Cheukting/mathqa huggingface dataset:
Question (geometry): find the area of the quadrilateral of one of its diagonals is 26 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 195 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 26 ( 9 + 6 ) = 195 cm 2 answer : d"
Answer: d
Question (other): irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did nell bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 11.7 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , nell baked 10 * 2.05 cookies or 20 cookies ( approx ) % share = 20 / 170 = 11.7 approx hence , answer is c ."
Answer: c
Question (physics): a train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds . its length is ?
Options: a ) 275 , b ) 287.5 , c ) 288 , d ) 233.5 , e ) 245.6
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 23 = > y = x / 23 x + 125 / 33 = x / 23 x = 287.5 m . answer : b"
Answer: b
Question (gain): a bookseller sells his books at a 25 % markup in price . if he sells a book for $ 12.5 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 11.00 , d ) $ 9.60 , e ) $ 10.00
Rationale: "let the cost price of book = x selling price of book = 12.5 $ markup % = 25 ( 125 / 100 ) x = 12.5 = > x = 10 answer e"
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a . ?
Options: a ) rs . 9000.30 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none of these
Rationale: "explanation : amount = rs . [ 25000 x ( 1 + 12 / 100 ) 3 ] = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 answer is c"
Answer: c
Question (general): a soft drink company had 5000 small and 12000 big bottles in storage . if 15 % of small 18 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 14090 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 16075
Rationale: 5000 + 12000 - ( 0.15 * 5000 + 0.18 * 12000 ) = 14090 . answer : a .
Answer: a
Question (general): 4 - fifths of 3 - eighths of a number is 24 . what is 250 per cent of that number ?
Options: a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) none of these
Rationale: let the number = x . 4 ⁄ 5 × 3 ⁄ 8 x = 24 or x = 24 × 2 × 5 / 3 = 80 ∴ 250 per cent of the number = 250 ⁄ 100 × 80 = 200 answer d
Answer: d
Question (general): rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 6 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 430 , b ) $ 1620 , c ) $ 1650 , d ) $ 1110 , e ) $ 1770
Rationale: "for 100 - 40 - 10 = 50 pages only cost is 10 $ per page for the first time page is typed - 50 * 10 = 500 $ ; for 40 pages the cost is : first time 5 $ + 6 $ of the first revision - 40 * ( 5 + 6 ) = 440 $ ; for 10 pages the cost is : first time 5 $ + 6 $ of the first revision + 6 $ of the second revision - 10 ( 5 + 6 + 6 ) = 170 $ ; total : 500 + 440 + 170 = 1110 $ . answer : d ."
Answer: d
Question (general): find the mean proportional between 7921 & 9409 ?
Options: a ) 8163 , b ) 8633 , c ) 8663 , d ) 8636 , e ) none of these
Rationale: "explanation : formula = √ a × b a = 7921 and b = 9409 √ 7921 × 9409 = 89 × 97 = 8633 answer : option b"
Answer: b
Question (gain): 25 % of 1250
Options: a ) 330 , b ) 315 , c ) 312.5 , d ) 370 , e ) 350
Rationale: 1 % of 1250 is = 12.50 25 % of 1250 is = 12.50 * 25 = 312.5 answer : c
Answer: c
Question (general): there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 7 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of milk and water ?
Options: a ) 59 : 31 , b ) 3 : 2 , c ) 118 : 126 , d ) 193 : 122 , e ) 201 : 132
Rationale: 7 : 3 = > 7 x + 3 x = 10 x 2 : 1 = > 2 y + 1 y = 3 y 3 : 2 = > 3 z + 2 z = 5 z 10 x = 3 y = 5 z take lcm of 10 , 3,5 = 30 or simply ; x = 3 y = 10 z = 6 so , ratio of milk : water = ( 7 x + 2 y + 3 z ) / ( 3 x + y + 2 z ) = 59 / 31 ans : a
Answer: a
Question (general): from a total of 5 boys and 5 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 60 , d ) 100 , e ) 240
Rationale: "answer = d = 100 no of 4 person committees that can be formed = 5 c 2 * 5 c 2 = 100 answer d"
Answer: d
Question (physics): a train moves with a speed of 108 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 25 , d ) 30 , e ) none
Rationale: "sol . 108 kmph = [ 108 x 5 / 18 ] m / sec = 30 m / sec . answer d"
Answer: d
Question (general): ( 132 ) ^ 7 × ( 132 ) ^ ? = ( 132 ) ^ 11.5 .
