Cheukting/mathqa huggingface dataset:
Question (gain): suganya and suriya are partners in a business . suganya invests rs . 32,000 for 8 months and suriya invests rs . 28,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 912.54 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 32000 ã — 8 ) : ( 28000 ã — 10 ) = 32 : 35 . suganya ' s share = rs . ( 31570 ã — 2 / 67 ) = rs . 912.54 . answer c"
Answer: c
Question (general): a number when divided by a divisor leaves a remainder of 24 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 13 , b ) 59 , c ) 35 , d ) 37 , e ) 12
Rationale: "explanatory answer decoding ` ` a number when divided by a divisor leaves a remainder of 24 ' ' let the original number be ' a ' . let the divisor be ' d ' . let the quotient of dividing ' a ' by ' d ' be ' x ' . therefore , we can write the division as a / d = x and the remainder is 24 . i . e . , a = dx + 24 decoding ` ` when twice the original number is divided by the same divisor , the remainder is 11 ' ' twice the original number is divided by d means 2 a is divided by d . we know that a = dx + 24 . therefore , 2 a = 2 ( dx + 48 ) or 2 a = 2 dx + 48 when ( 2 dx + 48 ) is divided by ' d ' the remainder is 11 . 2 dx is divisible by ' d ' and will therefore , not leave a remainder . the remainder of 11 would be the remainder of dividing 48 by d . the question is ` ` what number will leave a remainder of 11 when it divides 48 ? ' ' when 37 divides 48 , the remainder is 11 . hence , the divisor is 37 . choice d"
Answer: d
Question (gain): an uneducated retailer marks all his goods at 65 % 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 ) 23.75 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 165 . s . p . = 75 % of rs . 165 = rs . 123.75 . ∴ gain % = 23.75 % . answer d"
Answer: d
Question (physics): a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 126 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 126 / 21 = 6 hours option c
Answer: c
Question (general): if 7 a = 2 b = 15 , then 42 ab =
Options: a ) 75 , b ) 125 , c ) 675 , d ) 1100 , e ) 1250
Rationale: "7 a * 2 b = 15 * 15 = 225 14 ab = 225 i . e . 42 ab = 675 answer : option c"
Answer: c
Question (general): 10 friends went to a hotel and decided to pay the bill amount equally . but 9 of them could pay rs . 50 each as a result 10 th has to pay rs . 180 extra than his share . find the amount paid by him .
Options: a ) 130 , b ) 140 , c ) 110 , d ) 120 , e ) none
Rationale: "explanation : average amount paid by 9 persons = rs . 50 increase in average due to rs . 50 paid extra by the 10 th men = rs . 180 / 9 = rs . 20 therefore , average expenditure of 10 friends = rs . 50 + rs . 20 = rs . 70 therefore , amount paid by the 10 th men = rs . 70 + rs . 50 = rs . 120 correct option : d"
Answer: d
Question (general): if 0.75 : x : : 5 : 7 , then x is equal to :
Options: a ) 1.05 , b ) 1.16 , c ) 1.2 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 7 ) x = 5.25 / 5 = 1.05 answer : a"
Answer: a
Question (general): a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 67 / 90 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think a - 67 / 90 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 7 x so old = x , new = 6 x now 1 / 3 of x are occupied and 1 / 5 of 6 x are occupied which simplifies to ( 6 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 6 / 5 of x occupied in the new ward . add them up to get 23 / 15 of x there are 6 x beds in new tower so ratio is : ( 23 / 15 ) x / 6 x = 23 / 90 of x subtract that from 90 / 90 of x and you get the number of un - occupied beds to total capacity of new tower = 67 / 90 . a"
Answer: a
Question (physics): a man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes . his rowing speed in s ɵ ll water is
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) none of these
Rationale: explanation : rate upstream = ( 750 / 675 ) = 10 / 9 m / sec rate downstream ( 750 / 450 ) m / sec = 5 / 3 m / sec rate in still water = ( 1 / 2 ) * [ ( 10 / 9 ) + ( 5 / 3 ) ] m / sec . = 25 / 18 m / sec = ( 25 / 18 ) * ( 18 / 5 ) kmph = 5 kmph answer : b
Answer: b
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3500 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 2100 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3500 / 25 = 140 so , a ’ s amount = 120 × 15 = rs . 2100 . answer : option c"
Answer: c
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 7350 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 1287 , c ) 125 , d ) 988 , e ) 175
Rationale: "3 x * 2 x = 7350 = > x = 35 2 ( 105 + 70 ) = 350 m 350 * 1 / 2 = rs . 175 answer : e"
Answer: e
Question (probability): the probability that a number selected at random from the first 50 natural numbers is a composite number is - .
