = 360 x x = 45 answer is d"
Answer: d
Question (general): what is the smallest number which when increased by 3 is divisible by 18 , 70 , 25 and 21 ?
Options: a ) 2327 , b ) 2757 , c ) 3147 , d ) 3587 , e ) 3997
Rationale: "when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is c ."
Answer: c
Question (other): the dimensions of a field are 10 m by 10 m . a pit 10 m long , 5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 2 m , b ) 3 m , c ) 4 m , d ) 5 m , e ) 1.5 m
Rationale: "the volume of the earth removed is 10 * 5 * 4 = 200 m ^ 3 . the remaining area of the field is 10 * 10 - 10 * 5 = 50 m ^ 2 . 200 m ^ 3 of the earth evenly spread over the area of 50 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 200 / 50 = 4 m . answer : c"
Answer: c
Question (general): in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 25.5 % , b ) 21.5 % , c ) 17.5 % , d ) 13.5 % , e ) 9.5 %
Rationale: "fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 3 / 5 = 3 / 40 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 3 / 40 = 7 / 40 = 17.5 % the answer is c ."
Answer: c
Question (physics): a truck covers a distance of 296 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 6.5 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 5.5 hours , d ) 8 hours , e ) none
Rationale: explanation : speed of the truck = distance / time = 296 / 8 = 37 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 37 + 18 ) = 55 kmph distance travelled by car = 296 + 6.5 = 302.5 km time taken by car = distance / speed = 302.5 / 55 = 5.5 hours . answer – c
Answer: c
Question (probability): a bag contains 12 red jellybeans and 12 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability 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 = 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 ) = 3 / 10 answer : option e"
Answer: e
Question (gain): a candidate got 10 % of the votes polled and he lost to his rival by 16000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 20000 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "10 % - - - - - - - - - - - l 90 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 80 % - - - - - - - - - - 16000 100 % - - - - - - - - - ? = > 20000 answer : b"
Answer: b
Question (physics): if i walk at 8 km / h , i miss the bus by 14 minutes . if i walk at 9 km / h , i reach 16 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 3.4 km , b ) 2.9 km , c ) 2.4 km , d ) 2.6 km , e ) 2.8 km
Rationale: d = product of speed difference of time / difference of speed d = 8 x 9 / 60 [ 14 â ˆ ’ ( â ˆ ’ 16 ) / 9 - 8 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 2.4 km answer c
Answer: c
Question (geometry): the length of a rectangle is 2 cm more than the width of the rectangle . the perimeter of the rectangle is 20 cm . find the length and the width of the rectangle .
Options: a ) l = 2 , w = 9
b ) l = 5 , w = 8
c ) l = 6 , w = 4
d ) l = 1 , w = 7
e ) l = 2 , w = 3
Rationale: let length l = x , width w = x − 2 and perimeter = p ∴ p = 2 l + 2 w = 2 x + 2 ( x − 2 ) 20 = 2 x + 2 x − 4 4 x = 24 x = 6 l = 6 cm and w = l − 2 = 4 cm answer is c .
Answer: c
Question (general): a certain sum becomes 4 times itself at simple interest in 8 years . in how many years does it become 10 times itself ?
Options: a ) 24 , b ) 55 , c ) 77 , d ) 99 , e ) 01
Rationale: let the sum be rs . x , then it becomes rs . 4 x in eight years rs . 3 x is the interest on x for eight years . r = ( 100 * 3 x ) / ( x * 8 ) = 300 / 8 % if the sum becomes ten times itself , then interest is 9 x . the required time period = ( 100 * 9 x ) / ( x * 300 / 8 ) = ( 100 * 9 x * 8 ) / ( x * 300 ) = 24 years . answer : a
Answer: a
Question (general): product of two natural numbers is 5 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b"
Answer: b
Question (general): certain stocks in january were 20 % less than they were in february and 30 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 31 % , b ) 45 % , c ) 52 % , d ) 61 % , e ) 25 %
Rationale: "let , stock in february = 100 then , stock in january = 100 - ( 20 / 100 ) * 100 = 80 january = 30 % greater than march = 1.3 * stock in march i . e . stock in march = 90 / 1.3 = 69 approximately % decrease from february to march = ( 69 - 100 ) * 100 / 100 = 31 % approximately answer : option a"
Answer: a
Question (general): if a ( a + 2 ) = 35 and b ( b + 2 ) = 35 , where a ≠ b , then a + b =
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 2 , e ) - 10
Rationale: "i . e . if a = 5 then b = - 7 or if a = - 7 then b = 5 but in each case a + b = 5 - 7 = - 2 answer : d"
Answer: d
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 10 to produce 80 units ?
