Cheukting/mathqa huggingface dataset:
Question (probability): find the probability that a year chosen at random has 53 mondays .
Options: a ) 5 / 28 , b ) 3 / 28 , c ) 1 / 28 , d ) 3 / 28 , e ) 3 / 27
Rationale: "explanation : there are 2 kinds of year leap year - probability = 1 / 4 ( out of 4 years one is a leap year ) non leap year - probability = 3 / 4 so it ' s either this or that now in non leap year , there are 365 days meaning 52 weeks with one day extra that one day can be monday out of 7 possible days . hence the probability = 1 / 7 similarly in leap year , there are 366 days and so 366 / 7 = 52 weeks with 2 days extra now probability of occurrence of monday out of possible 7 days = 2 / 7 so what we essentially want is ( a non leap year and monday ) or ( a leap year and monday ) so it ' ll be [ 3 / 4 * 1 / 7 ] + [ 1 / 4 * 2 / 7 ] = 5 / 28 answer : a"
Answer: a
Question (gain): a pair of articles was bought for $ 360 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 360 / 2 = $ 180 let m . p = $ x 90 % of x = 360 x = 180 * 100 / 90 = $ 200 answer is a"
Answer: a
Question (gain): the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned
Options: a ) 19828.88 , b ) 19828.8 , c ) 19828.87 , d ) 19828.81 , e ) 19828.82
Rationale: "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : b"
Answer: b
Question (general): if x ^ 2 + y ^ 2 = 18 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 11 , c ) 14 , d ) 12 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 18 - 2 * 3 = 12 . . answer d"
Answer: d
Question (general): the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use π = 22 ⁄ 7 )
Options: a ) 40 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 × 2 π rh = 5 × 2 × 22 ⁄ 7 × 0.7 × 2 = 44 m 2 answer b"
Answer: b
Question (general): what is the dividend . divisor 16 , the quotient is 8 and the remainder is 4
Options: a ) 127 , b ) 128 , c ) 130 , d ) 131 , e ) 132
Rationale: "e = d * q + r e = 16 * 8 + 4 e = 128 + 4 e = 132"
Answer: e
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 / 4 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 ) 4 / 5 , e ) 5 / 12
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 / 4 m = 15 books total = 25 books m ' = 25 = 5 / 12 * 60 ratio : 5 / 12 ans : e"
Answer: e
Question (physics): if a , b and c together can finish a piece of work in 4 days . a alone in 36 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "c = 1 / 4 - 1 / 36 – 1 / 18 = 1 / 6 = > 6 days ' answer : e"
Answer: e
Question (general): in a coconut grove , ( x + 1 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 1 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above
Rationale: "( x + 1 ) × 60 + x × 120 + ( x − 1 ) × 180 / ( x + 1 ) + x + ( x − 1 ) = 100 ⇒ 360 x − 120 / 3 x = 100 ⇒ 60 x = 120 ⇒ x = 2 answer a"
Answer: a
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 2400 x = 40 the numbers are 3 * 40 , 4 * 40 , 5 * 40 hence required h . c . f . = 40 answer is c"
Answer: c
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 per metre approximately
Options: a ) 4457
b ) 4567
c ) 4235
d ) 4547
e ) 4675
Rationale: explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . answer : option a
Answer: a
Question (general): a certain no . whendivided by 35 leaves a remainder 25 , what is the remainder if the same no . be dividedby 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b
Answer: b
Question (general): . on dividing a number by 357 , we get 36 as remainder . on dividing the same number 17 , what will be the remainder ?
