Cheukting/mathqa huggingface dataset:
Question (general): for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Question (general): what is the remainder when 1271 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 11 , d ) 9 , e ) 7
Rationale: "in this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 . . . the remainder which comes now will be the answer . 1271 div by 12 = = > remainder = 11 1275 div by 12 = = > rema = 3 1285 div by 12 = = > remain = 1 1277 div by 12 = = > rema = 5 now multiply the remainder = 165 165 div by 12 rem = 9 answer : d"
Answer: d
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg , what is his percent ?
Options: a ) 20 % , b ) 25 % , c ) 29 % , d ) 55 % , e ) 100 %
Rationale: "500 - - - 500 100 - - - ? = > 100 % answer : e"
Answer: e
Question (general): ( 7895632 x 881 ) = ?
Options: a ) 6846381250 , b ) 6584638130 , c ) 6584638135 , d ) 6584638140 , e ) 6956051792
Rationale: 7895632 x 881 = 6956051792 ans e
Answer: e
Question (general): solve the equation for x : 8 x - 40 + 2 x = 5 + 10 - x
Options: a ) 4 , b ) 10 , c ) 7 , d ) 5 , e ) 3
Rationale: "d 5 10 x + x = 15 + 40 11 x = 55 = > x = 5"
Answer: d
Question (general): a waitress ' s income consists of her salary and tips . during one week , her tips were 9 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 9 / 13 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9
Rationale: her tips were 9 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 9 / 4 ) ( $ 4 ) = $ 9 so , her total income = $ 4 + $ 9 = $ 13 what fraction of her income for the week came from tips $ 9 $ 13 = 9 / 13 = a
Answer: a
Question (physics): a can do a piece of work in 8 days . b can do it in 12 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 16 days , d ) 24 days , e ) 36 days
Rationale: "c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d"
Answer: d
Question (general): find the value of m 62519 x 9999 = m ?
Options: a ) 724533811 , b ) 625127481 , c ) 545463251 , d ) 725117481 , e ) 677899932
Rationale: "62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b"
Answer: b
Question (gain): the difference between compound interest and simple interest on a sum for 3 years at 10 % p . a . is rs . 124 find the sum .
Options: a ) rs . 5000 , b ) rs . 4000 , c ) rs . 6000 , d ) rs . 8000 , e ) rs . 7000
Rationale: "for 3 years , we know c . i - s . i = p ( r / 100 ) ^ 3 + 3 ( r / 100 ) ^ 2 so , putting all values we have , 124 = p ( ( 10 / 100 ) ^ 3 + 3 ( 10 / 100 ) ^ 2 ) = 4000 answer : b"
Answer: b
Question (general): an italian sausage is 8 inches long . how many pieces of sausage can be cut from the 8 - inch piece of sausage if each piece is to be 2 / 3 of an inch ?
Options: a ) 12 , b ) 32 , c ) 22 , d ) 15 , e ) 20
Rationale: number of pieces = italian sausage ÷ 2 / 3 of an inch = 8 ÷ 2 / 3 = 8 / 1 ÷ 2 / 3 = 8 / 1 * 3 / 2 = 24 / 2 = 12 . answer is a .
Answer: a
Question (gain): a is a working partner and b is a sleeping partner in the business . a puts in rs . 3500 and b rs . 2500 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 6000
Rationale: "35 : 25 = > 7 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 12 = 5040 + 960 = 6000 answer : e"
Answer: e
Question (general): what is the dividend . divisor 20 , the quotient is 8 and the remainder is 6
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 166
Rationale: "d = d * q + r d = 20 * 8 + 6 d = 160 + 6 d = 166 answer : e"
Answer: e
Question (physics): a train 550 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 30 , b ) 60 , c ) 25 , d ) 40 , e ) 10
Rationale: speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 550 * 3 / 55 ] sec = 30 sec answer : a
Answer: a
Question (general): given that 268 x 74 = 19732 , find the value of 2.68 x . 74 .
Options: a ) 1.9732 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9732 answer a"
Answer: a
Question (general): bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 70 more . what was his original selling price ?
