regisss/math_qa huggingface dataset:
Problem: a can run 160 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 20 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 160 / 32 = 5 m / s distance covered by b in 4 seconds = speed ã — time = 5 ã — 4 = 20 metre i . e . , a beat b by 20 metre answer is c"
Answer: c
Problem: a club wants to mix 20 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 8 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 160 + 5 w = > w = 40 answer c
Answer: c
Problem: by selling an article at rs . 600 , a profit of 30 % is made . find its cost price ?
Options: a ) 400 , b ) 267 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 50 ) ] = 600 * [ 100 / 150 ] = rs . 400 answer : a"
Answer: a
Problem: a student gets 60 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject .
Options: a ) 75 % , b ) 80 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 60 + 70 + x = 3 * 70 130 + x = 210 x = 210 - 130 = 80 answer : b"
Answer: b
Problem: if a ' s height is 30 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 42.85 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: excess of b ' s height over a ' s = [ ( 30 / ( 100 - 30 ) ] x 100 % = 42.85 % answer : a )
Answer: a
Problem: if 13 = 13 w / ( 1 - w ) , then ( 2 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 2 w = 1 2 w * 2 = 1 * 2 = 2 answer : d"
Answer: d
Problem: what is the perimeter of a square field whose diagonal is 4 √ 2 ?
Options: a ) 16 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m
Rationale: "4 a = 16 m answer : a"
Answer: a
Problem: if the sides of a triangle are 4 cm , 9 cm and 13 cm , what is its area ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 26 , e ) 28
Rationale: "the triangle with sides 4 cm , 9 cm and 13 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 4 * 9 = 18 cm 2 answer : option a"
Answer: a
Problem: of the 65 cars on a car lot , 45 have air - bag , 30 have power windows , and 12 have both air - bag and power windows . how many of the cars on the lot have neither air - bag nor power windows ?
Options: a ) 8 , b ) 2 , c ) 10 , d ) 15 , e ) 18
Rationale: total - neither = all air bag + all power windows - both or 65 - neither = 45 + 30 - 12 = 63 . = > neither = 2 , hence b . answer : b
Answer: b
Problem: a large field of 700 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 315 , b ) 339 , c ) 288 , d ) 299 , e ) 111
Rationale: explanation : let the areas of the two parts be x and ( 700 - x ) hectares therefore , so , the two parts are 385 and 315 . hence , area of the smaller = 315 hectares answer : a ) 315
Answer: a
Problem: if 2994 ã · 14.5 = 177 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 177 in the place of 2994 / 14.5 ] = 177 / 10 = 17.7 answer is d ."
Answer: d
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent t should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked t will be 25 % greater than the original number . the answer is c .
Answer: c
Problem: tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?
Options: a ) 9 / 10 , b ) 6 / 10 , c ) 2 / 10 , d ) 3 / 10 , e ) 5 / 10
Rationale: "explanation : here , s = { 1 , 2 , 3 , 4 , . . . . , 19 , 20 } = > n ( s ) = 20 let e = event of getting a multiple of 4 or 15 = multiples od 4 are { 4 , 8 , 12 , 16 , 20 } and multiples of 15 means multiples of 3 and 5 = { 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 15 , 20 } . = the common multiple is only ( 15 ) . = > e = n ( e ) = 6 required probability = p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 . answer is d"
Answer: d
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 4 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 95 , d ) 112 , e ) 140
Rationale: first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 4 hrs therefore , 4 = d / 75 + d / 105 lcm of 75 and 105 = 525 4 = d / 75 + d / 105 = > 4 = 7 d / 525 + 5 d / 525 = > d = 525 / 3 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 3 x 75 ) = > t 1 = ( 7 x 60 ) / 3 - - in minutes = > t 1 = 140 minutes . e
Answer: e
Problem: what could be the range of a set consisting of odd multiples of ( 6 + 1 ) ?
Options: a ) 70 , b ) 24 , c ) 35 , d ) 62 , e ) 21
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 7 * ( 2 n + 1 ) where n is any positive integer . range = 7 * ( 2 m + 1 ) - 7 * ( 2 n + 1 ) = 7 * 2 * ( m - n ) = 14 * ( m - n ) . m , n - any positive integers the answer must be divisible by 14 , which is only 70 . the correct answer is a ."
Answer: a
Problem: the apartment on king - williams street is an asset that its value is tramping about . from the year 1973 to 1983 it ' s value decreased by 16 % and from 1983 to 1993 it ' s value increased by 16 % . what is the value of the asset in 1993 if in 1973 it was worth $ 55000 ?
Options: a ) $ 38,796 . , b ) $ 40,000 . , c ) $ 38,976 . , d ) $ 39,679 . , e ) $ 53,592 .
Rationale: 55,000 * 1.16 * . 84 = 53,592 answer e
Answer: e
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "the equation of the line can be re written as y = ( 1 / 2 ) x - 5 / 2 . slope = 1 / 2 , which means for every 1 unit increase in the y co - ordinate , x will increase by 2 units . hence k = 1 . answer : b"
Answer: b
Problem: the difference between c . i . and s . i . on an amount of $ 15,000 for 2 years is $ 54 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 54 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 15000 * x . the interest on the first year ' s interest is 15000 * x * x 15000 * x ^ 2 = 54 x = 0.06 the answer is b ."
