Cheukting/mathqa huggingface dataset:
Question (general): real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 30 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 12 / 13 , b ) 11 / 15 , c ) 11 / 17 , d ) 11 / 14 , e ) 11 / 7
Rationale: "let the retail price be = x selling price of z = 0.70 x selling price of x = 0.70 * 0.80 x = 0.56 x selling price of y = ( ( 0.70 x + 0.56 x ) / 2 ) * 0.70 = 0.63 x * 0.70 = 0.44 x 0.44 x = k * 0.56 x k = 0.44 / 0.56 = 44 / 56 = 11 / 14 answer : d"
Answer: d
Question (general): a student has to obtain 33 % of the total marks to pass . he got 92 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 400 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 92 + 40 33 x / 100 = 132 x = 400 answer is a"
Answer: a
Question (physics): p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 150 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 75 days , c ) 120 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 400 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 150 days - - > 150 / 250 work done = > 60 % 30 % work left . . . r alone will take 30 % * 400 = 120 days answer is ( c )"
Answer: c
Question (general): what is the sum of the multiples of 6 from 48 to 72 , inclusive ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 300 , e ) 400
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 72 / 6 ) - ( 48 / 6 ) + 1 multiply these together so what we show average * total numbers = sum ( 48 + 72 ) / 2 * ( 72 / 6 ) - ( 48 / 6 ) + 1 = sum 60 * 5 = 300 d"
Answer: d
Question (general): if d = 1 / ( 2 ^ 3 * 5 ^ 10 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 10 ) = multiply and divide by 2 ^ 7 = 2 ^ 7 / ( 2 ^ 3 * 2 ^ 7 * 5 ^ 10 ) = 2 ^ 7 / 10 ^ 10 = > non zero digits are 128 = > ans c
Answer: c
Question (gain): a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 3300 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 600 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 3300 x ( 2 / 11 ) ) = rs . 600 answer is d ."
Answer: d
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 10 meters and a circumference of 11 meters , and the interior of tank b has a height of 11 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 110 % , e ) 125 %
Rationale: "the radius of tank a is 11 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 121 / ( 4 * pi ^ 2 ) = 605 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 11 * pi * 100 / ( 4 * pi ^ 2 ) = 550 / ( 2 * pi ) tank a / tank b = 605 / 550 = 11 / 10 = 110 % the answer is d ."
Answer: d
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1335 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: "explanation : 1500 - - - - 165 100 - - - - ? = > 11 % answer : e"
Answer: e
Question (general): each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.6 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: "x : 0.5 % is 0.1 % - points from 0.6 % . y : 0.8 % is 0.2 % - points from 0.6 % . therefore the ratio of products checked by y : x is 1 : 2 . thus , worker y checked 1 / 3 of the products . the answer is c ."
Answer: c
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 15 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,105 r = x / 100 * 0.1 r answer b"
Answer: b
Question (gain): a shopkeeper sells 300 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 50 , e ) 65
Rationale: sp per metre = 18000 / 300 = rs . 60 loss per metre = rs . 5 cp per metre = 60 + 5 = rs . 65 . answer : e
Answer: e
Question (gain): ? % of 360 = 144
Options: a ) 277 , b ) 36 , c ) 64 , d ) 40 , e ) none of these
Rationale: "? % of 360 = 144 or , ? = 144 × 100 / 360 = 40 answer d"
Answer: d
Question (general): linda spent 5 / 6 of her savings on furniture and the rest on a tv . if the tv cost her $ 500 , what were her original savings ?
Options: a ) $ 9000 , b ) $ 3000 , c ) $ 6000 , d ) $ 7000 , e ) $ 8000
Rationale: "if linda spent 5 / 6 of her savings on furniture , the rest 6 / 6 - 5 / 6 = 1 / 6 on a tv but the tv cost her $ 500 . so 1 / 6 of her savings is $ 500 . so her original savings are 6 times $ 500 = $ 3000 correct answer b"
Answer: b
Question (physics): how many bricks , each measuring 40 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 1400 , b ) 2400 , c ) 4000 , d ) 7000 , e ) 3400
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 40 x 11.25 x 6 ) = 4000 answer : c"
Answer: c
Question (gain): find the simple interest on rs . 64,000 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 64000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 64,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8000 answer is b ."