Options: a ) 17 / 25 , b ) 17 / 27 , c ) 17 / 18 , d ) 17 / 22 , e ) 17 / 09
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : a"
Answer: a
Question (general): there are certain number of hats and gloves in a box . they are of 41 red , 23 green , 11 orange . power gone but a woman can differentiate between hats and gloves . how many draws are required to obtain a pair of each color ?
Options: a ) 66 , b ) 67 , c ) 68 , d ) 69 , e ) 70
Rationale: the worst case senario will be first take 40 red then take 22 green then take 1 + 1 red + green then take 2 orange . so total 40 + 22 + 2 + 2 = 66 answer : a
Answer: a
Question (general): 19.19 / 2000 is equal to :
Options: a ) 1.01252633 , b ) 0.01262533 , c ) 0.12526333 , d ) 0.012793333 , e ) 0.12725333
Rationale: "19.19 / 2000 = 2525 / 200000 = 0.012793333 answer : d"
Answer: d
Question (general): the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 49 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 49 = 21 ( x – 5 ) x = 56 answer : b"
Answer: b
Question (general): harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 3 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 3 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 3 x = 9 x august tips as a fraction of total tips = 3 x / 9 x = 1 / 3 . so answer is a"
Answer: a
Question (physics): how many shots of 1 cm radius can be prepared from a sphere of 3 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 88 , e ) 99
Rationale: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π * 1 * 1 * 1 * x x = 27 answer : c"
Answer: c
Question (physics): two trains each 190 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 65 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 10.7 sec , b ) 2.7 sec , c ) 11.9 sec , d ) 12.7 sec , e ) 25.7 sec
Rationale: "explanation : d = 190 m + 190 m = 380 m rs = 65 + 50 = 115 * 5 / 18 = 319 / 10 t = 380 * 10 / 319 = 11.9 sec answer : option c"
Answer: c
Question (physics): a 600 m long train crosses a tree in 60 sec , how much time will it take to pass a platform 450 m long ?
Options: a ) 288 , b ) 190 , c ) 188 , d ) 188 , e ) 105
Rationale: "l = s * t s = 600 / 60 s = 10 m / sec . total length ( d ) = 1050 m t = d / s t = 1050 / 10 t = 105 sec answer : e"
Answer: e
Question (gain): the price of rice falls by 10 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 10 % , new price for 20 kg rice , = ( 100 - 10 % of 100 ) = 90 new price of rice = 90 / 20 = rs . 4,5 per kg . rice can bought now at = 100 / 4,5 = 22,22 kg . answer : option e"
Answer: e
Question (general): the least number , which when divided by 12 , 15 , 20 and 63 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 542 , d ) 1268 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 63 ) + 8 = 1260 + 8 = 1268 . answer : d"
Answer: d
Question (other): in a class of 50 students , 3 / 5 went away do painting , 1 / 5 went to play in the field . how many students are left in the classroom ?
Options: a ) 20 , b ) 30 , c ) 5 , d ) 8 , e ) 10
Rationale: 3 / 5 + 1 / 5 are the students who have left the classroom 3 / 5 + 1 / 5 = ( 3 + 1 ) / 5 , since denominator is same for both fractions = 4 / 5 remaining students in the classroom = 1 - 4 / 5 = 5 / 5 - 4 / 5 = ( 5 - 4 ) / 5 = 1 / 5 1 / 5 of 50 = 10 ans : e
Answer: e
Question (gain): a statue is being carved by a sculptor . the original piece of marble weighed 300 kg . in the first week 30 percent is cut away . in the second week 30 percent of the remainder is cut away . in the third week the statue is completed when 15 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "d 125 kg 300 ã — 0.7 ã — 0.7 ã — 0.85 = 125 kg ."