Options: a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
Rationale: "let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d"
Answer: d
Question (general): george baked a total of 50 pizzas for 5 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: 3 / 5 of the 50 pizzas cooked on saturday = 30 pizzas 3 / 5 of the remaining pizzas on sunday = 12 pizzas we ' re left with ( 50 - 30 - 12 ) = 8 pizzas for the remaining 3 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w 5 2 1 = 8 w = 1 e
Answer: e
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "explanatory answer let the original number be x . let a be the value obtained when x is increased by 12.5 % . therefore , a = x + 12.5 % of x let b be the value obtained when x is decreased by 25 % . therefore , b = x - 25 % of x the question states that a - b = 30 i . e . , x + 12.5 % of x - ( x - 25 % of x ) = 30 x + 12.5 % of x - x + 25 % of x = 30 37.5 % of x = 30 x = 30 / 37.5 * 100 = 80 the correct choice is ( b )"
Answer: b
Question (gain): a man walking at a rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 1492 , c ) 1667 , d ) 2500 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 15 minutes = 50 / 18 * 15 * 60 = 2500 m answer is d"
Answer: d
Question (general): in a company of 12 employees , 5 employees earn $ 36000 , 4 employees earn $ 45000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47500 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000
Rationale: 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c .
Answer: c
Question (general): dames school has 2000 boys and 5000 girls . what is the percentage increase from boys to total attendance and girls to total attendance ?
Options: a ) a ) 40 % , b ) b ) 10 % , c ) c ) . 4 % , d ) d ) 50 % , e ) e ) 12 %
Rationale: ratio of boys to total attendance ( 2 / 7 ) ratio of girls to total attendance ( 5 / 7 ) percentage increase is ( difference / initial quantity ) * 100 ( 2 / 7 ) / ( 5 / 7 ) * 100 = 40 % correct answer is a
Answer: a
Question (physics): a man swims downstream 76 km and upstream 48 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 1.5 kmph , c ) 3.5 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 76 - - - 4 ds = 19 ? - - - - 1 48 - - - - 4 us = 12 ? - - - - 1 s = ? s = ( 19 - 12 ) / 2 = 3.5 answer : option c"
Answer: c
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 35 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 16000 x 7 ) + 6000 ( x - 7 ) x = 35 . answer c"
Answer: c
Question (general): n = 1 / 3 + 1 / 4 what is the value of n ?
Options: a ) 7 / 12 , b ) 1 / 6 , c ) 1 / 8 , d ) 5 / 17 , e ) 12 / 7
Rationale: to sum 1 / 3 and 1 / 4 multiply both sides by 12 12 * n = 12 * 1 / 3 + 12 * 1 / 4 12 * n = 4 + 3 n = 7 / 12 ans : a
Answer: a
Question (general): how many even multiples of 55 are there between 549 and 1101 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "550 = 10 * 55 1100 = 20 * 55 the even multiples are 55 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Question (physics): sum of two numbers prime to each other is 15 and their l . c . m . is 56 . what are the numbers ?
Options: a ) 9 and 8 , b ) 5 and 10 , c ) 7 and 9 , d ) 7 and 8 , e ) 10 and 8
Rationale: "as two numbers are prime , only options satisfy ie option a and d and c but option d will make the product of numbers i . e 56 answer : d"
Answer: d
Question (general): if - 3 x + 2 y = 28 and 3 x + 6 y = 84 , what is the product of x and y ?
Options: a ) 264 . , b ) 428 , c ) 0 , d ) 462 , e ) 642
Rationale: "given - 3 x + 2 y = 28 - - - eq 1 3 x + 6 y = 84 - - eq 2 sum both eqns we get 8 y = 112 = > y = 14 sum 2 y in eq 1 = > - 3 x - 28 = 28 . = > x = 0 now xy = 0 * 14 = 0 . option c is correct answer ."
Answer: c
Question (physics): before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 10 , d ) 1 / 45 , e ) 1 / 60
Rationale: "pete covered 5 * 60 = 300 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 300 = 1 / 60 . answer : e ."
Answer: e
Question (geometry): a sphere is inscribed in a cube with an edge of 10 . what is the shortest possible distance from one of the vertices of the cube to the surface of the sphere ?
