Cheukting/mathqa huggingface dataset:
Question (general): a student has to obtain 40 % of the total marks to pass . he got 150 marks and failed by 50 marks . the maximum marks are ?
Options: a ) 500 , b ) 650 , c ) 400 , d ) 575 , e ) 610
Rationale: "let the maximum marks be x then , 40 % of x = 150 + 50 40 x / 100 = 200 x = 500 answer is a"
Answer: a
Question (general): david has $ 1,800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Answer: b
Question (general): what number is 75 more than three - fourth of itself ?
Options: a ) 138 , b ) 225 , c ) 300 , d ) 324 , e ) 336
Rationale: "3 / 4 x + 75 = x that means 75 = 1 / 4 x x = 75 * 4 = 300 c is the answer"
Answer: c
Question (general): kamal was 4 times as old as his son 8 years ago . after 8 years , kamal will be twice as old as his son . find out the present age of kamal .
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: let age of the son before 8 years = x then , age of kamal before 8 years ago = 4 x after 8 years , kamal will be twice as old as his son ⇒ 4 x + 16 = 2 ( x + 16 ) ⇒ x = 8 present age of kamal = 4 x + 8 = 4 × 8 + 8 = 40 answer is c .
Answer: c
Question (gain): 80 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 600 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 80 / 100 ) * x + 120 = x 2 x = 1200 x = 600 answer : a"
Answer: a
Question (general): find the least number of complete years in which a sum of money put out at 13 % compound interest will be more than double of itself ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "6 years answer : b"
Answer: b
Question (general): kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ? a . b . c . none of these d . answer : option b explanation :
Options: a ) 1900 , b ) 3500 , c ) 4000 , d ) 2000 , e ) 2500
Rationale: let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : b
Answer: b
Question (gain): a man sells a car to his friend at 12 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 21136.36 , b ) rs . 31136.36 , c ) rs . 51136.36 , d ) rs . 61136.36 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 12 % . now s . p = rs . 45000 and loss = 12 % c . p . rs . [ 100 / 88 ã — 45000 ] = rs . 51136.36 correct option : c"
Answer: c
Question (geometry): the breath of a rectangle is three - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the length is 10 units ?
Options: a ) 370 sq . units
b ) 270 sq . units
c ) 170 sq . units
d ) 470 sq . units
e ) 570 sq . units
Rationale: given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units breath of the rectangle = 3 / 5 * 45 = 27 units given that length = 10 units area of the rectangle = lb = 27 * 10 = 270 sq . units answer : b
Answer: b
Question (general): there are 3 workers in the factory a , b , c . the age of a is 4 more than the age of b and the age of b is 4 more than the age of c . if the sum of the square of the ages is 1202 . what is the sum of their ages ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: let age of b = x ; age of a = x + 4 ; age of c = x - 4 ; sum of squares of ages = > 3 x ^ 2 + 32 = > x = 19.7 = > 20 sum of ages = 60 answer : c
Answer: c
Question (physics): if 12 men can reap 120 acres of land in 36 days , how many acres of land can 54 men reap in 54 days ?
Options: a ) 186 , b ) 188 , c ) 810 , d ) 167 , e ) 861
Rationale: "12 men 120 acres 36 days 54 men ? 54 days 120 * 54 / 12 * 54 / 36 10 * 54 * 3 / 2 54 * 15 = 810 answer : c"
Answer: c
Question (probability): how many cubes of 4 cm edge can be cut out of a cube of 28 cm edge
Options: a ) 343 , b ) 232 , c ) 216 , d ) 484 , e ) none of these
Rationale: "explanation : number of cubes = ( 28 x 28 x 28 ) / ( 4 x 4 x 4 ) = 343 answer : a"
Answer: a
Question (geometry): the area of a square is equal to four times the area of a rectangle of dimensions 52 cm * 13 cm . what is the perimeter of the square ?
