Cheukting/mathqa huggingface dataset:
Question (geometry): rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ?
Options: a ) 13 1 / 2
b ) 20
c ) 18 3 / 4
d ) 21
e ) 24
Rationale: the area of a rectangle is : area = length x width we are given that floor x is 10 feet by 18 feet and that floor y is 9 feet wide . so we can say : length of x = 10 width of x = 18 width of y = 9 length of y = n we also can say : area of floor x = area of floor y ( length of x ) ( width of x ) = ( length of y ) ( width of y ) ( 10 ) ( 18 ) = 9 n ( 10 ) ( 2 ) = n 20 = n answer b .
Answer: b
Question (general): find the product of the localvalue and absolutevalue of 6 in 20618 ?
Options: a ) 6300 , b ) 1100 , c ) 1200 , d ) 1300 , e ) 3600
Rationale: "local value of 6 = 6 x 100 = 600 place value of 6 = 6 there fore = 6 x 600 = 3600 e"
Answer: e
Question (gain): a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 18 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 25 , b ) $ 26 , c ) $ 27 , d ) $ 28 , e ) $ 29
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 18 ) = 0.8 x x = 1.2 ( 18 ) / 0.8 = 1.5 ( 18 ) = $ 27 the answer is c ."
Answer: c
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 47 kg , then the weight of b is :
Options: a ) 39 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 47 x 2 ) = 94 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 174 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 39 . b ’ s weight = 39 kg . answer : a"
Answer: a
Question (physics): 6 women can do 75 units of work in 8 days by working 5 hrs / day . in how many days can 4 women do 30 units of work by working 8 hrs / day ?
Options: a ) 3 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 7 days
Rationale: 6 x 8 x 5 / 75 = 4 x 8 xa / 30 solve this for a then we get a = 3 days answer : a
Answer: a
Question (physics): the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 18 minutes is :
Options: a ) 9.5 , b ) 5.5 , c ) 7.5 , d ) 6.5 , e ) 5.1
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 18 / 60 ) ) km = 7.5 km . answer : c"
Answer: c
Question (gain): michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 14 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 138 % , e ) 145 %
Rationale: "since michelle earns 14 % interest compounded semiannually , then she earns 7 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 7 % * 5 = 35 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 35 % , only answer choice d fits . answer : d"
Answer: d
Question (general): the average of the marks of 30 students in a class is 45 . if the marks of each student are doubled , find the new average ?
Options: a ) 85 , b ) 77 , c ) 33 , d ) 90 , e ) 75
Rationale: "sum of the marks for the 30 students = 30 * 45 = 1350 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1350 * 2 = 2700 . so , the new average = 2700 / 30 = 90 . answer : d"
Answer: d
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 25 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 33 %
Rationale: "lets assume that candidate got 25 % votes and total votes is 100 . candidate won = 25 remaining = 75 to get 50 % , candidate requires 25 votes from 100 which is 25 % and 25 votes from 75 . 25 / 75 = 33.33 % which is approx 33 % . hence the answer is e"
Answer: e
Question (general): a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 100 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 52 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 100 - - > $ 52 answer is c"
Answer: c
Question (other): the price of precious stone is directly proportional to square of its weight . what will be the loss incurred if a stone weighing 28 gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15 : 13 ?
Options: a ) no loss , b ) 10,000 , c ) 28,000 , d ) 9,500 , e ) 14,000
Rationale: x = 28000 / 28 ^ 2 = 35.71 cost of 15 g = 35.71 * 15 ^ 2 = 8035.714 cost of 13 g = 35.71 * 13 ^ 2 = 6035.714 total cost = 14071.428 loss = 28000 - 14071.428 = 13928.5 = 14000 answer : e
Answer: e
Question (general): roy is now 6 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 90 , d ) 96 , e ) 108
Rationale: r = j + 6 = k + 3 r + 4 = 2 ( j + 4 ) ( j + 6 ) + 4 = 2 j + 8 j = 2 r = 8 k = 5 in 4 years ( r + 4 ) ( k + 4 ) = 12 * 9 = 108 the answer is e .
Answer: e
Question (physics): what is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad
Options: a ) 814 , b ) 256 , c ) 3258 , d ) 896 , e ) 745
Rationale: "explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm ^ 2 . required number of tiles = ( 1517 x 902 / 41 * 41 ) = 814 . answer : a"
Answer: a
Question (other): x starts a business with rs . 45000 . y joins in the business after 4 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 9 : 4
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 8 = 45 ã — 12 : 30 ã — 8 = 3 ã — 12 : 2 ã — 8 = 9 : 4 answer : option e"
Answer: e
Question (gain): a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 38,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 105 , d ) 115 , e ) 120
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 38000 - 30000 = 8000 so 20 more machines . . total = 120 machines imo e . . ."