Options: a ) 63 , b ) 20 , c ) 42 , d ) 65 , e ) 84
Rationale: "5 machines would produce 80 units in 40 hours . increasing the amount of machines by 2 would mean dividing 40 hours by 2 . 40 / 2 = 20 answer : b"
Answer: b
Question (gain): jar a has 26 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 7.6 % , b ) 8.3 % , c ) 9.6 % , d ) 10.3 % , e ) 11.5 %
Rationale: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 126 marbles . now , for both jars to have equal marbles we should move 13 marbles from a to b , which is 13 / 126 = ~ 10.3 % of a . answer : d ."
Answer: d
Question (general): the average weight of 5 students decreases by 4 kg when one of them weighing 92 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 4 kg = > ( 92 - x ) / 5 = 4 = > x = 72 answer : d"
Answer: d
Question (general): of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 500 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 25 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 25 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 500 = 20 t 19 t + 500 = 20 t 500 = t there are a total of 500 students in the math class . answer is d ."
Answer: d
Question (geometry): a 10 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 5
Rationale: "the longer wire will form a square with an area more than 4 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 10 = 2 / 5 . the answer is d ."
Answer: d
Question (gain): an uneducated retailer marks all his goods at 55 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 155 . s . p . = 75 % of rs . 155 = rs . 116.25 . ∴ gain % = 16.25 % . answer e"
Answer: e
Question (general): the sum of ages of 5 children born 4 years different each is 70 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 22 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) and ( x + 16 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 70 5 x = 30 x = 6 x + 16 = 6 + 16 = 22 answer : c"
Answer: c
Question (gain): the difference between simple and compound interest on rs . 1400 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.25 , b ) 3.5 , c ) 9.0 , d ) 3.15 , e ) 2.0
Rationale: "s . i . = ( 1400 * 10 * 1 ) / 100 = rs . 140 c . i . = [ 1400 * ( 1 + 5 / 100 ) 2 - 1400 ] = rs . 143.5 difference = ( 143.5 - 140 ) = rs . 3.50 answer : b"
Answer: b
Question (general): if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 2 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4
Rationale: "6 * 15 * 2 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 2 + 1 ) = ( √ 8 * 18 ) / 3 = ( √ 144 ) / 3 = 12 / 3 = 4 . answer is e"
Answer: e
Question (geometry): the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 420 m , its area is ?
Options: a ) 150 , b ) 882 , c ) 277 , d ) 210 , e ) 281
Rationale: "5 x + 12 x + 13 x = 420 = > x = 14 a = 70 , b = 168 , c = 182 s = ( 70 + 168 + 182 ) / 2 = 210 answer : d"
Answer: d
Question (physics): a train 500 m long , running with a speed of 180 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 10 sec , e ) 12 sec
Rationale: speed = 180 * 5 / 18 = 50 m / sec time taken = 500 * 1 / 50 = 10 sec answer : d
Answer: d
Question (gain): 33 1 / 3 % of 330 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 330 = 110 c )"
Answer: c
Question (gain): the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 40 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 , b ) 800 , c ) 600 , d ) 700 , e ) 500
Rationale: "volume of pool = 40 * 150 * 10 cu . ft , 80 % full = 40 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 40 * 150 * 10 * 0.8 / 60 min = 800 min b"
Answer: b
Question (general): you collect pens . suppose you start out with 7 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "solution start with 7 pens . mike gives you 22 pens : 7 + 22 = 29 pens . cindy doubles the number of pens you have : 29 × 2 = 58 pens . sharon takes 19 pens from you : 58 - 19 = 39 pens . so you have 39 at the end . correct answer : a"
Answer: a
Question (gain): the difference between simple and compound interest on rs . 1300 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.0 , b ) 3.25 , c ) 9.15 , d ) 3.13 , e ) 2.0
Rationale: s . i . = ( 1300 * 10 * 1 ) / 100 = rs . 130 c . i . = [ 1300 * ( 1 + 5 / 100 ) 2 - 1300 ] = rs . 133.25 difference = ( 133.25 - 130 ) = rs . 3.25 answer : b
Answer: b
Question (general): the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 90 inclusive is the digital sum a multiple of 7 ?
Options: a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 10 ways . . a"
Answer: a
Question (gain): ravi and kavi start a business by investing â ‚ ¹ 3000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 24 , b ) 5 : 24 , c ) 7 : 24 , d ) 1 : 24 , e ) 3 : 24
Rationale: ratio of profit = ratio of investments = 3000 : 72000 = 1 : 24 answer : d
Answer: d
Question (general): in august , a cricket team that played 120 matches won 30 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 55 , c ) 68 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 36 + x by solving we get x = 55 answer : b"
Answer: b
Question (general): jim ’ s taxi service charges an initial fee of $ 2.05 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 5.20 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: let the fixed charge of jim ’ s taxi service = 2.05 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.05 + ( 3.6 / . 4 ) * . 35 = 2.05 + 9 * . 35 = 5.2 $ answer a
Answer: a
Question (general): if a = 105 and a ^ 3 = 21 × 25 × 45 × w , what is the value of w ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × w = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x w = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x w w = 7 ^ 2 = 49 answer d"
Answer: d
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 40 miles per gallon , and from town b to town c , the car averaged 50 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 42.85 , b ) 40 , c ) 35 , d ) 41 , e ) 39
Rationale: "step 1 ) took lcm of 40 and 50 . . came as 200 . step 2 ) 200 distance between b to c . . . do 200 / 50 hence 4 gallons used step 3 ) twice distance . . hence 200 * 2 = 400 . . . do as above . . 400 / 40 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 200 + 400 = 600 miles hence . . average of whole journey = 600 / 14 which comes to 42.85 answer : a"
Answer: a
Question (physics): a fill pipe can fill 2 / 5 of cistern in 30 minutes in how many minutes , it can fill 4 / 5 of the cistern ?