Options: a ) 4.5 , b ) 3 , c ) 4 , d ) 3.5 , e ) 8.5
Rationale: "( 132 ) ^ 7 × ( 132 ) ^ x = ( 132 ) ^ 11.5 = > 7 + x = 11.5 = > x = 11.5 - 7 = 4.5 answer is a"
Answer: a
Question (general): a batsman in his 10 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 53 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 10 th innings = 85 - 3 × 10 = 50 average score after 10 th innings = > 50 + 3 = 53 answer : b"
Answer: b
Question (general): a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 2 / 3 = 4 were right - handed and 2 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 2 = 7 . the ratio = 5 / 7 . answer : c"
Answer: c
Question (general): martin bought 5 packet milk at an average price ( arithmetic mean ) of 20 ¢ . if martin returned two packet to the retailer , and the average price of the remaining millk packet was 12 ¢ , then what is the average price , in cents , of the two returned milk packets ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: total price of 5 packet milk = 5 * 20 = 100 total price of 3 packet milk = 3 * 12 = 36 total price of 2 packet returned milk = 100 - 36 = 64 average price of 2 packet milk = 64 / 2 = 32 correct option answer : c
Answer: c
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 18 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 22 . , b ) 24 . , c ) 30 . , d ) 36 , e ) 38 .
Rationale: total work = 20 * 18 = 360 beaver hours 12 beaver * x = 360 beaver hours x = 360 / 12 = 30 answer : c
Answer: c
Question (physics): a , b , c , d and e are ve consecutive odd numbers the sum of a and c is 146 . what is the value of e ?
Options: a ) 75 , b ) 81 , c ) 71 , d ) 79 , e ) none of these
Rationale: a + c = 146 ⇒ a + a + 4 = 146 ⇒ a = 146 - 4 / 2 = 71 ∴ e = a + 8 = 71 + 8 = 79 answer d
Answer: d
Question (general): in the coordinate plane , points ( x , 5 ) and ( 9 , y ) are on line k . if line k passes through the origin and has slope 5 / 9 , then x - y =
Options: a ) 4 , b ) 6 , c ) 5 , d ) 8 , e ) 7
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 5 / 9 * x . thus : ( x , 5 ) = ( 9 , 5 ) and ( 9 , y ) = ( 9,5 ) - - > x - y = 9 - 5 = 4 . answer : a"
Answer: a
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 520 sq cm
b ) 840 sq cm
c ) 440 sq cm
d ) 120 sq cm
e ) 5 sq cm
Rationale: explanation : r = 7 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 10 ) = 440 sq cm answer : c
Answer: c
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3
Options: a ) 26 , b ) 22 , c ) 25 , d ) 30 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 3 = 2 ^ 22 x 7 ^ 5 x 11 ^ 3 total number of prime factors = ( 22 + 5 + 3 ) = 30 . answer is d ."
Answer: d
Question (other): a jar contains 20 red , 20 blue , 6 yellow and 4 pink balls . if two balls are to be selected at random and without replacement , approximately what is the probability both of them to be the same colour ?