Answer: b
Question (probability): three unbiased coins are tossed . what is the probability of getting at most 2 heads ?
Options: a ) 7 / 8 , b ) 5 / 8 , c ) 3 / 8 , d ) 7 / 5 , e ) 3 / 5
Rationale: "here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting at least two heads = { ttt , tth , tht , htt , thh , hth , hht } p ( e ) = n ( e ) / n ( s ) = 7 / 8 . answer a ."
Answer: a
Question (general): the average height of 15 girls out of a class of 60 is 138 cm . and that of the remaining girls is 142 cm . the average height of the whole class is :
Options: a ) 132 cms , b ) 141 cms , c ) 142 cms , d ) 152 cms , e ) 161 cms
Rationale: "explanation : average height of the whole class = ( 15 × 138 + 45 × 142 / 60 ) = 141 cms answer b"
Answer: b
Question (physics): a cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.57 hrs , b ) 5 hrs , c ) 6.57 hrs , d ) 7.2 hrs , e ) 9.27 hrs
Rationale: "net part filled in 1 hour = 1 / 2 - 1 / 9 = 7 / 18 therefore the cistern will be filled in 18 / 7 hours or 2.57 hours . answer : a"
Answer: a
Question (physics): the edges of a cuboid are 6 cm , 5 cm and 6 cm . find the volume of the cuboid ?
Options: a ) 120 , b ) 160 , c ) 210 , d ) 368 , e ) 180
Rationale: "6 * 5 * 6 = 180 answer : e"
Answer: e
Question (other): a began business with rs . 45000 and was joined afterwards by b with rs . 27000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2
Rationale: "45 * 12 : 27 * x = 2 : 1 x = 10 12 - 10 = 2 answer : e"
Answer: e
Question (general): 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 9 / 20 =
Options: a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6
Rationale: "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 9 / 20 . answer : d"
Answer: d
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 4 : 3 . the ratio of economy cars to sport utility vehicles is 6 : 5 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 10 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 4 : 3 - - > e : l = 4 : 3 = 24 : 18 . the ratio of economy cars to sport utility vehicles is 6 : 5 - - > e : s = 6 : 5 = 24 : 20 . thus , l : s = 18 : 20 = 9 : 10 . answer : a ."
Answer: a
Question (other): which digits should come in place of @ and # if the number 62684 @ # is divisible by both 8 and 5 ?
Options: a ) 4,0 , b ) 0,4 , c ) 4,4 , d ) 0,0 , e ) none
Rationale: explanation : since the given number is divisible by 5 , so 0 or 5 must come in place of # . but , a number ending with 5 is never divisible by 8 . so , 0 will replace # . now , the number formed by the last three digits is 4 @ 0 , which becomes divisible by 8 , if @ is replaced by 4 . hence , digits in place of @ and # are 4 and 0 respectively . answer : a
Answer: a
Question (gain): a invested $ 300 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find b ' s shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 25 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 300 * 12 : 200 * 6 a : b = 1 : 1 b ' s share = 100 * 1 / 4 = $ 25 answer is c"
Answer: c
Question (general): ashok secured average of 76 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 86
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 76 therefore total marks in 6 subjects = 76 * 6 = 456 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 456 – 370 = 86 answer : e"
Answer: e
Question (general): a man has a certain number of small boxes to pack into parcles . if he packs 3 , 4 , 5 or 6 in a parcel , he is left with one over ; if he packs 7 in a parcle , none is left over . what is the number of boxes , he may have to pack ?