Options: a ) 200 , b ) 208 , c ) 210 , d ) 220 , e ) 228
Rationale: "area of the square = s * s = 4 ( 52 * 13 ) = > s = 52 cm perimeter of the square = 4 * 52 = 208 cm . answer : option b"
Answer: b
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1100 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1500 , c ) rs . 2200 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1100 x = 1100 . b ' s share = rs . 2 x = rs . ( 2 x 1100 ) = rs . 2200 . answer = c"
Answer: c
Question (general): find the sum lend at c . i . at 5 p . c per annum will amount to rs . 500 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 453 , d ) 288 , e ) 171
Rationale: explanation : 500 = p ( 21 / 20 ) 2 p = 453.51 answer : c
Answer: c
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 20 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 200 , d ) 257 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 20 * 10 = 200 m . the length of the faster train = 200 m . answer : c"
Answer: c
Question (general): x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 4 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 16
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 4 ^ 2 = 9 / 16 answer : e"
Answer: e
Question (general): the sum of all solutions for x in the equation x ^ 2 – 4 x + 14 = | x – 4 | + 8 is equal to :
Options: a ) – 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "x ^ 2 - 4 x + 6 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 5 x + 10 = 0 x ^ 2 - 3 x + 2 = 0 x = 5 , 2,1 we test all 3 values in original equation , all ok . thus , sum = 5 + 2 + 1 = 8 ans ( b )"
Answer: b
Question (physics): r is the set of positive odd integers less than 50 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "squares < 50 { 1 , 4,9 , 16,25 , 36,49 } s = { 1,9 , 25,49 } r = { 1,3 , . . . . . 49 } hence c ."
Answer: c
Question (other): in a sports club with 27 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 27 38 - 2 x + x = 27 38 - x = 27 x = 11 so 8 members play both badminton and tennis . e"
Answer: e
Question (physics): a & b can separately do a piece of work in 20 & 15 days . they worked together for 6 days , after which b was replaced by c . the work was finished in next 5 days . the no . of days in which c alone could do the work is
Options: a ) 10 days , b ) 20 days , c ) 30 days , d ) 40 days , e ) 50 days
Rationale: b worked for 6 days = > in 6 days b completed = 6 x 1 15 = 2 5 th work a worked for first 6 days and later 4 days = > in 10 days a completed = 10 x 1 20 = 1 2 of the work total work done by a and b = 2 5 + 1 2 = 4 + 5 10 = 9 10 balance work = 1 - 9 10 = 1 10 th of total work balance work was completed by c in 5 days c can do 1 / 10 of the work in 5 days . therefore c alone can do the work in 50 days . e
Answer: e
Question (probability): a string of 13 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.02 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.02 , b ) ( 0.02 ) ^ 13 , c ) 1 - ( 0.02 ) ^ 13 , d ) ( 0.98 ) ^ 13 , e ) 1 - ( 0.98 ) ^ 13
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 13 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.02 = 0.98 the the probability that none of the 13 light bulbs fails is 0.98 ^ 13 . hence , the probability that at least one light bulb fails is 1 - 0.98 ^ 13 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 13 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.02 = 2 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: e
Question (general): 145 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 58 liters
Rationale: "milk = 3 / 5 * 145 = 87 liters water = 58 liters 87 : ( 58 + p ) = 3 : 4 174 + 3 p = 348 = > p = 58 58 liters of water are to be added for the ratio become 3 : 4 . answer : e"
Answer: e
Question (physics): edward ' s home have 3 taps , one tap , working alone at its maximum constant rate , can fill a certain sink in 270 seconds . a second tap working alone at its maximum constant rate , can fill a certain sink in 274 seconds . a third tap , working alone at its maximum constant rate , can fill the same sink in 276 seconds . if all taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 91 seconds , b ) 102 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 270 secs tap 2 : 274 secs tap 3 : 276 secs considering the average of these 3 taps : 273.33 secs . so 1 tap can fill the tank in 273.33 secs , so 3 taps can fill the tank in 273.33 / 3 = 91.11 secs . closest answer is a .
Answer: a
Question (general): the overall age of x and y is 12 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: "c 12 ( x + y ) – ( y + z ) = 12 x – z = 12"
Answer: c
Question (other): the compound ratio of 1 : 3 , 1 : 2 and 1 : 5 ?
Options: a ) 1 : 30 , b ) 1 : 5 , c ) 1 : 7 , d ) 1 : 1 , e ) 1 : 6
Rationale: 1 / 3 * 1 / 2 * 1 / 5 = 1 / 30 1 : 30 answer : a
Answer: a
Question (gain): what is rate of interest if principal . amount be 400 , simple interest 140 and time 2 year .