Answer: b
Problem: $ 600 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 200 , e ) $ 240
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 600 * 2 / 5 = $ 240 answer is e"
Answer: e
Problem: what is the smallest no . which must be added to 532869 so as to obtain a sum which is divisible by 9 ?
Options: a ) 9 , b ) 2 , c ) 1 , d ) 3 , e ) 6
Rationale: "for 532869 , 5 + 3 + 2 + 8 + 6 + 9 = 33 3 must be added to 532869 to make it divisible by 9 . now , 5 + 3 + 2 + 8 + 7 + 2 = 27 = > 27 is a multiple of 9 and hence 532869 is also divisible by 9 d"
Answer: d
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 51
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 12 / 60 ) ) km = 5 km . answer : b"
Answer: b
Problem: a sum was put at simple interest at a certain rate for 6 years had it been put at 4 % higher rate , it would have fetched 144 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 144 = p × 6 x 4 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 144 × 100 / 6 × 4 = 600 answer b"
Answer: b
Problem: what least no . must be subtracted from 427398 so that remaining no . is divisible by 10 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 3
Rationale: "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted option a"
Answer: a
Problem: the number of students enrolled at school xx this year is 7 percent more than it was last year . the number of students enrolled at school yy this year is 3 percent more than it was last year . if school xx grew by 40 more students than school yy did , and if there were 4000 total enrolled students last year at both schools , how many students were enrolled at school yy last year ?
Options: a ) 480 , b ) 1600 , c ) 1920 , d ) 2080 , e ) 2400
Rationale: given info : no . of students enrolled in school x is = 7 % more than previous year ' s strength = 7 x / 100 no . of students enrolled in school y is = 3 % more than previous year ' s strength = 3 y / 100 given that ` ` this year ' ' school x have 40 students more than school y . so the increase in strength can be written as 7 x / 100 = 40 + 3 y / 100 7 x = 4000 + 3 y . . . . . . . . . . . . . . . . . . . . ( 1 ) and total students on previous year are x + y = 4000 . . . . . . . . . . . . . . . . . . . . . . ( 2 ) equating & solving we get , y = 2400 ans is e
Answer: e
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio t of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore , tw _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 3.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 252 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 3.50 ) or $ 252 . the best answer is therefore a . answer : a ."
Answer: a
Problem: the average runs scored by a batsman in 35 matches is 36 . in the next 14 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 35 , c ) 29 , d ) 25 , e ) 30
Rationale: total score of the batsman in 35 matches = 1260 . total score of the batsman in the next 14 matches = 210 . total score of the batsman in the 30 matches = 1470 . average score of the batsman = 1470 / 49 = 30 . answer : e
Answer: e
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 18 , and k < m < r < s < t . if t is 40 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 23 , c ) 19 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 18 which means that in effect , all numbers are equal to 18 . if the largest number is 40 , it is 22 more than 18 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 17 less than 18 and 2 is 16 less than 18 which means k and m combined are 33 less than the average . 40 is already 22 more than 18 and hence we only have 33 - 22 = 11 extra to distribute between r and s . since s must be greater than r , r can be 18 + 5 = 23 and s can be 18 + 6 = 24 . so r is 23 answer ( b )"
Answer: b
Problem: how many positive integers less than 7,000 are there in which the sum of the digits equals 5 ?
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . c"
Answer: c
Problem: 4 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.11111 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 4 / 36 = . 1111 answer ( b )"
Answer: b
Problem: by selling 16 pencils for a rupee a man loses 28 % . how many for a rupee should he sell in order to gain 28 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "72 % - - - 16 128 % - - - ? 72 / 128 * 16 = 9 answer : b"
Answer: b
Problem: if the radius of a circle is diminished by 10 % , then the area is diminished by :
Options: a ) 200 % , b ) 210 % , c ) 300 % , d ) 310 % , e ) none of these
Rationale: "explanation : let the original radius be r cm . new radius = 2 r area = π r 2 new area = π 2 r 2 = 4 π r 2 increase in area = ( 4 π r 2 − π r 2 ) = 3 π r 2 increase percent = 3 π r 2 / π r 2 ∗ 100 = 300 % option c"
Answer: c
Problem: a parking garage rents parking spaces for $ 10 per week or $ 24 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 232 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 24 = 288 $ 520 - 288 = 232 ans d"
Answer: d
Problem: a boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream , it takes 3 hours . what is the speed of the boat in still water ?
Options: a ) 8 kmph , b ) 5 kmph , c ) 4 kmph , d ) 6 kmph , e ) 7 kmph
Rationale: "speed downstream = 12 / 2 = 6 kmph speed upstream = 12 / 3 = 4 kmph speed of the boat in still water = 6 + 4 / 2 = 5 kmph answer : b"
Answer: b
Problem: what is the area of a square field whose diagonal of length 20 m ?