Options: a ) 0 , b ) 3 , c ) 5 , d ) 8 , e ) 2
Rationale: let x be the number and y be the quotient . then , x = 357 x y + 36 = ( 17 x 21 x y ) + ( 17 x 2 ) + 2 = 17 x ( 21 y + 2 ) + 2 ) required remainder = 2 . answer : option e
Answer: e
Question (physics): there is a point p on the circle . a and b started running in two constant different speeds . a in clockwise and b in anti - clockwise . first time 500 m in clockwise from p then 400 anti - clockwise . if b is yet to complete one round , what is the circumference of the circle ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: let the speeds of a & b be u and v resp . and let circumference be c . let their first meeting be after time t then ut + vt = c and ut = 500 ∴ vt = c − 500 and u / v = 500 / ( c − 500 ) for their second meeting after time t , ut + vt = 2 c and vt = 400 ∴ ut = 2 c − 400 and u / v = ( 2 c − 400 ) / 400 hence 500 / ( c − 500 ) = ( 2 c − 400 ) / 400 simplifying , 100000 = ( c − 200 ) ( c − 500 ) = c ² − 700 c + 100000 → c = 700 answer : a
Answer: a
Question (general): carina has 55 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 55 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 55 - > y = 45 / 15 . = 3 e
Answer: e
Question (general): how many two - digit numbers yield a remainder of 2 when divided by both 5 and 16 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 16 p + 2 - - - > 18,34 , 50,66 , 82,96 . out of these , there is only one number ( 82 ) is also of the form 5 q + 2 . thus 1 is the answer . b is the correct answer ."
Answer: b
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 50 per component . shipping costs for delivering the components are $ 8 per unit . further , the manufacturer has costs of $ 16,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 200 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 135 , b ) 129 , c ) 131 , d ) 138 , e ) 141
Rationale: "$ 16000 is a fixed cost each component is $ 58 ( $ 50 to produce , $ 8 to ship ) manufacturer will be producing and selling 200 components so therefore the equation to find price would be 200 * p = 16000 + ( 200 * 50 ) + ( 200 * 8 ) p = ( 16000 + 10000 + 1600 ) / 200 p = 138 answer : d"
Answer: d
Question (geometry): the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ?
Options: a ) 22 , b ) 32 , c ) 44 , d ) 55 , e ) 56
Rationale: "we can divide the trapezoid into two triangles and a rectangle sides of triangle , t 1 - - > h 1 = 5 , b 1 = 3 , s 1 = root ( 25 - 9 ) = 4 = s 2 of triangle t 2 area of triangle = ( 1 / 2 ) * 4 * 3 = 6 side of the rectangle = 8 * 4 = 32 total area of the trapezoid = 32 + 6 + 6 = 44 answer : c"
Answer: c
Question (general): a rope of which a calf is tied is increased from 15 m to 18 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 1212 , c ) 1210 , d ) 3 . 11.14 , e ) 291.1
Rationale: "π ( 182 – 152 ) = 311.14 answer : d"
Answer: d
Question (geometry): the radius of a circle is increased by 1 % . find how much % does its area increases ?
Options: a ) 2.21 %
b ) 2.07 %
c ) 2.08 %
d ) 2.01 %
e ) 2.11 %
Rationale: r = 100 r = 101 r 2 = 10000 r 2 = 10201 10000 - - - - 201 100 - - - - ? = > 2.01 % answer : d
Answer: d
Question (other): in gabriel ' s sheep herd , every sheep has either fleas or lice or both . half of the sheep have lice , and 84 sheep have both pests . if 94 sheep have lice , how many sheep have only fleas ?
Options: a ) 10 , b ) 20 , c ) 84 , d ) 94 , e ) 178
Rationale: n ( lice ) = n ( only lice ) + n ( both lice and fleas ) n ( both lice and fleas ) = 84 n ( lice ) = 94 n ( only lice ) = 94 - 84 = 10 since , it is also said that exactly half the sheep have lice , it can be inferred that half the number of sheep is 94 . therefore , the total number of sheep having only fleas is 10 ans : ( option a )
Answer: a
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 7 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 56 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 7 = 112 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 112 pi / 200 pi = 0.56 a"
Answer: a
Question (physics): the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds ?