Options: a ) 106 , b ) 301 , c ) 309 , d ) 400 , e ) 450
Rationale: explanation : clearly , the required number would be such that it leaves a remainder of 1 when divided by 3 , 4 , 5 , or 6 and no remainder when divided by 7 . thus , the number must be of the form ( l . c . m of 3 , 4 , 5 , 6 ) x + 1 i . e . , ( 60 x + 1 ) and a multiple of 7 . clearly , for x = 5 , the number is a multiple of 7 . so the number is 301 . answer : b ) 301
Answer: b
Question (general): find b and c so that the parabola with equation y = 4 x 2 - bx - c has a vertex at ( 2 , 4 ) ?
Options: a ) - 10 , b ) - 20 , c ) - 30 , d ) - 40 , e ) - 50
Rationale: h = b / 8 = 2 : formula for x coordinate of vertex b = 16 : solve for b y = 4 for x = 2 : the vertex point is a solution to the equation of the parabola 4 ( 2 ) 2 - 16 ( 2 ) - c = 4 c = - 20 : solve for c correct answer b
Answer: b
Question (physics): pipe a can fill a tank in 8 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 66
Rationale: let the pipe b be closed after x minutes . 30 / 8 - x / 24 = 1 = > x / 24 = 30 / 8 - 1 = 11 / 4 = > x = 11 / 4 * 24 = 66 . answer : e
Answer: e
Question (general): a call center has two teams . each member of team a was able to process 2 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 5 , d ) 1 / 2 , e ) 1 / 5
Rationale: let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 2 calls , so total calls for team a = 10 fraction for team b = 40 / ( 40 + 10 ) = 4 / 5 = answer = c
Answer: c
Question (physics): if the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 11.2 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 15 * x = 1056 = > x = 11.2 answer : b"
Answer: b
Question (general): a sum of rs . 1190 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 210 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1190 = > 17 x / 12 = 1190 = > 1190 x 12 / 17 = rs . 840 hence , b ’ s share = rs . ( 840 / 4 ) = rs . 210 . answer b
Answer: b
Question (gain): a number increased by 40 % gives 1680 . the number is ?
Options: a ) 1680 , b ) 1600 , c ) 1200 , d ) 1500 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 40 % = 140 % 140 % - - - - - - - > 1680 ( 140 ã — 12 = 1680 ) 100 % - - - - - - - > 1200 ( 100 ã — 12 = 1200 ) option ' c '"
Answer: c
Question (general): if each digit in the set a = { 1 , 2 , 3 , 4 , 5 } is used exactly once , in how many ways can the 5 digits be arranged ?
Options: a ) 6 , b ) 24 , c ) 72 , d ) 96 , e ) 120
Rationale: "use the slot method for all the possible arrangements : we have 5 options for the 1 st slot , 4 for the 2 nd , 3 for 3 rd , 2 for 4 th and 1 for the 5 th , giving the total number of arrangements = 5 * 4 * 3 * 2 * 1 = 120 , e is the correct answer ."
Answer: e
Question (physics): two pipes a and b can fill a tank in 12 hours and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 10 hours , d ) 12 hours , e ) 7 4 / 9 hours
Rationale: "part filled by a in 1 hour = 1 / 12 part filled by b in 1 hour = 1 / 15 part filled by ( a + b ) in 1 hour = 1 / 12 + 1 / 15 = 9 / 60 both the pipes together fill the tank in 60 / 9 = 7 4 / 9 hours answer is e"
Answer: e
Question (geometry): the sides of the triangle are in the ratio 5 : 6 : 7 and its perimeter is 720 cm . the length of the longest side is ?
Options: a ) 150 cm
b ) 200 cm
c ) 162 cm
d ) 220 cm
e ) 280 cm
Rationale: ratio of sides = 5 : 6 : 7 largest side = 720 * 7 / 18 = 280 cm answer is e
Answer: e
Question (gain): jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid , approximately how many liters of the 2 percent solution will be required ?
Options: a ) 18 , b ) 12 , c ) 24 , d ) 36 , e ) 42
Rationale: "let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 1 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 1 ( 60 ) = > 2 a + 12 b = 600 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 600 = > 10 a = 120 hence a = 12 . answer : b"
Answer: b
Question (general): a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 220 per month . what is his monthly salary ?