Options: a ) 1 / 25 , b ) 1 / 15 , c ) 1 / 3 , d ) 1 / 2 , e ) 1
Rationale: ok so jar contains 20 red 20 blue 6 yellow and 4 pink . . adding the number of balls we get 50 total . . now its a counting + probability exercise . . 2 stages exist : pick first ball then second ball . . denominator for first ball = 50 since there are 50 balls denominator for second ball = 49 since only 49 would remain for each type ball i constructed probability of getting 2 of same . . i used a counting method . . first ball 20 chances blue and 2 nd ball 19 chances blue and so on and so forth blue = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 red = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 yellow = ( 6 * 5 ) / ( 50 * 49 ) rounded to 30 / 2500 pink = ( 4 * 3 ) / ( 49 * 50 ) rounded to 12 / 2500 then i summed these individual probabilities to get 842 / 2500 this is ~ 1 / 3 as 800 * 3 = 2400 ans : c
Answer: c
Question (general): diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 8 gallon of paint . how many statues can she paint ?
Options: a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 7 / 8 ÷ 1 / 8 = 7 / 8 * 8 / 1 = 7 / 1 = 7 answer is a ."
Answer: a
Question (physics): jonathan can type a 10 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 10 / 40 + 10 / 30 + 10 / 24 = 10 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Question (physics): a train 220 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 12 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 220 * 3 / 55 = 12 sec . answer : option a"
Answer: a
Question (general): in the hillside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 20 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 35 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to or 20 % . . if we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it . now boys are 80 % and girls are 20 % . ( out of 100 students = 80 boys + 20 girls ) . imo option a is correct ."
Answer: a
Question (general): a cyclist rides a bicycle 8 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
Options: a ) 8.58 , b ) 8.76 , c ) 9.04 , d ) 9.12 , e ) 9.25
Rationale: "distance = 19 km time = 8 / 11 + 11 / 8 = ( 64 + 121 ) / 88 = 185 / 88 hours average speed = ( 19 * 88 ) / 185 = 9.04 km / h the answer is c ."
Answer: c
Question (gain): the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 20 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 10.4 % , d ) 16.66 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 20 % , the selling price must be 92 + ( 20 / 100 ) * 92 = $ 110.4 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 110.4 , the mark up is simply 10.4 % . ans : c"
Answer: c
Question (general): how many numbers from 13 to 76 are exactly divisible by 10 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' b ' 13 / 10 = 1 and 76 / 10 = 7 = = > 7 - 1 = 6 numbers"
Answer: b
Question (general): among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 60 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 42 , c ) 56 , d ) 70 , e ) 58
Rationale: i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 60 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 60 = 140 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 30 = 70 . thus d is the correct answer choice
Answer: d
Question (general): 90 % of the population of a village is 8100 . the total population of the village is ?
Options: a ) 9000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 90 / 100 ) = 8100 x = 90 * 100 x = 9000 answer : a"
Answer: a
Question (physics): a tank is filled by 3 pipes a , b , c in 4 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 28 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 4 7 / x = 1 / 4 x = 28 hours answer is e"
Answer: e
Question (geometry): a rectangular garden is to be twice as long as it is wide . if 240 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 240 so , 2 ( l + b ) = 240 or , l + b = 120 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 80 l = 80 ; b = 40 l + b = 120 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( d )"
Answer: d
Question (gain): at what rate percent on simple interest will rs . 415 amount to rs . 514 in 4 years ?
Options: a ) 4.58 % , b ) 5.96 % , c ) 6.52 % , d ) 4.98 % , e ) none of these
Rationale: "explanation : difference in amount = 514 - 415 = 99 99 = ( 415 x 4 x r ) / 100 r = 5.96 % answer is b"
Answer: b
Question (geometry): the number 90 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 5 ^ 2 + 4 ^ 2 = 49 + 25 + 16 = 90 7 + 5 + 4 = 16 hence answer is b"
Answer: b
Question (geometry): the diagonals of a rhombus are 14 cm and 18 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 150 , d ) 126 , e ) 292
Rationale: "1 / 2 * 14 * 18 = 126 answer : d"
Answer: d
Question (gain): 75 is what percent of 125 ?
