Cheukting/mathqa huggingface dataset:
Question (general): instead of multiplying a number by 3 , the number is divided by 5 . what is the percentage of error obtained ?
Options: a ) 92.33 % , b ) 91.33 % , c ) 95.33 % , d ) 93.33 % , e ) 94.33 %
Rationale: "let the number be x the right number is 3 x the wrong number is x / 5 error is ( 3 x - x / 5 ) = 14 x / 5 percentage of error is ( ( 14 x / 5 ) / 3 x ) * 100 = 93.33 % answer : d"
Answer: d
Question (gain): a man sold 18 toys for rs . 23100 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1100
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 23100 . gain = sp â € “ cp 3 x = 23100 â € “ 18 x 21 x = 23100 x = rs . 1100 . answer : option e"
Answer: e
Question (general): if ( a – b ) is 17 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 7 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 17 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 17 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 17 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 17 = ( c – a ) – 3 = > 2 ( a – c ) = 14 = > ( a – c ) = 7 answer : d"
Answer: d
Question (general): in an objective competitive exam , a correct answer score 4 marks and on a wrong answer 2 marks are negatively added . a student scores 420 marks from 150 question . how many answers were correct ?
Options: a ) 150 , b ) 155 , c ) 140 , d ) 120 , e ) 165
Rationale: let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 . . . . . ( 1 ) = > 4 x - 2 y = 420 . . . . . ( 2 ) by solving ( 1 ) & ( 2 ) , we get = > 6 x = 720 hence x = 120 therefore , number of correct answers are 120 . answer d
Answer: d
Question (general): in a division , divident is 690 , divisior is 36 and quotient is 19 . find the remainder .
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6
Rationale: "explanation : 690 = 36 x 19 + r 690 = 684 + r r = 690 - 684 = 6 answer : option e"
Answer: e
Question (general): running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 24 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 4 * 6 = 24 days to produce 4 w widgets . answer : d"
Answer: d
Question (physics): a car traveled 75 % of the way from town a to town b at an average speed of 50 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 50 miles per hour . what is s ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 50
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 50 = 1.5 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 50 = 1.5 + t » 100 / 50 = 1.5 + t » 2 = 1.5 + t » t = 0.5 back to 2 nd part of the trip formula : 25 / s = 0.5 » s = 50 ans e"
Answer: e
Question (general): excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 30 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 30 , c ) 77 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 30 km with stoppages . stoppage time = time take to travel ( 60 - 30 ) km i . e 30 km at 60 km / hr . stoppage time = 30 / 60 hrs = 30 min . answer : b"
Answer: b
Question (general): if a + b + c = 13 , then find the ab + bc + ca :
Options: a ) 22 , b ) 99 , c ) 50 , d ) 29 , e ) 11
Rationale: answer : c ) 50
Answer: c
Question (gain): indu gave bindu rs . 6250 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 10 , d ) 5 , e ) 1
Rationale: 6250 = d ( 100 / 4 ) 2 d = 10 answer : c
Answer: c
Question (other): if log 102 = 0.3010 , what is the value of log 101600 ?