Answer: d
Question (gain): a $ 500 investment and a $ 1,500 investment have a combined yearly return of 10 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 10 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 11 % ( option d ) answer : d
Answer: d
Question (general): the number of positive integer solutions for the equation x + y + z + t = 18 is
Options: a ) 640 , b ) 780 , c ) 380 , d ) 540 , e ) 680
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 18 - 1 c 4 - 1 = 17 c 3 = 680 answer : e"
Answer: e
Question (general): the average age of a group of n people is 15 years old . one more person aged 37 joins the group and the new average is 17 years old . what is the value of n ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "15 n + 37 = 17 ( n + 1 ) 2 n = 20 n = 10 the answer is a ."
Answer: a
Question (physics): the ratio between the speeds of two trains is 7 : 8 . if the second train runs 400 km in 4 hours , what is the the speed of the first train ?
Options: a ) 87.0 , b ) 87.5 , c ) 87.2 , d ) 87.1 , e ) 87.4
Rationale: speed and time are inversely proportional ( when distance is constant ) ⇒ speed ∝ 1 time ( when distance is constant ) here distance is constant and hence speed and time are inversely proportionalspeed ∝ 1 time ⇒ speed 1 speed 2 = time 2 time 1 ⇒ 78 = 4 time 1 ⇒ time 1 = 4 × 87 hr ⇒ speed of the first train = distancetime 1 = 400 ( 4 × 87 ) = 100 × 78 = 12.5 × 7 = 87.5 km / hr answer : b
Answer: b
Question (general): what is the unit digit of ( 8 ! * 4 ! / 8 ! * 3 ! ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 8 ! * 4 ! / 8 ! * 3 ! ) = ( 4 ! / 3 ! ) = 24 / 6 = 4 units digit of the above product will be equal to 4 answer e"
Answer: e
Question (geometry): area of square with side x is equal to the area of a triangle with base x . the altitude of the triangle is
Options: a ) x / 2
b ) x
c ) 2 x
d ) 4 x
e ) 3 x
Rationale: x ^ 2 = 1 / 2 ã ƒ â € ” x ã ƒ â € ” h or h = 2 x ^ 2 / x = 2 x answer : c
Answer: c
Question (gain): a baseball card decreased in value 60 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 64 %
Rationale: let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 60 / 100 ) * 100 = 40 after second year , value of baseball card = ( 1 - 10 / 100 ) * 40 = 36 total percent decrease of the card ' s value over the two years = ( 100 - 36 ) / 100 * 100 % = 64 % answer e
Answer: e
Question (probability): there are 10 books on a shelf , of which 4 are paperbacks and 6 are hardbacks . how many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback ?
Options: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252
Rationale: "paperbacks - 4 , hardbacks - 6 5 books in total and at least 1 from each . total combinations for 5 books = ( 1 pb , 4 hb ) + ( 4 pb , 1 hb ) + ( 3 pb , 2 hb ) + ( 2 pb , 3 hb ) 1 pb , 4 hb = 4 c 1 * 6 c 4 = 60 4 pb , 1 hb = 4 c 4 * 6 c 1 = 6 3 pb , 2 hb = 4 c 3 * 6 c 2 = 60 2 pb , 3 hb = 4 c 2 * 6 c 3 = 120 total combinations of 5 books = 60 + 6 + 60 + 120 = > 246 ans d ."
Answer: d
Question (physics): a walk 20 m towards north east . b walk towards east 8 m and then 12 m south . now calculate distance between a and b ?
Options: a ) 30 m , b ) 20 m , c ) 35 m , d ) 40 m , e ) 38 m
Rationale: its coming 30.4 m since 1 st triangle we get 18.31 and extra 12 so 18.31 + 12 = 30.31 = 30 m answer : a
Answer: a
Question (gain): if the difference between compound interest ( interest compounded yearly ) and simple interest on a sum for 3 years at 20 % p . a . is rs . 132 , then the sum is
Options: a ) rs . 3500 , b ) rs . 1500 , c ) rs . 2500 , d ) rs . 3000 , e ) none
Rationale: "c . i - s . i = 132 c . i = a - p a = p ( 1 + ( r / 100 ) ) ^ n a = x ( 1 + ( 20 / 100 ) ) ^ 3 a = x ( 6 / 5 ) ^ 3 a = 216 / 125 ( x ) c . i = ( 91 / 125 ) x s . i = ( pnr ) / 100 = ( x * 3 * 20 ) / 100 = ( 6 / 10 ) x diff = 132 diff = ( 91 / 25 ) x - ( 6 / 10 ) x = ( 182 x - 150 x ) / 250 = 32 x / 250 32 x / 250 = 132 x = ( 132 * 250 ) / 32 x = 1031.25 answer : e"
Answer: e
Question (geometry): the mass of 1 cubic meter of a substance is 700 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.42 , c ) 8.0 , d ) 12.5 , e ) 80.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 700 kg / 1 m ^ 3 = 700 kg / m ^ 3 or 1 g / 1.42 cm ^ 3 = 0.7 g / cm ^ 3 . next , ask yourself if 700,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 700,000 = 10 / 8 = 1.42 cubic centimeters . answer is b"
Answer: b
Question (physics): a plot abcd is as shown in figure , where af = 30 m , ce = 40 m , ed = 50 m , ae = 120 m . find the area of the plot abcd ?
