Cheukting/mathqa huggingface dataset:
Question (gain): we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 052.50 . how much money did we invest at 3 % ?
Options: a ) $ 160 , b ) $ 190 , c ) $ 220 , d ) $ 250 , e ) $ 280
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.06 ( 1000 - x ) = 1052.50 . 0.03 x = 1060 - 1052.50 . 0.03 x = 7.50 . 3 x = 750 . x = 250 . the answer is d ."
Answer: d
Question (general): | x + 3 | – | 4 - x | = | 9 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 b"
Answer: b
Question (geometry): the area of a rectangular plot is 460460 square metres . if the length is 15 % 15 % more than the breadth , what is the breadth of the plot ?
Options: a ) 14 metres , b ) 20 metres , c ) 18 metres , d ) 12 metres , e ) 16 metres
Rationale: "explanation : length 115 % of breadth . length × breadth = 460 m 2 ⇒ 115 % of breadth × breadth = 460 m 2 ⇒ 115 / 100 × breadth × breadth = 460 m 2 ⇒ breadth × breadth = 400 m 2 ⇒ breadth = 20 m answer : option b"
Answer: b
Question (physics): two pipes a and b can separately fill a tank in 16 and 18 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 18 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 720 liters , c ) 740 liters , d ) 860 liters , e ) 620 liters
Rationale: "1 / 16 + 1 / 18 - 1 / x = 1 / 18 x = 16 16 * 45 = 720 answer : b"
Answer: b
Question (other): 17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 1 / 7 , b ) 3 / 14 , c ) 5 / 23 , d ) 7 / 34 , e ) 9 / 41
Rationale: p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d .
Answer: d
Question (physics): aarti can do a piece of work in 9 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 27 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 9 days . three times of work of same type can be done in 9 x 3 = 27 days answer d"
Answer: d
Question (general): what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 7 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 7 = > m = 21 answer d"
Answer: d
Question (probability): there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 40 , b ) 49 , c ) 41 , d ) 56 , e ) 42
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 7 and for second = 6 so total methods = 7 * 6 = 42 answer : e"
Answer: e
Question (general): what is the lowest positive integer that is divisible by 4 through 6 , inclusive ?
Options: a ) 120 , b ) 48 , c ) 82 , d ) 76 , e ) 160
Rationale: "the integer should be divisible by : 4 , 5 , and 6 . the least common multiple of these integers is lcm = 4 * 5 * 6 = 7920 answer : a"
Answer: a
Question (physics): when a stone is dropped from a building 200 m high , its speed is proportional to the time elapsed after dropping . the distance traveled is proportional to the square of the time elapsed . after 1 second the speed of the train was 10 m / sec and it was 190 m above the ground . when its speed is 25 m / sec , what would be its distance from the ground ?
Options: a ) 140 m , b ) 137.5 m , c ) 125.75 m , d ) 142.5 m , e ) 152.5 m
Rationale: v = x * t and s = y * t ^ 2 10 = x * 1 , hence x = 10 units ( 200 - 190 ) = y * 1 * 1 y = 10 when speed = 25 m / sec , time elapsed = 25 / 10 = 2.5 sec distance travelled by stone = 10 * ( 2.5 ) ^ 2 = 62.5 mts so distance of stone above ground = 200 - 62.5 = 137.5 mtrs answer : b
Answer: b
Question (general): if 2 x = 3 y = 10 , then 15 xy = ?
Options: a ) 1,200 , b ) 200 , c ) 120 , d ) 40 , e ) 250
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 15 xy = 15 * 5 * 10 / 3 = 250 answer : e ."
Answer: e
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 30 km / hr and 90 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 90 + 30 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b"
Answer: b
Question (other): the ratio of three numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the three numbers is ?
Options: a ) 24 , b ) 26 , c ) 27 , d ) 400 , e ) 30
Rationale: "5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d"
Answer: d
Question (general): in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 8
Rationale: let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a
Answer: a
Question (physics): a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 250 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the distance between the nest and the ditch is 250 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 250 = 7500 . d = st 7500 / 1.5 = t , i think we can take 7500 meters as 7.5 km , then only we get t = 5 . ( 1000 meters = 1 km ) d )"
Answer: d
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b ."
Answer: b
Question (gain): on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 40 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 500 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 40 % . 4 x = 200 = > x = 500 answer a"
Answer: a
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 36 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b"
Answer: b
Question (physics): how much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 92 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 380 + 540 = 920 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 920 / 10 = 92 sec . answer : d"
Answer: d
Question (gain): the area of a circle is increased by 800 % . by what percent has the radius of the circle increased ?
Options: a ) 100 % , b ) 400 % , c ) 300 % , d ) 600 % , e ) 200 %
Rationale: "the area of the circle is increased by 800 % , thus the area is increased 9 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 3 times ( diameter increase 3 times = area increase 9 times ) , which is increase by 200 % . answer : e ."
Answer: e
Question (gain): adam borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years , and at the rate of 14 % p . a . for the period beyond 5 years . 1 £ he pays a total interest of rs . 11400 at the end of 9 years how much money did he borrow ?