Options: a ) 10 ( √ 3 - 1 )
b ) 5
c ) 10 ( √ 2 - 1 )
d ) 5 ( √ 3 - 1 )
e ) 5 ( √ 2 - 1 )
Rationale: as sphere is inscribed in cube then = > the edge of the cube equals to the diameter of a sphere - - > diameter = 10 diagonal of a cube equals to diagonal = square _ root ( 10 ^ 2 + 10 ^ 2 + 10 ^ 2 ) = 10 √ 3 . half of diagonal - diameter is gap between the vertex of a cube and the surface of the sphere = ( 10 √ 3 - 10 ) / 2 = 5 ( √ 3 - 1 ) answer : d
Answer: d
Question (gain): by selling 20 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 80 , b ) 60 , c ) 50 , d ) 30 , e ) 10
Rationale: "80 % - - - 20 120 % - - - ? 80 / 120 * 20 = 30 answer : d"
Answer: d
Question (general): 25.25 / 2000 is equal to :
Options: a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.12625 , e ) 0.12725
Rationale: "25.25 / 2000 = 2525 / 200000 = 0.012625 answer : b"
Answer: b
Question (gain): on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 10 % , b ) 11 % , c ) 12 % , d ) 10.5 % , e ) none
Rationale: "solution difference in c . i and s . i for 2 years = rs ( 696.30 - 660 ) = rs . 36.30 . s . i for one years = rs 330 . s . i on rs . 330 for 1 year = rs . 36.30 rate = ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer b"
Answer: b
Question (gain): a certain tire company can produce tires at a cost of $ 22500 per batch plus $ 8 per tire . the company can sell tires to the wholesaler at a cost of $ 20 per tire . if a batch of 15000 tires is produced and sold , what is the company ’ s profit per tire ?
Options: a ) $ 9.00 , b ) $ 9.50 , c ) $ 10.50 , d ) $ 13.50 , e ) $ 20.00
Rationale: cp ( 15000 tires ) = $ 22500 + ( $ 8 × 15000 ) = $ 142500 sp ( 15000 tires ) = $ 20 × 15000 = $ 300000 profit = sp - cp = $ 300000 - $ 142500 = $ 157500 profit / tire = $ 157500 / 15000 = $ 10.50 answer c
Answer: c
Question (other): at a certain company , two - thirds of the employees had cell phones and two - fifths had pagers . if one - third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers ?
Options: a ) 7 / 5 , b ) 6 / 11 , c ) 2 / 5 , d ) 1 / 3 , e ) 4 / 15
Rationale: let there be 15 employees cell phone = 10 pagers = 6 neither pager nor cell phone = 5 so , 10 = 10 + 6 - x or , x = 6 so , fraction of the employees had both cell phones and pagers = 6 / 15 = > 2 / 5 answer : c
Answer: c
Question (general): the original price of a suit is $ 200 . the price increased 30 % , and after this increase , the store published a 30 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 30 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 182 , b ) $ 191 , c ) $ 200 , d ) $ 209 , e ) $ 219
Rationale: "given the foregoing discussion , it may be obvious now the trap - mistake answer is ( c ) . even if you can ’ t remember the correct thing to do , at the very least , learn to spot the trap ! the multiplier for a 30 % increases is 1 + 0.30 = 1.3 , and the multiplier for a 30 % decrease is 1 – 0.30 = 0.70 , so the combined change is 1.3 * 0.7 = 0.91 , 91 % percent of the original , or a 9 % decreases . now , multiply $ 200 * 0.91 = $ 182 . answer = ( a ) ."
Answer: a
Question (physics): a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 81 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 81 km time taken = distance / speed = 81 / 27 = 3 hours . answer : option c"
Answer: c
Question (physics): a man can do a piece of work in 5 days , but with the help of his son he can do it in 4 days . in what time can the son do it alone ?
Options: a ) 2 days , b ) 6 days , c ) 12 days , d ) 20 days , e ) none of these
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 4 − 1 / 5 ) = ( 5 − 4 ) / 20 = 1 / 20 so son will do whole work in 20 days answer : d"
Answer: d
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 149 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 64 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 149 x = 4 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 4 = 64 answer b"
Answer: b
Question (gain): a dealer offers a cash discount of 15 % and still makes a profit of 36 % when he further allows 25 articles to be sold at the cost price of 20 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 60 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 150 %
Rationale: given cash discount - 15 % profit - 36 % items sold - 25 price sold at = list price of 20 assume list price = $ 10 total invoice = $ 200 - 15 % cash discount = $ 170 let cost price of 25 items be x so total cost = 25 * x given the shopkeeper had a profit of 36 % 25 * x * 136 / 100 = 170 or x = $ 5 which means his products were listed at $ 10 which is a 100 % markup over $ 5 answer c
Answer: c
Question (general): if x + y = 2 and x 2 y 3 + y 2 x 3 = 32 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "xy = 4 as x + y = 2 x 2 y 3 + y 2 x 3 = 32 x 2 y 2 ( y + x ) = 32 substituting x + y x 2 y 2 = 16 xy = 4 answer : d"
Answer: d
Question (physics): a man swims downstream 72 km and upstream 45 km taking 3 hours each time ; what is the speed of the current ?