Options: a ) 4 , b ) 9 , c ) 15 , d ) 48 , e ) 33
Rationale: given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 6 ) = 6 ^ 2 + 2 * 6 = 48 therefore z ( 7 ) - z ( 3 ) = 48 - 15 = 33 km / hr option e
Answer: e
Question (general): notebooks are sold in packages of 4 or 7 only . if wilson bought 69 notebooks exactly , what could be the number of large packs wilson bought ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: let number of packs of four = f let number of packs of seven = s 4 f + 7 s = 69 now , we need to test for values of s . since sum 69 is odd and 4 f will always be even , e ca n ' t be even . now , we can test for values e = 3 , 7 and 9 4 * 5 + 7 * 7 = 20 + 49 = 69 answer c
Answer: c
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 340 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 340 = ( p * 4 * 8 ) / 100 p = 500 answer : d"
Answer: d
Question (general): a total of 40 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 15 / 40 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 40 . female = 60 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 20 = 4 geese ( males ) and now we know out of the total 20 geese , 4 are male , then 16 have to be female . now the ratio part , male geese ratios = 4 / 40 = 1 / 10 . - a female geese ratios = 16 / 60 = 4 / 15 - b cross multiply equations a and b and you get = 15 / 40 . ans a"
Answer: a
Question (physics): a contractor isengaged for 30 days on the condition that he receives rs . 25 for eachday he works & fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 21
Rationale: 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = b
Answer: b
Question (physics): a garrison of 2000 men has provisions for 54 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 30 days more . what is the reinforcement ?
Options: a ) 1800 men , b ) 3900 men , c ) 600 men , d ) 3800 men , e ) 900 men
Rationale: "2000 - - - - 54 2000 - - - - 39 x - - - - - 20 x * 30 = 2000 * 39 x = 2600 2000 - - - - - - - 600 answer : c"
Answer: c
Question (general): the ages of two person differ by 20 years . if 4 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 4 ) = ( x + 20 - 4 ) = > 4 x = 36 = > x = 9 their present ages are 29 years and 9 year . answer : c"
Answer: c
Question (physics): 28 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 28 * 10 / 40 = 7 answer is d"
Answer: d
Question (gain): sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1400 , what is the gain percent ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "selling price / total cost = 1400 / 1000 = 1.4 the gain percent is 40 % . the answer is c ."
Answer: c
Question (physics): a jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 18 seconds , b ) 26 seconds , c ) 36 seconds , d ) 16 seconds , e ) 46 seconds
Rationale: total distance ( d ) = 240 + 120 = 360 meter relative speed ( s ) = 45 - 9 = 36 kmph = 36 * 5 / 18 = 10 mps d = s * t 360 = 10 * t t = 36 seconds answer : c
Answer: c
Question (physics): a woman complete a journey in 15 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 336 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 544 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 15 - - > x / 21 + x / 24 = 30 - - > x = 336 km . a"
Answer: a
Question (general): how many 3 - digit integers exist such that all their digits are odd ?
Options: a ) 80 , b ) 100 , c ) 120 , d ) 125 , e ) 135
Rationale: so last digit can be filled in 5 ways - 1 , 3,5 , 7,9 there are 5 possibilities . the answer is 5 ∗ 5 ∗ 5 = 125 the correct answer is d
Answer: d
Question (general): matt gets a $ 1,300 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1300 new average = ( xy + 1300 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1300 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1300 ) = ( xy + x + 150 y + 150 ) i . e . ( 1150 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 6 new sales = y + 1 = 7 answer : option d"
Answer: d
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds . what is length of the train ?
Options: a ) 140 meter , b ) 145 meter , c ) 150 meter , d ) 155 meter , e ) 160 meter
Rationale: "explanation : let the length of the train is x meter and speed of the train is y meter / second then x / y = 15 [ because distance / speed = time ] = > y = 15 / x x + 100 / 25 = x / 15 x = 150 meters so length of the train is 150 meters answer is c"
Answer: c
Question (gain): 25 % of 30 % of 45 % is equal to ?
Options: a ) 0.03375 , b ) 0.03372 , c ) 0.0337 , d ) 0.03377 , e ) 0.03376
Rationale: "( 25 / 100 ) * ( 30 / 100 ) * ( 45 / 100 ) 1 / 4 * 3 / 10 * 9 / 20 27 / 800 = 0.03375 answer : a"
Answer: a
Question (physics): a student reached his school late by 20 mins by travelling at a speed of 9 kmph . if he had travelled at a speed of 12 kmph , he would have reached his school 20 mins early . what is the distance between house and school ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: distance = distance either student reaches school before time or after time 9 ( t + 20 / 60 ) = 12 ( t - 20 / 60 ) i . e 9 ( t + 1 / 3 ) = 12 ( t - 1 / 3 ) 9 ( 3 t + 1 ) = 12 ( 3 t - 1 ) t = 7 / 3 put t value in any of distance equation put t = 7 / 3 in 9 ( t + 1 / 3 ) we get 24 km answer : a
Answer: a
Question (geometry): the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate w , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e
Answer: e
Question (physics): the sum of four consecutive even numbers is 292 . what would be the smallest number ?