Options: a ) 10 , b ) 17.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 140 = 800 r / 100 r = 140 / 8 = 17.5 % answer b"
Answer: b
Question (gain): the population of a village is 12000 . it increases annually at the rate of 24 % p . a . what will be its population after 2 years ?
Options: a ) 14567 , b ) 18451 , c ) 18789 , d ) 18786 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 12000 × 124 / 100 × 124 / 100 = 18451 b"
Answer: b
Question (general): a school has received 40 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 77.78
Rationale: "let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 77.78 e"
Answer: e
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 40 meters . how many times did the ball bounce ?
Options: a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total distance travelled will be 16 + 16 + 8 ans : 2"
Answer: a
Question (gain): a trader sold an item at a loss of 35 % . if he had increased the price by $ 80 he would have made a gain of 5 % . what is the cost price of the item ?
Options: a ) $ 245 , b ) $ 150 , c ) $ 260 , d ) $ 220 , e ) $ 250
Rationale: "let c . p . be $ x then 105 % of x - 65 % of x = 100 40 % of x = 100 40 / 100 * x = 100 40 x = 10 000 x = 250 answer is e"
Answer: e
Question (physics): a and b can do a piece of work in 10 days , b and c in 15 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 70 days , b ) 55 days , c ) 24 days , d ) 40 days , e ) 11 days
Rationale: "2 c = 1 / 15 + 1 / 12 – 1 / 10 = 1 / 20 c = 1 / 40 = > 40 days answer : d"
Answer: d
Question (general): a certain telephone company company charges 3.10 cents for the first 1 / 5 of a minute plus 0.40 cents for each additional 1 / 5 of a minute . what would this company charge for a talk time of 8 minutes long ?
Options: a ) 15.60 , b ) 16.0 , c ) 17.8 , d ) 18.7 , e ) 19.1
Rationale: first 1 / 5 minute charge = 3.10 cents rest of the minute = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the minute = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 cents answer is d .
Answer: d
Question (physics): a certain number of men complete a piece of work in 60 days . if there were 8 men more , the work could be finished in 10 days less . how many men were originally there ?
Options: a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 45
Rationale: originally 1 et there be x men . more men , less days ( x + 8 ) : x ∷ 60 : 50 so , x + 8 / x = 60 / 50 or x = 40 . answer : d
Answer: d
Question (physics): how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 7.5 m x 6 m x 22.5 cm ?
Options: a ) 6000 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 750 x 600 x 22.5 / 25 x 11.25 x 6 = = 6000 answer : a"
Answer: a
Question (general): if the function q is defined by the formula q = 5 w / ( 4 vf ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , f is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: "we just need to find the factor thats all , w - > quadrupled - > 4 w f - > doubled - > 2 f z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and f * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"
Answer: b
Question (general): what is the remainder when 43 ^ 91 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 91 has the form 4 k + 3 so the units digit of 43 ^ 91 is 7 . the remainder when dividing by 5 is 2 . the answer is c ."
Answer: c
Question (general): if a and b are integers and ( a * b ) ^ 5 = 64 y , y could be :
Options: a ) 16 , b ) 32 , c ) 64 , d ) 128 , e ) 256
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 64 y find the prime factorization of 64 . this is 2 ^ 5 * 2 ^ 1 we need 2 ^ 4 ( or some other power of 2 that will give us a multiple of 2 ^ 5 as our second term ) . 2 ^ 4 = 16 the answer is a ."
Answer: a
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men ’ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : a"
Answer: a
Question (other): each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 40 ?
Options: a ) 1 / 6 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "200 = the # of factors 200 has is = 12 ( see below ) ; so out of 12 factors only two are multiples of 40 : 40 and 200 , itself ; so , the probability is 2 / 12 = 1 / 6 . answer : a ."