Options: a ) 7207
b ) 7206
c ) 7203
d ) 7200
e ) 7201
Rationale: area of plot abcd = area of ade + area of afb + area of bcef = 1 / 2 * 50 * 120 + 1 / 2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600 = 7200 sq . m answer : d
Answer: d
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 126 km / hr
Options: a ) 8.5 seconds , b ) 2.86 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 126 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 100 / 35 = 2.86 seconds answer : b"
Answer: b
Question (physics): two bullet train s 140 m and 170 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.16 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 170 ) m = 310 m . required time = 310 x 9 / 250 = 11.16 sec . answer c"
Answer: c
Question (geometry): a rectangular garden is 12 m by 5 m , what is its area ?
Options: a ) 12 square meters
b ) 5 square meters
c ) 44 square meters
d ) 60 square meters
e ) 22 square meters
Rationale: area of a rectangle : a = w × h d ) 60 square meters
Answer: d
Question (gain): indu gave bindu rs . 3125 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 2 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "3125 = d ( 100 / 4 ) 2 d = 5 answer : c"
Answer: c
Question (other): if the ratio of a to b is 7 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 / 5 , d ) 4 / 5 , e ) 7 / 15
Rationale: "a : b = 7 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 7 : 15 answer e"
Answer: e
Question (general): the average of first 18 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17
Rationale: "sum of 18 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : a"
Answer: a
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 238 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 350 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 238 = ( p * 4 * 8 ) / 100 p = 350 answer : b"
Answer: b
Question (general): for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 99 ) – g ( 97 ) ?
Options: a ) 98 , b ) 100 , c ) 0 , d ) 99 , e ) 97
Rationale: g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 g ( 99 ) - g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 - 1 * 3 * 5 * 7 * 9 * . . . * 97 = 1 * 3 * 5 * 7 * 9 * . . . * 97 * ( 99 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 * 98 hence : a .
Answer: a
Question (gain): in the first 5 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 200 runs ?
Options: a ) 6.25 , b ) 6.28 , c ) 6.31 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 200 - ( 2.1 * 5 ) ] / 30 = 189.50 / 30 = 6.31 answer : c"
Answer: c
Question (general): what is the sum of all even numbers from 1 to 901 ?
Options: a ) 122821 , b ) 202950 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 900 / 2 = 450 450 * 451 = 202950 answer : b"
Answer: b
Question (physics): the lcm and hcf of two numbers are 100 and 10 respectively . find the larger of the two numbers if their sum is 110 .
Options: a ) 100 , b ) 12 , c ) 35 , d ) 466 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100 * 10 = 1000 so the answer which we are looking for has to be a factor of 1000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Question (general): a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 1 boy ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 1 / 2
Rationale: "sample space = 2 ^ 4 = 16 . favourable events = { bbgg } , { bgbg } , { bggb } , { ggbb } , { gbgb } , { gbbg } . { bggg } , { gbbb ) probability = 8 / 16 = 1 / 2 . ans ( e ) ."
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 16197.12
Rationale: "amount = [ 40000 * ( 1 + 12 / 100 ) 3 ] = 40000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 56197.12 c . i . = ( 56197.12 - 40000 ) = rs : 16197.12 answer : e"
Answer: e
Question (general): a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Question (general): if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80
Rationale: "3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d"
Answer: d
Question (geometry): a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ?
Options: a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 27 / 3 = 9 total feet squirrel travels = 9 * 3 = 27 feet answer : c"
Answer: c
Question (general): how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b .
Answer: b