Options: a ) 3.208 , b ) 3.202 , c ) 3.209 , d ) 3.204 , e ) 3.2112
Rationale: explanation : log 101600 = log 10 ( 16 × 100 ) = log 10 ( 16 ) + log 10 ( 100 ) = log 10 ( 24 ) + log 10 ( 102 ) = 4 log 10 ( 2 ) + 2 = ( 4 × 0.3010 ) + 2 = 1.204 + 2 = 3.204 answer : option d
Answer: d
Question (gain): a man can row his boat with the stream at 16 km / h and against the stream in 12 km / h . the man ' s rate is ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 2 kmph , d ) 4 kmph , e ) 1 kmph
Rationale: "ds = 16 us = 14 s = ? s = ( 16 - 2 ) / 2 = 2 kmph answer : c"
Answer: c
Question (gain): if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 350 , e ) 3500
Rationale: first of all , let us write the information in form of equations and numbers 125 j = 5 k or 5 j = k ( i ) 150 k = 50 l or 3 k = l ( ii ) 175 l = 75 m or 7 l = 3 m ( iii ) we need to find a relation between j and m from ( i ) and ( ii ) , 15 j = l multiplying this by 7 , 105 j = 7 l = 3 m hence , 35 j = m now , we are asked : 20 % of m is equal to what percent of 200 % of j assume j = 1 , hence m = 35 20 % of m = 7 and 200 % of j = 2 20 % of m = 3.5 ( 200 % of j ) = ( 350 / 100 ) * ( 200 % of j ) hence 20 % of m = 350 % of 200 % of j . option d
Answer: d
Question (general): a library has an average of 570 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 295 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 570 x 5 + 240 x 25 ) / 30 ) = 295 answer : option d"
Answer: d
Question (general): in a room filled with 7 people , 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 21 , d ) 5 / 7 , e ) 16 / 21
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 6 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 6 - - 6 c 2 = 15 total = 1 + 1 + 15 = 17 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 17 / 21 ( 21 is 7 c 2 ) = 1 - 17 / 21 = 4 / 21 ans c"
Answer: c
Question (geometry): the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 676 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 39 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 676 x ^ 2 = 169 x = 13 length = 4 * 13 = 52 difference = 52 - 13 = 39 a is the answer"
Answer: a
Question (geometry): the area of a rectangular plot is 360 square metres . if the length is 25 % less than the breadth , what is the breadth of the plot ?
Options: a ) 32 m
b ) 12 m
c ) 20 m
d ) 22 m
e ) 25 m
Rationale: length = 75 % of breadth . length × breadth = 360 m 2 ⇒ 75 % of breadth × breadth = 360 m 2 ⇒ 75 / 100 × breadth × breadth = 360 m 2 ⇒ breadth × breadth = 480 m 2 ⇒ breadth = 22 m answer : d
Answer: d
Question (physics): a 60 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 17.1 , e ) e ) 52
Rationale: "explanation : 1 : 2 / 5 = 5 : 2 2 / 7 * 60 = 20 answer : option d"
Answer: d
Question (general): one week , a certain truck rental lot had a total of 24 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 24 , b ) 16 , c ) 12 , d ) 8 , e ) 4
Rationale: n - not rented trucks ; r - rented trucks n + r = 24 n + r / 2 = 12 r = 24 a
Answer: a
Question (physics): if two projectiles are launched at the same moment from 1455 km apart and travel directly towards each other at 470 km per hour and 500 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 90 , b ) 85 , c ) 80 , d ) 75 , e ) 70
Rationale: "the projectiles travel a total of 970 km per hour . the time to meet is 1455 / 970 = 1.5 hours = 90 minutes the answer is a ."
Answer: a
Question (general): if the least common addition of two prime numbers x and y is 36 , where x < y , then the value of 4 x + y is
Options: a ) 32 , b ) 45 , c ) 59 , d ) 73 , e ) 87
Rationale: ( x + y ) = 36 and both x an y are prime . the only values of x and y can be 17 and 19 ( x = 17 and y = 19 ) 4 x + y = 4 * 17 + 19 = 87 correct option : e
Answer: e
Question (physics): a man can do a job in 10 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 5.3 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 10 + 1 / 20 + 1 / 25 ) = 19 / 100 so , all three together will complete the work in 100 / 19 = 5.3 days . answer : c"
Answer: c
Question (physics): a train 2500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 178 , b ) 180 , c ) 182 , d ) 184 , e ) 186
Rationale: "length = speed * time speed = l / t s = 2500 / 50 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : b"
Answer: b
Question (geometry): a semicircle has a radius of 14 . what is the approximate perimeter of the semicircle ?
Options: a ) 72 , b ) 76 , c ) 80 , d ) 84 , e ) 88
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 14 + 2 * 14 which is about 72 . the answer is a ."