Answer: a
Question (other): a certain bag contains 100 balls — 50 white , 30 green , 10 yellow , 7 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 10 ) / 100 = 90 / 100 = 0.9 . answer is a"
Answer: a
Question (general): if ( n + 2 ) ! = 2550 ( n ! ) ; find ’ n ’
Options: a ) 38 , b ) 35 , c ) 49 , d ) 43 , e ) 34
Rationale: "( n + 2 ) ! = 2550 ( n ! ) ( n + 2 ) ( n + 1 ) ( n ! ) = 2550 ( n ! ) ( n + 2 ) ( n + 1 ) = 2550 2 n + 3 n + 2 - 2550 = 0 2 n + 3 n - 2548 = 0 2 n + 52 n - 49 n - 2548 = 0 n ( n - 49 ) ( n + 52 ) = 0 n = 49 or n = - 52 answer : c"
Answer: c
Question (general): find the remainder when 32 ^ 33 ^ 34 is divided by 11
Options: a ) 22 , b ) 10 , c ) 99 , d ) 76 , e ) 28
Rationale: "so 32103210 gives remainder 1 . now we have to write 32 ^ 33 ^ 34 in this format . so we have to find the remainder 33 ^ 34 when divided by 10 . the remainder is nothig but unit digit of the number . click here to learn this concept 33 ^ 34 gives unit digit of 9 . so 33 ^ 34 = 10 k + 9 323334 = 32 ( 10 k + 9 ) = ( 3210 ) k . 329323334 = 32 ( 10 k + 9 ) = ( 3210 ) k . 329 now this expression when divided by 11 leaves a remainder of 329329 which inturn is equal to ( − 1 ) 9 = − 1 = 10 answer : b"
Answer: b
Question (general): a heap of coconuts is divided into groups of 2 , 3 and 11 and each time one coconut is left over . the least number of coconuts in the heap is ? a . 31 b . 41 c . 51 d . 61
Options: a ) a ) 31 , b ) b ) 41 , c ) c ) 51 , d ) d ) 67 , e ) e ) 71
Rationale: lcm = 66 = > 66 + 1 = 67 answer : d
Answer: d
Question (physics): along a yard 441 metres long , 22 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 12
Rationale: "explanation : 22 trees have 21 gaps between them , required distance ( 441 / 21 ) = 21 option d"
Answer: d
Question (geometry): calculate the area of a triangle , if the sides are 30 cm , 21 cm and 10 cm , what is its area ?
Options: a ) 145 cm 2 , b ) 105 cm 2 , c ) 125 cm 2 , d ) 115 cm 2 , e ) 135 cm 2
Rationale: "the triangle with sides 30 cm , 21 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 21 * 10 = 105 cm 2 answer : b"
Answer: b
Question (physics): the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done 5 more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 750 ft , d ) 900 ft , e ) 2400 ft
Rationale: point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 32 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 75 . sub x = 75 either in ( x + 5 ) * 30 or in x * 32 to get the distance , which is 2400 . so the correct choice is e .
Answer: e
Question (physics): two pipes a and b can fill a cistern in 12 and 15 minutes respectively . both are opened together but after 4 minutes a is turned off . after how much more time will the cistern be filled ?
Options: a ) 6 , b ) 8 1 / 1 , c ) 8 1 / 4 , d ) 8 1 / 2 , e ) 8 3 / 7
Rationale: "4 / 12 + ( 4 + x ) / 15 = 1 x = 6 answer : a"
Answer: a
Question (gain): find the annual income derived by investing $ 6800 in 50 % stock at 136 .
Options: a ) 550 , b ) 2500 , c ) 250 , d ) 3000 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 50 . by investing $ 6800 , income obtained = $ [ ( 50 / 136 ) * 6800 ] = $ 2500 . answer b ."
Answer: b
Question (physics): a boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 0.5 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate down stream = 1 / 15 * 60 = 4 kmph rate of the current = ½ ( 4 - 3 ) = 0.5 kmph answer : b"
Answer: b
Question (gain): a motorcyclist x drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist y at a rate of 4 rounds per hour . after how long they will cross each other for the first time ?
Options: a ) 10 min , b ) 20 min , c ) 30 min , d ) 40 min , e ) none of these
Rationale: explanation : since x and y move in the same direction they cross each other when there is a difference of two round between the two . relative speed of x and y = 4 - 2 = 2 . time taken to complete one round at this speed = 1 / 2 hour = 30 minutes answer : c
Answer: c
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 30 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 30 % syrup solution , the result solution must have 105 l syrup and 45 l syrup . therefore we are taking 25 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 25 l syrup in 53.6 l solution we started by multiplying 10 now to get to the result we need to divide by 25 = > amount of solution to be replaced with water = ( 53.6 / 25 ) = 2.14 . correct option : c"
Answer: c