Options: a ) 48 min , b ) 63 min , c ) 25 min , d ) 30 min , e ) 60 min
Rationale: "2 / 5 of the cistern can fill in 30 min 4 / 5 of the cistern can fill in = 30 * 5 / 2 * 4 / 5 = 60 min answer is e"
Answer: e
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 10 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 20 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 10 ) = 4 / 5 20 x = 4 ( 3 x + 10 ) 8 x = 40 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer is d ."
Answer: d
Question (general): a car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: "let the time for which car averages 75 mph = t 65 * ( t + 4 ) = 45 * 4 + 75 t = > 10 t = 80 = > t = 8 total duration of the trip = 8 + 4 = 12 answer a"
Answer: a
Question (general): the sum of the present age of henry and jill is 40 . what is their present ages if 8 years ago henry was twice the age of jill ?
Options: a ) 13 and 27 , b ) 16 and 24 , c ) 18 and 22 , d ) 11 and 29 , e ) none of these
Rationale: "let the age of jill 8 years ago be x , age of henry be 2 x x + 8 + 2 x + 8 = 40 x = 8 present ages will be 16 and 24 answer : b"
Answer: b
Question (general): the cricket team of 11 members is 25 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: let the average age of the whole team be x years . 11 x - ( 25 + 28 ) = 9 ( x - 1 ) = > 11 x - 9 x = 44 = > 2 x = 44 = > x = 22 . so , average age of the team is 22 years . b
Answer: b
Question (physics): the speed of a boat in still water is 24 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 15 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 3.6 km , d ) 6.75 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 24 + 3 ) kmph = 27 kmph . distance travelled = ( 27 x 15 / 60 ) km = 6.75 km option d"
Answer: d
Question (general): louie takes out a 3 - month loan of $ 2000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?
Options: a ) a ) 333 , b ) b ) 383 , c ) c ) 402 , d ) d ) 433 , e ) e ) 804
Rationale: here ' s the calculation for that case , assume monthly payment is x . after 1 st month : ( 2000 ) ( 1.1 ) - x = 2200 - x after 2 nd month : ( 2200 - x ) ( 1.1 ) - x = 2420 - 2.21 x after 3 rd month : ( 2420 - 2.21 x ) ( 1.1 ) - x = 2662 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 2662 - 3.31 x = 0 x = 2662 / 3.31 = 804 answer e
Answer: e
Question (general): 50 ^ 51 ^ 52 / 11
Options: a ) 6 , b ) 4 , c ) 7 , d ) 3 , e ) 5
Rationale: "we know that 6 ^ 1 = 6 or 6 ^ 2 = 36 so for all power of 6 unit digit is 6 now que is 50 ^ 51 ^ 52 now if we divide 50 / 11 then rem is 6 means 6 ^ 51 = 6 at unit place same for 6 ^ 52 salso give 6 at unit place now finally 50 ^ 51 ^ 52 gives 6 at unit place now 6 / 11 = 6 answer : a"
Answer: a
Question (gain): some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 45 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "45 % is 20 % - points above 25 % and 5 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 1 : 4 . 1 / 5 of the original paint was replaced . the answer is b ."
Answer: b
Question (general): if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 2 , b ) 7 / 2 , c ) 10 / 3 , d ) 15 / 4 , e ) 25 / 3
Rationale: "n = 3 d / 5 j = n / 3 = d / 5 the average of november and january is ( n + j ) / 2 = 4 d / 5 / 2 = 2 d / 5 d is 5 / 2 times the average of november and january . the answer is a ."
Answer: a
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross - section is 640 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 28 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 10 + 6 ) = 640 d = 80 answer : d"
Answer: d
Question (general): the jogging track in a sports complex is 528 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 3.84 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 528 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 528 m apart , they take ( 100 / 825 * 528 / 1000 ) hrs = ( 528 / 8250 * 60 ) min = 3.84 min . answer : b"
Answer: b
Question (general): a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2500 so 200 * x + 230 * x = 2500 = > 430 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 we are not taking 12 as answer because say 11 th person has minimum of 180 weight then 200 * 6 + 230 * 6 = 2580 ( which is more than 2500 ) answer e ."
Answer: e