Options: a ) rs . 8000 , b ) rs . 09000 , c ) rs . 11000 , d ) rs . 10000 , e ) rs . 12000
Rationale: let the sum borrowed be x . then , ( x * 2 * 6 ) / 100 + ( x * 9 * 3 ) / 100 + ( x * 14 * 4 ) / 100 = 11400 ( 3 x / 25 + 27 x / 100 + 14 x / 25 ) = 11400 95 x / 100 = 11400 x = ( 11400 * 100 ) / 95 = 12000 . hence , sum borrowed = rs . 12000 answer is e .
Answer: e
Question (general): which number need to add to 859622 to get a number divisible by 456 ?
Options: a ) 565771 , b ) 456578 , c ) 676885 , d ) 788090 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Question (physics): if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 50 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 50 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 100 ans a"
Answer: a
Question (general): in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 8,4 ) , and ( 8,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 32 . p ( x + y < 4 ) = 8 / 32 = 1 / 4 the answer is d ."
Answer: d
Question (general): harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 5 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 11 / 30 , e ) 5 / 6
Rationale: "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 5 m = 12 books total = 22 books m ' = 22 = 11 / 30 * 60 ratio : 11 / 30 ans : d"
Answer: d
Question (general): let the number which when multiplied by 16 is increased by 375 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 25 , e ) 30
Rationale: "solution let the number be x . then , 16 x - x = 375 ‹ = › 15 x = 375 x ‹ = › 25 . answer d"
Answer: d
Question (physics): a can finish a work in 60 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 25 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 60 work is done by a in 1 day 5 / 12 work is done by a in 60 * 5 / 12 = 25 days answer is b"
Answer: b
Question (general): jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 24
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e
Answer: e
Question (general): a cricket player whose bowling average was 21.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 111 , d ) 721 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 21.5 w + 52 total wickets after last match = w + 5 ( 21.5 w + 52 ) / ( w + 5 ) = 21.5 - 0.5 = 21 w = 106 so total wickets aftr last match = w + 5 = 111 answer : c"
Answer: c
Question (physics): 8 men , working 8 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 8 * 18 = 1152 12 × 12 × ( x ) = 1152 x = 8 the answer is c ."
Answer: c
Question (general): 1 , 8 , 27 , 64 , 125 , 216 , ( . . . . )
Options: a ) 354 , b ) 343 , c ) 245 , d ) 392 , e ) 400
Rationale: "the pattern is 1 ^ 3 , 2 ^ 3 , 3 ^ 3 , 4 ^ 3 , 5 ^ 3 , 6 ^ 3 , etc hence , next number is 7 ^ 3 = 343 answer is b"
Answer: b
Question (physics): if 3 men or 4 women can do a piece of work in 16 days , in how many days can 12 men and 8 women do the same piece of work ?
Options: a ) 8 / 3 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "3 men can finish a work in 16 days , so in 1 day 3 men finish 1 / 16 th of work and in 1 day 1 men can finish , 1 / 48 th of work . similarly , in 1 day 1 women can finish 1 / 64 th of work . 12 men in 1 day can finish , 12 / 48 = 1 / 4 , 8 women in 1 day can finish = 8 / 64 = 1 / 8 1 / 4 + 1 / 8 = 3 / 8 . hence number of days to complete is 8 / 3 days . answer : a"
Answer: a
Question (physics): two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 24 seconds , the speed of each train ( in km / hr ) is
Options: a ) 18 , b ) 36 , c ) 28 , d ) 20 , e ) 24
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 24 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 24 = 10 m / s speed of each train = v = 10 / 2 = 5 m / s = 5 × 36 / 10 km / hr = 18 km / hr answer : option a"
Answer: a
Question (general): john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e
Answer: e
Question (general): a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?
Options: a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 800 , e ) rs . 900
Rationale: solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c
Answer: c
Question (physics): the speed of a car is 85 km in the first hour and 45 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 65 kmph , c ) 30 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: s = ( 85 + 45 ) / 2 = 65 kmph answer : b
Answer: b
Question (general): find the number which multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 27
Rationale: "let the number be x . then , 15 x - x = 196 x = 14 answer : a"
Answer: a
Question (general): the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?
Options: a ) 0 and 0.5 , b ) 0.5 and 1 , c ) 1 and 1.5 , d ) 1.5 and 2 , e ) 2 and 2.5
Rationale: trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d .
Answer: d
Question (other): the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 300 , c ) 299 , d ) 322 , e ) 345
Rationale: "the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b"
Answer: b
Question (other): two numbers are in the ratio of 1 : 2 . if 6 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 6 ) / ( y + 6 ) = 3 / 5 = > x = 12 and y = 24 answer : b"
Answer: b
Question (geometry): carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.66 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b"
Answer: b
Question (geometry): points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a"
Answer: a
Question (gain): the cash difference between the selling prices of an article at a profit of 4 % and 2 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 51 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 102 % of x = 104 / 102 = 52 / 51 = 52 : 51 answer : a"
Answer: a
Question (other): two whole numbers whose sum is 100 can not be in the ratio
Options: a ) 2 : 23 , b ) 5 : 45 , c ) 10 : 10 , d ) 2 : 6 , e ) 2 : 3
Rationale: d ) 2 : 6
Answer: d
Question (general): what least number must be added to 696 , so that the sum is completely divisible by 20 ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "if we divide 696 by 20 remainder is 16 20 - 16 = 4 answer : b"
Answer: b