Options: a ) 60 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 75 / 125 × 100 = 50 % answer : a
Answer: a
Question (gain): how much more would rs . 50000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 1205 , c ) 992 , d ) 837 , e ) 923
Rationale: "50000 ( 11 / 10 ) 4 - 50000 ( 6 / 5 ) 2 = 1205 answer : b"
Answer: b
Question (general): a certain psychologist charges $ 40 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 375 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 174 , e ) $ 192
Rationale: let the charge for first hour = x + 40 then charge for each additional hour = x x + 40 + 4 x = 375 = > 5 x = 335 = > x = 67 total charge for patient for 3 hours of therapy = x + 40 + x = 2 x + 40 = 174 $ answer d
Answer: d
Question (general): if the product 4864 * 9 p 2 is divisible by 12 , the value of p ?
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: explanation : clearly 4864 is divisible by 4 so 9 p 2 must be divisible by 3 . so ( 9 + p + 2 ) must be divisible by 3 . so p = 1 . answer : a ) 1
Answer: a
Question (general): the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked the second cow in the second year ?
Options: a ) 4730 lt , b ) 4356 lt , c ) 7665 lt , d ) 2314 lt , e ) 6545 lt
Rationale: "let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % or 10 % so 8100 + 15 / 100 ⋅ x + 10 / 100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . correct answer a"
Answer: a
Question (general): how many multiples of 4 are there between 20 and 112 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 5 up to 4 * 28 . 28 - 5 + 1 = 24 . the answer is d ."
Answer: d
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 90 % of the total ?
Options: a ) 515 . , b ) 572 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is b : 572 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 90 % of total is 515 , so 100 % is approx . 572 ."
Answer: b
Question (gain): a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 750 less than the sum lent . what was the sum lent ?
Options: a ) 1000 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 1110
Rationale: p - 750 = ( p * 5 * 5 ) / 100 p = 1000 answer : a
Answer: a
Question (general): the product x of two prime numbers is between 15 and 90 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 85
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 85 = 5 * 17 > > answer answer = e"
Answer: e
Question (physics): if an object travels at ten feet per second , how many feet does it travel in one hour ?
Options: a ) 34880 , b ) 37780 , c ) 36000 , d ) 18000 , e ) 28810
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 36000 answer : c ) 36000"
Answer: c
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.32 – 6.32 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 0.32 , d ) 0.25 , e ) 6.32
Rationale: since z * is defined as the greatest positive even integer less than or equal to z , then 6.32 * = 6 ( the greatest positive even integer less than or equal to 6.32 is 6 ) . hence , 6.32 – 6.32 * = 6.32 - 6 = 0.32 answer : c .
Answer: c
Question (geometry): the area of a triangle will be when a = 2 m , b = 4 m , c = 6 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 6 , e ) 4
Rationale: "s = ( 2 + 4 + 6 ) / 2 = 6 answer : d"
Answer: d
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 20 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: let the total solution is 150 l with 80 l water 70 l syrup . to make 20 % syrup solution , the result solution must have 120 l syrup and 30 l syrup . therefore we are taking 40 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 40 l syrup in 85.7 l solution we started by multiplying 10 now to get to the result we need to divide by 40 = > amount of solution to be replaced with water = ( 85.7 / 40 ) = 2.14 . correct option : c
Answer: c
Question (general): the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 27 , c ) 21 , d ) 18 , e ) 11
Rationale: ( a + b ) - ( b + c ) = 18 a - c = 18 . c is younger than a by 18 years . answer : d
Answer: d
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 4 of the mice are white . if there are 16 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 36 , c ) 34 , d ) 39 , e ) 42
Rationale: "let total number of mice = m number of white mice = 2 / 4 m number of brown mice = 2 / 4 m = 16 = > m = 32 answer a"
Answer: a
Question (general): if x is divided by 7 , the remainder is 5 . what is the remainder if 4 x is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: x = 7 q + 5 4 x = 7 * 4 q + 20 4 x = 7 * 4 q + 7 * 2 + 6 4 x = 7 ( 4 q + 2 ) + 6 4 x = 7 k + 6 ( k = 4 q + 2 ) answer d
Answer: d