Answer: e
Question (general): a certain city with a population of 192,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 16,000 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 192 k x = 16,000 answer : b"
Answer: b
Question (general): the mean of 50 observations was 36 . it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none of these
Rationale: "solution correct sum = ( 36 × 50 + 48 - 23 ) = 1525 . ∴ correct mean = 1825 / 50 = 36.5 answer c"
Answer: c
Question (general): there are 750 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 750 . hence , we have m + f = 750 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 750 / 3 = 250 solving the three equations yields the solution f = 250 , m = 500 , and d = 250 . the number of female democratic participants equals half the female participants equals 250 / 2 = 125 . answer : c"
Answer: c
Question (geometry): in 2 triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 . find the ratio of their bases ?
Options: a ) 10 : 8 , b ) 11 : 8 , c ) 16 : 9 , d ) 17 : 19 , e ) 17 : 10
Rationale: "given a 1 / a 2 = 4 / 3 , h 1 / h 2 = 3 / 4 also , we know that a 1 / a 2 = ( 1 / 2 × b 1 × h 1 ) / ( 1 / 2 × b 2 × h 2 ) on substituting in above equation , we get b 1 / b 2 = 16 / 9 therefore b 1 : b 2 = 16 : 9 c"
Answer: c
Question (gain): in what ratio must water be mixed with milk to gain 16 2 / 3 % on selling the mixture at cost price ?
Options: a ) 1 : 9 , b ) 1 : 1 , c ) 1 : 2 , d ) 1 : 6 , e ) 1 : 5
Rationale: required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : step i ) let c . p of 1 litre of mild be rs . 1 and s . p of 1 litre of mild be rs . 1 gain = 50 / 3 per cent  c . p of 1 litre of mixture =              1 3 50 100 100 x = re . 100 x 3 / 350 x 1 = 6 / 7 ( mean price ) step ( ii ) by the rule of allegation i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 1 iii . mean price ( p ) = 6 / 7 iv . d – m = 1 – 6 / 7 = 1 / 7 v . m – c = 6 / 7 - 0 = 6 / 7  ratio of water and milk = 1 / 7 : 6 / 7 = 1 : 6 answer : d
Answer: d
Question (general): 9 friends decided to divide the hotel bill evenly . if the bill was $ 124.15 dollars , how much money did they pay if 1 cent is the smallest unit ?
Options: a ) $ 124.11 , b ) $ 124.12 , c ) $ 124.13 , d ) $ 124.14 , e ) $ 124.15
Rationale: this is equivalent to finding the first number that is divisible by 9 that occurs after 12415 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 12415 = 13 and 9 is divisible by 9 . hence , we need to remove 4 to this number for it to be divisible by 9 correct option : a
Answer: a
Question (general): on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 36 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 36 . . 4 x + 12 = 36 . . x = 6 . . ans = x + 4 = 6 + 4 = 10 answer e"
Answer: e
Question (general): in a room with 8 people , 5 people have exactly 1 friend in the room and 4 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 25 / 28
Rationale: "( 5 / 8 ) ( 6 / 7 ) + ( 4 / 8 ) ( 5 / 7 ) if you choose one of the 5 with one other friend , then you have a 6 / 7 chance of not picking their friend 2 nd . if you choose one of the 4 with 2 friends , you have a 5 / 7 chance of not picking one of their friends second . add them up . 30 / 56 + 20 / 56 50 / 56 = 25 / 28 e . 25 / 28"
Answer: e
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 2000 resolutions ?
Options: a ) 1187 m , b ) 1704 m , c ) 2816 m , d ) 2827 m , e ) 2897 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2000 resolutions . = 2000 * 2 * 22 / 7 * 22.4 = 281600 cm = 2816 m answer : c"
Answer: c
Question (geometry): find the smallest number which should be multiplied with 560 to make it a perfect square .
Options: a ) 60 , b ) 55 , c ) 45 , d ) 25 , e ) 35
Rationale: "560 = 2 * 2 * 2 * 2 * 7 * 5 required smallest number = 7 * 5 = 35 35 is the smallest number which should be multiplied with 560 to make it a perfect square . answer : e"
Answer: e
Question (physics): earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 300 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 300 envelopes they will take 300 / 60 mins . i . e . , 5 mins . answer : b"
Answer: b
Question (general): the sum of first 45 natural numbers is ?
Options: a ) 1030 , b ) 1034 , c ) 1035 , d ) 1037 , e ) 1040
Rationale: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . c )"
Answer: c
Question (physics): vehicle x is 22 miles ahead of vehicle y , which is traveling the same direction along the same route as vehicle x . if vehicle x is traveling at an average speed of 36 miles per hour and vehicle y is traveling at an average speed of 45 miles per hour , how long will it take vehicle y to overtake and drive 23 miles ahead of vehicle x ?