Options: a ) 49 , b ) 68 , c ) 60 , d ) 57 , e ) 70
Rationale: "e 70 let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 292 = > x = 37 smallest number is : 2 ( x - 2 ) = 70 ."
Answer: e
Question (general): a student is ranked 13 th from right and 8 th from left . how many are there ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "13 th from right means = x + 12 8 th from left means = 7 + x total = 12 + 7 + 1 = 20 answer : c"
Answer: c
Question (general): how many 4 - digit odd numbers do not use any digit more than once ?
Options: a ) 1728 , b ) 2160 , c ) 2240 , d ) 2268 , e ) 2520
Rationale: let a 4 - digit number be represented by abcd here a can have any value between 1 to 9 - so total 9 b can have any value between 0 to 9 , but not a - so total 9 c can have any value between 0 to 9 , but not a or b - so total 8 d can have any value between 0 to 9 , but not a , b or c - so total 7 no . of all possible 4 - digit nos ( without repeating any digit ) = 9 * 9 * 8 * 7 = 4536 half of these would be odd . therefor , no . of odd possible 4 - digit nos ( without repeating any digit ) = 4536 / 2 = 2268 answer should be d .
Answer: d
Question (general): revenues were recorded for store a and store b over a period of 3 months . in the first month , store a ' s revenues were $ 12000 higher than store b ' s revenues . in the second month , store a ' s revenues were $ 8000 higher than store b ' s revenues . if store a ' s average ( arithmetic mean ) monthly revenue for the 3 months was $ 2000 greater than store b ' s average monthly revenue , then store b ' s revenue in the third month was how much greater than store a ' s revenue ?
Options: a ) $ 14,000 , b ) $ 15,000 , c ) $ 42,000 , d ) $ 46,000 , e ) $ 50,000
Rationale: answer : cit may be tempting to come up with a lot of variables , one each for each month ' s revenue for each company . however , focus on the differences . in the first month , the difference was + 12 in favor of a . ( note that we can drop the thousands since every number in the question is in terms of thousands . ) in the second , the difference was + 8 in favor of a . the average was + 2 in favor of a . with these numbers , use the average formula to find the third month ( t ) : ( 12 + 8 + t ) / 3 = 2 20 + t = 6 t = - 14 since positive numbers indicate a difference in favor of a , negative numbers are in favor of b . - 14 represents a $ 14,000 advantage in favor of store b . choice ( a ) is correct .
Answer: a
Question (general): a is older than b by 5 years . 7 years hence , thrice a ' s age shall be equal to 4 times that of b . find their present ages .
Options: a ) 14 , 7 , b ) 10 , 5 , c ) 13 , 8 , d ) 12 , 8 , e ) 8 , 12
Rationale: explanation : let the present ages of a and b be ' a ' and ' b ' respectively . 3 ( a + 7 ) = 4 ( ( b + 7 ) - - - ( 1 ) = > 3 a - 4 b = 7 - - - - - - - ( 1 ) a - b = 5 - - - - - - - ( 2 ) solving ( 1 ) and ( 2 ) we get b = 8 substituting b = 8 in second equation , we get a = 13 . answer : c = > 2 a = 32 = > a = 16 . answer : c
Answer: c
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m is 2400 . their h . c . f is ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 44 , e ) 11
Rationale: "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 * 40 ) , ( 4 * 40 ) and ( 5 * 40 ) . hence , required h . c . f = 40 . answer : a"
Answer: a
Question (general): what is x if x + 2 y = 20 and y = 5 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 20 - 2 y x = 20 - 10 . x = 10 answer : a"
Answer: a
Question (general): a certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8
Rationale: one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 34 * 2 = 68 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 68 - 40 = 28 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 28 / 2 = 14 . so the greatest possible value of the # of teachers who had 3 classes is 14 . only answer b has this option .
Answer: b
Question (physics): nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 48 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 24 seconds , d ) 30 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 48 for cristina = c = 5 * t @ t = 24 , n = 120 c = 120 right answer ans : c"
Answer: c