Options: a ) 1.5 , b ) 3.5 , c ) 4.5 , d ) 2.5 , e ) 5.5
Rationale: "72 - - - 3 ds = 24 ? - - - - 1 45 - - - - 3 us = 15 ? - - - - 1 s = ? s = ( 24 - 15 ) / 2 = 4.5 answer : c"
Answer: c
Question (probability): there are 4 books on a shelf , of which 3 are paperbacks and 6 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 111
Rationale: "approach 1 at - least 1 paper back = total - no paper back 9 c 4 - 6 c 4 = 111 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 6 c 3 + 3 c 2 * 6 c 2 + 3 c 3 * 6 c 1 = 111 answer is e"
Answer: e
Question (general): if the price of a book is first decreased by 20 % and then increased by 10 % , then the net change in the price will be :
Options: a ) 10 , b ) 12 , c ) 37 , d ) 29 , e ) 22
Rationale: explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 10 % on rs 80 = 80 + 8 = 88 net change in price = 100 - 88 = 12 answer : b
Answer: b
Question (general): a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 880.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 12.57 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 880 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 880 / 70 ~ 12.57 b"
Answer: b
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 7 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 9 3 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 7 ½ h . d = 5 / 4 * 15 / 2 = 75 / 8 = 9 3 / 8 km answer : c"
Answer: c
Question (gain): the regular price per can of a certain brand of soda is $ 0.60 . if the regular price per can is discounted 20 percent when the soda is purchased in 24 - can cases , what is the price of 72 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 34.56 , e ) $ 28.80
Rationale: "the discounted price of one can of soda is ( 0.8 ) ( $ 0.60 ) , or $ 0.48 therefore , the price of 72 cans of soda at the discounted price would be ( 72 ) ( $ 0.48 ) = 34.56 answer : d ."
Answer: d
Question (gain): the cost price of an article is 36 % of the marked price . calculate the gain percent after allowing a discount of 20 % .
Options: a ) 22.2 % , b ) 36 % , c ) 80 % , d ) 122.2 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 36 . s . p = rs . 80 . â ˆ ´ gain % = [ 44 / 36 * 100 ] % = 122.2 % . answer d"
Answer: d
Question (general): the cost of 2 chairs and 3 tables is rs . 1300 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 50 , b ) 60 , c ) none of these , d ) 70 , e ) 100
Rationale: "c 100 2 c + 3 t = 1300 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 100 = > t - c = 100"
Answer: c
Question (other): he ratio between the sale price and the cost price of an article is 5 : 1 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . x and s . p . = rs . 5 x . then , gain = rs . 4 x required ratio = 2 x : x = 2 : 1 answer : d"
Answer: d
Question (general): the average of first five multiples of 5 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 15 , e ) 7
Rationale: "average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 = 15 . answer : d"
Answer: d
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 19008 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 1584 , e ) 1625
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 19008 ⁄ 12 = 1584 answer d"
Answer: d
Question (physics): express 15 mps in kmph ?
Options: a ) 22 , b ) 88 , c ) 90 , d ) 21 , e ) 54
Rationale: "15 * 18 / 5 = 54 kmph answer : e"
Answer: e
Question (general): if | 5 x - 30 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 12 , d ) - 3 , e ) 4
Rationale: "| 5 x - 30 | = 100 5 x - 30 = 100 or 5 x - 30 = - 100 5 x = 130 or 5 x = - 70 x = 26 or x = - 14 sum = 26 - 14 = 12 answer is c"
Answer: c
Question (general): the class mean score on a test was 60 , and the standard deviation was 5 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 30 , b ) 31 , c ) 45 , d ) 40 , e ) 89
Rationale: "1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 65 to 55 , where 65 is within sd above the mean and 55 within 1 sd below the mean 2 sd = 5 twice = 10 from the the mean , which is 70 to 40 , where 70 is within 2 sd above the mean and 40 is within 2 sd below the mean . answer = d"
Answer: d
Question (gain): a man buy a book in rs 50 & sale it rs 80 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 60 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 80 profit = 80 - 50 = 30 % = 30 / 50 * 100 = 60 % answer : b"
Answer: b
Question (gain): find the simple interest on rs . 71,200 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8900 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 71200 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 71,200 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8900 answer is b ."
Answer: b
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 51 . what is that number
Options: a ) 4 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 51 = > 2 x + 9 = 17 = > x = 4 answer : option a"
Answer: a