Answer: a
Question (general): the average of 25 results is 24 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 740 , b ) 228 , c ) 690 , d ) 780 , e ) 458
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 24 or , x = 228 . answer : option b"
Answer: b
Question (other): a starts business with rs . 4500 and after 7 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 16200 , d ) 9000 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 7 = 5 months . so there profit ratio = ( 4500 ã — 12 ) : ( 5 x ) = 2 : 3 â ‡ ’ x = 16200 answer : c"
Answer: c
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.5 , c ) 3.5 , d ) 3.6 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.70 - ( 6.8 + 7.7 ) = 23.70 - 14.5 = 9.20 . required average = ( 9.2 / 2 ) = 4.6 . e"
Answer: e
Question (physics): some persons can do a piece of work in 12 days . two times the number of such persons will do half of that work in
Options: a ) 9 , b ) 8 , c ) 4 , d ) 3 , e ) 1
Rationale: "explanation : let x men can do the in 12 days and the required number of days be z more men , less days [ indirect proportion ] less work , less days [ direct proportion ] answer : d ) 3 days"
Answer: d
Question (other): find the number of zero ’ s in 173 ! ( 173 factorial ) ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: no of zeroes in 173 ! is 173 / 5 = 34 ( quotient ) 34 / 5 = 6 ( quotient ) 6 / 5 = 1 ( quotient ) 34 + 6 + 1 = 41 ans 41 zeroes answer : d
Answer: d
Question (general): 270 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 30 , d ) 39 , e ) 43
Rationale: "explanation : 270 ã · ? ã — 15 = 405 - 270 = 135 ( 270 ã — 15 ) / ? = 135 ? = ( 270 ã — 15 ) / 135 = 30 answer : option c"
Answer: c
Question (general): what is the sum of the odd integers from 55 to 65 , inclusive ?
Options: a ) 495 , b ) 360 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 60 . sum = mean ( # of elements ) there are 6 odd numbers between 55 - 65 inclusive . 6 * 60 = 360 b"
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 6 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 60000
Rationale: "perimeter = distance covered in 6 min . = 12000 x 6 m = 1000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1000 or x = 100 . length = 300 m and breadth = 200 m . area = ( 300 x 200 ) m 2 = 60000 m 2 . e"
Answer: e
Question (general): when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of e ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . e * 23 + 39 = 25 * ( e + 1 ) e = 7 ans . ( a )
Answer: a
Question (general): the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father as age will be 8 years more than twice the age of the son . find the present age of the father .
Options: a ) 88 , b ) 77 , c ) 33 , d ) 44 , e ) 27
Rationale: explanation : let the present age be ' x ' years . then father ' s present age is 3 x + 3 years . three years hence ( 3 x + 3 ) + 3 = 2 ( x + 3 ) + 8 x = 8 hence father ' s present age = 3 x + 3 = [ ( 3 x 8 ) + 3 ] = 27 years . answer : e
Answer: e
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 2500 ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 2500 , then the greatest possible length of integer z is 11 . the answer is c ."
Answer: c
Question (geometry): in measuring the sides of a rectangle , one side is taken 6 % in excess , and the other 5 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 53 / 50 ) x ( 19 / 20 ) y = ( 144 / 143 ) ( xy ) error in measurement = ( 144 / 143 ) xy - xy = ( 1 / 143 ) xy error percentage = [ ( 1 / 143 ) xy ( 1 / xy ) 100 ] % = ( 7 / 10 ) % = 0.7 % . answer is b ."
Answer: b
Question (general): a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.95 ?
Options: a ) 980 , b ) 1170 , c ) 1530 , d ) 1720 , e ) 1960
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.95 - $ 0.65 = $ 1.30 the charge for the next 1200 grams is $ 1.20 which leaves a charge of $ 0.10 the weight is somewhere between 1450 and 1550 . the answer is c ."