Options: a ) 5 hours , b ) 7 hours 20 minutes , c ) 4 hours , d ) 3 hours 45 minutes , e ) 2 hours 30 minutes
Rationale: relative speed = 45 - 36 = 9 miles per hour dist required = 22 + 23 = 45 miles time taken to overtake = 45 / 9 = 5 hours . a is the answer .
Answer: a
Question (general): in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 5 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2400
Rationale: "sugar : flour = 5 : 5 = 10 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 10 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 10 x = 2400 answer : e ."
Answer: e
Question (general): the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?
Options: a ) 94 kg , b ) 85 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 70 + 24 ) kg = 94 kg . answer : a"
Answer: a
Question (gain): a worker is paid a regular rate of rs . 10 for completing a survey . the worker completes 50 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 30 % higher than her regular rate . if she completed 35 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 605 , b ) 505 , c ) 105 , d ) 100 , e ) 200
Rationale: "earning 35 surveys using her cell phone = 13 * 35 = 455 balance 15 surveys = 10 x 15 = 150 total = 455 + 150 = 605 answer : a"
Answer: a
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 9060 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 10 = rs . 9060 answer : a"
Answer: a
Question (physics): a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 7 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 42 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 7 6 / x = 1 / 7 = > x = 42 so , b takes 21 hours to finish the work . answer : d"
Answer: d
Question (geometry): right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 3 ( 9 horizontal dots and 3 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 3 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 2 c 1 , ( 3 - 1 = 2 as 1 vertical dot is already occupied by a ) . 9 c 1 * 3 c 1 * 8 c 1 * 2 c 1 = 432 . answer : b ."
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 7 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 117600
Rationale: "perimeter = distance covered in 7 min . = 12000 x 7 m = 1400 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1400 or x = 140 . length = 420 m and breadth = 280 m . area = ( 420 x 280 ) m 2 = 117600 m 2 . e"
Answer: e
Question (general): a man can swim in still water at 4.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.0 , b ) 1.9 , c ) 1.6 , d ) 1.5 , e ) 1.1
Rationale: "m = 4.5 s = x ds = 4.5 + x us = 4.5 + x 4.5 + x = ( 4.5 - x ) 2 4.5 + x = 9 - 2 x 3 x = 4.5 x = 1.5 answer : d"
Answer: d
Question (general): 0.99998 + 0.11112 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.1111 , e ) 1.111
Rationale: "0.99998 + 0.11112 = 0.99998 + 0.1111 + 0.00002 = ( 0.99998 + 0.00002 ) + 0.1111 = 1 + 0.1111 = 1.1111 d"
Answer: d
Question (general): there are 2 red chips and 3 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ b _ b so . . 5 ! / number of repeated letters ( 2 ! ) ( 3 ! ) = 10 ans : e"
Answer: e
Question (physics): in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 700 m ?
Options: a ) 148.75 m , b ) 127.5 m . , c ) 122.2 m , d ) 222.9 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 700 m , the number of meters by which a beats c = ( 700 * 212.5 ) / 1000 = 148.75 m . answer : a"
Answer: a
Question (general): ifaequals the sum of the even integers from 2 to 120 , inclusive , andbequals the sum of the odd integers from 1 to 119 , inclusive , what is the value of a - b ?
Options: a ) 60 , b ) 10 , c ) 19 , d ) 20 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 120 - 2 ) / 2 + 1 = 60 even integers . ( 120 + 2 ) / 2 = 61 is the average of the even set . sum = avg * ( # of elements ) = 61 * 60 = 3660 = a odd numbers : ( 119 - 1 ) / 2 + 1 = 60 odd integers . ( 119 + 1 ) / 2 = 60 is the average of the odd set . sum = avg * ( # of elements ) = 60 * 60 = 3600 = b a - b = 3660 - 3600 = 60 . answer : a"
Answer: a
Question (general): the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 10 more than the number who did not , and if receipts for registration and lunch totaled $ 61720 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 1,300 , d ) 500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 10 more than the number who did not . that means , total number of people who registered and paid for lunch = 10 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 10 + x ) = 720 + 72 x now , total amount received was 61,720 . thus , from the above data , 50 x + 720 + 72 x = 61720 122 x = 61720 - 720 122 x = 61000 x = 500 . hence the correct ans is d"
Answer: d
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 7 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 63.84 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 93 / 100 ) = 59.375 mp = 63.84 answer : a"
Answer: a
Question (general): in may mrs lee ' s earnings were 50 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 55 , b ) 56 , c ) 34 , d ) 78 , e ) 23
Rationale: lets say the family income is 100 in may , lee earned 50 family income is 50 in june , lee earned 20 % more than may , so it is ( 50 + 20 * 50 / 100 = 60 ) family income is same 50 in june lee ' s income percent is 60 * 100 / 110 ~ 55 ans is a
Answer: a