Options: a ) 5500 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 220 = > 5500 answer : a"
Answer: a
Question (geometry): triangle atriangle b are similar triangles with areas 1536 units square and 2166 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10
b ) 17 : 19
c ) 23 : 27
d ) 13 : 17
e ) 16 : 19
Rationale: let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 2166 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 19 * 19 * 6 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 19 ^ 2 x / y = 16 / 19 ans = e
Answer: e
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 108 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: "answer : c 108 ° divided by 360 ° equals 0.3 , therefore the sector is equal to 30 % of the total"
Answer: c
Question (general): the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 2.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 2.50 + 0.50 ( x − 2 ) = 2.50 + . 5 * 3 = 2.5 + 1.5 = 4 $ answer d"
Answer: d
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 20 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 160 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,2 = 15 / 100 x = 80 * 20 / 100 x = 16 16 / 10 = 1,6 = 160 % , answer e"
Answer: e
Question (physics): a man walking at a constant rate of 6 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 12 miles per hour . the woman stops to wait for the man 10 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 5 , b ) 15 , c ) 10 , d ) 20 , e ) 25
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 10 * 12 / 60 = 2 miles and the man walks the distance mm , which is 10 * 6 / 60 = 1 mile . the difference of 2 - 1 = 1 miles ( mw ) will be covered by the man in ( 1 ) / 6 = 1 / 6 of an hour , which is 10 minutes . answer c ."
Answer: c
Question (general): a number when divided by 219 gives a remainder 32 , what remainder will be obtained by dividing the same number 12 ?
Options: a ) 7 , b ) 11 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 219 + 32 = 251 / 12 = 9 ( remainder ) answer : b"
Answer: b
Question (general): what is the difference between the c . i . on rs . 7000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.86 , e ) s . 2.42
Rationale: "c . i . when interest is compounded yearly = [ 7000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 7000 * 26 / 25 * 51 / 50 = rs . 7425.6 c . i . when interest is compounded half - yearly = [ 7000 * ( 1 + 2 / 100 ) 2 ] = ( 7000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 7428.46 difference = ( 7428.46 - 7425.6 ) = rs . 2.86 . answer : d"
Answer: d
Question (general): mary ' s income is 70 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 102 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 102 ( 70 percent more than tim ' s income ) . thus , mary ' s income ( 102 ) is 102 % of juan ' s income ( 100 ) . answer : b .
Answer: b
Question (general): a sum of money lent out at s . i . amounts to a total of $ 480 after 2 years and to $ 680 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 360 , b ) $ 380 , c ) $ 400 , d ) $ 420 , e ) $ 440
Rationale: "s . i for 5 years = $ 680 - $ 480 = $ 200 the s . i . is $ 40 / year s . i . for 2 years = $ 80 principal = $ 480 - $ 80 = $ 400 the answer is c ."
Answer: c
Question (general): 5.005 / 2.002 =
Options: a ) 2.05 , b ) 2.50025 , c ) 2.501 , d ) 2.5025 , e ) 2.5
Rationale: "5.005 / 2.002 = 5005 / 2002 = 5 ( 1001 ) / 2 ( 1001 ) = 5 / 2 = 2.5 the answer is e ."
Answer: e
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 148 cookies , what percent of the cookies did irin bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 56 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 150 cookies x = 150 / 16.4 = 9.14 ( approx ) so , irin baked 9.14 * 9.18 cookies or 84 cookies ( approx ) % share = 84 / 150 = 56 approx hence , answer is c ."
Answer: c
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer : d"
Answer: d
Question (gain): a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 55 % . staff are allowed a further 50 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.275 d , b ) 0.225 d , c ) 0.265 d , d ) 0.245 d , e ) 0.205 d
Rationale: "effective discount = a + b + ab / 100 = - 55 - 50 + ( - 55 ) ( - 50 ) / 100 = 77.5 sale price = d * ( 1 - 77.5 / 100 ) sale price = . 225 * d answer ( b )"
Answer: b