Answer: c
Question (geometry): if the diameter of circle r is 50 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 35 % , b ) 25 % , c ) 20 % , d ) 15 % , e ) 10 %
Rationale: "let diameter of circle r , dr = 50 and diameter of circle s , ds = 100 radius of circle r , rr = 25 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 25 / 50 ) ^ 2 = ( 5 / 10 ) ^ 2 = 25 % answer : b"
Answer: b
Question (physics): a can do a piece of work in 9 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 54 , e ) 12
Rationale: "8 / 9 + 6 / x = 1 x = 54 days answer : d"
Answer: d
Question (gain): john ' s bank ' s saving amount is decreased 50 % due to loan payment and current balance is rs . 50000 . find the actual balance before deduction ?
Options: a ) 100000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: "50 % decreased 50 % balance = 50000 100 % = 50000 / 50 * 100 = 100000 answer : a"
Answer: a
Question (physics): a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 192 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 12
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 192 - $ 120 = $ 72 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 72 / $ 6 = 12 ans is e"
Answer: e
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 294 , what is the least possible value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "294 = 2 * 3 * 7 * 7 , so n must be at least 14 . the answer is d ."
Answer: d
Question (physics): excluding stoppages , the speed of a train is 55 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 16 , c ) 12 , d ) 82 , e ) 18
Rationale: "explanation : t = 15 / 55 * 60 = 16 answer : option b"
Answer: b
Question (physics): a train travels 210 km in 3 hours and 270 km in 4 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 69 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 210 + 270 = 480 km thus , total speed = 7 hrs or , average speed = 480 / 7 or , 69 kmph . answer : b"
Answer: b
Question (general): 15 - 2 + 4 ÷ 1 / 2 × 8 = ?
Options: a ) 272 , b ) 77 , c ) 168 , d ) 56 , e ) 59
Rationale: explanation : 15 - 2 + 4 ÷ 1 / 2 × 8 = 15 - 2 + 4 × 2 × 8 = 15 - 2 + 64 = 77 answer : option b
Answer: b
Question (gain): the difference between the compound interest and simple interest on a certain sum at 20 % per annum for 2 years is $ 500 . find the sum ?
Options: a ) $ 10000 , b ) $ 50000 , c ) $ 15200 , d ) $ 12500 , e ) $ 15000
Rationale: "let the sum be $ x c . i . = x ( 1 + 20 / 100 ) ^ 2 - x = 35 x / 100 s . i . = ( x * 20 * 2 ) / 100 = 2 x / 5 c . i . - s . i . = ( 35 x / 100 ) - ( 2 x / 5 ) = 5 x / 100 5 x / 100 = 500 x = 10000 answer is a"
Answer: a
Question (geometry): the length of a rectangular garden is three times its width . if the area of the rectangular garden is 432 square meters , then what is the width of the rectangular garden ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the width of the garden . 3 x ^ 2 = 432 x ^ 2 = 144 x = 12 the answer is e ."
Answer: e
Question (general): the mean of 50 observations was 39 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 39 × 50 + 48 – 23 ) = 1975 . therefore correct mean = 1975 / 50 = 39.5 . answer e"
Answer: e
Question (general): when positive integer n is divided by 2 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 10 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 2 , the remainder is 1 i . e . , n = 2 x + 1 values of n can be one of { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17,19 , . . . . . . . . . . . . . . 31 , 33,35 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , 47 , 54 , 61 . . . . . . . . } combining both the sets we get n = { 19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 21 or 21 x in case of n = 5 p = 5 so for min value of p , we take min value of n . c is the answer ."
Answer: c
Question (other): how many odd factors does 160 have ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 160 = 2 * 5 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 } plus 1 to each = { 2 } product = 2 therefore , there are 2 odd factors of 160 . answer : a ."
Answer: a
Question (geometry): the length of a rectangle is doubled while its width is tripled . what is the % change in area ?
Options: a ) 250 %
b ) 300 %
c ) 500 %
d ) 650 %
e ) 700 %
Rationale: the original area is l * w the new area is 2 l * 3 w = 6 * l * w = l * w + 5 * l * w the area increased by 500 % . the answer is c .
Answer: c
Question (general): there were totally 100 men . 81 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 81 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 19 - 25 - 15 - 30 = 100 - 89 = 11 answer : a"
Answer: a