Options: a ) 288
b ) 289
c ) 200
d ) 112
e ) 178
Rationale: d 2 / 2 = ( 20 * 20 ) / 2 = 200 answer : c
Answer: c
Problem: a sum of rs . 12,500 amounts to rs . 15,500 in 4 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: s . i . = rs . ( 15500 - 12500 ) = rs . 3000 . rate = ( 100 x 3000 ) / ( 12500 x 4 ) % = 6 % answer : d
Answer: d
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) loss of rs . 200 , b ) loss of rs . 100 , c ) profit of rs . 100 , d ) profit of rs . 200 , e ) none of these
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"
Answer: d
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 8 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 30 , d ) 72 , e ) 60
Rationale: d 72 sum = ( n x n ) + n hence , 8 x 8 = 64 + 8 = 72
Answer: d
Problem: a and b can do a work in 5 days , b and c in 15 days and c and a in 25 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 26 / 18 , b ) 42 / 15 , c ) 48 / 63 , d ) 12 / 36 , e ) 150 / 23
Rationale: "one day work of a and b = 1 / 5 one day work of b and c = 1 / 15 one day work of c and a = 1 / 25 2 ( a + b + c ) = 1 / 5 + 1 / 15 + 1 / 25 2 ( a + b + c ) = 23 / 75 ( a + b + c ) = 23 / 150 number of days required = 150 / 23 days . answer : e"
Answer: e
Problem: 22 percent of 300
Options: a ) 50 , b ) 55 , c ) 62 , d ) 77 , e ) 66
Rationale: 1 % of 300 = 3 22 % of 300 = 22 * 3 = 66 answer : e
Answer: e
Problem: working individually , allison can sew dresses for 9 hours and al can sew dresses in 12 hours . if allison and al work together but independently at the task for 3 hours , at which point al leaves , how many remaining hours will it take allison to complete the task alone ?
Options: a ) 45 / 12 , b ) 23 / 12 , c ) 40 / 33 , d ) 34 / 12 , e ) 43 / 5
Rationale: in first 3 hrs al will finish 3 / 12 = 1 / 4 of work and allison will finish 3 / 9 = 1 / 3 work so total 1 / 4 + 1 / 3 = 7 / 12 work is finished and 1 - 7 / 12 = 5 / 12 work remaining . now allison will take ( 5 / 12 ) * 9 = 45 / 12 hrs to finish it . so answer is a .
Answer: a
Problem: 3 friends are planning to attend a concert . if another friend also goes with them , they will get a group discount on their tickets . if the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount , how much is the discount ?
Options: a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 33 %
Rationale: let x be the original price of one ticket . the total original cost is 3 x . the new cost is 4 y , where y is the discounted price of one ticket . 3 x = 4 y y = 3 x / 4 = 0.75 x which is a discount of 25 % . the answer is d .
Answer: d
Problem: the true discount on a bill of rs . 540 is rs . 90 . the banker ' s discount is :
Options: a ) rs . 60 , b ) rs . 108 , c ) rs . 110 , d ) rs . 112 , e ) rs . 122
Rationale: "p . w . = rs . ( 540 - 90 ) = rs . 450 . s . i . on rs . 450 = rs . 90 . s . i . on rs . 540 = rs . ( 90 / 450 ) x 540 = rs . 108 . b . d . = rs . 108 . answer : b"
Answer: b
Problem: when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.15 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 20
Rationale: by the definition of a remainder , the remainder here is equal to 3 / y . the remainder in decimal form is given as . 15 therefore , 3 / y = . 15 solve for y and get 20 . e
Answer: e
Problem: fetched a total simple interest of rs . 4216.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs . 8928 , b ) rs . 89228 , c ) rs . 8911 , d ) rs . 8925 , e ) rs . 8922
Rationale: explanation : principal = rs . = rs . = rs . 8925 answer : d
Answer: d
Problem: the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 22 , e ) 24
Rationale: "explanation : 10 * 15 + 36 – 26 = 160 / 10 = 16 a )"
Answer: a
Problem: if x is 20 percent greater than 98 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 117.6
Rationale: "x = 98 * 1.2 = 117.6 so the answer is e ."
Answer: e
Problem: 30 pens and 75 pencils were purchased for 450 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 450 – 150 ) = 300 ∴ average price of a pen = 360 ⁄ 60 = 10 answer a
Answer: a
Problem: a person is traveling at 100 km / hr and reached his destiny in 5 then find the distance ?
Options: a ) 250 km , b ) 300 km , c ) 500 km , d ) 450 km , e ) 350 km
Rationale: "t = 5 hr s = 100 km / hr d = t * s = 100 * 5 = 500 km answer is c"
Answer: c
Problem: if jake loses 29 pounds , he will weigh twice as much as his sister . together they now weigh 99 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 69 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: "j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 29 = 2 s j = 2 s + 29 ( equation 1 ) next , we are told that “ together they now weigh 89 pounds . ” we can also put this into an equation . j + s = 89 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 2 s + 29 = 89 - s 3 s = 60 s = 20 j + 20 = 89 j = 69 answer : a"
Answer: a
Problem: a man can row downstream at the rate of 18 kmph and upstream at 6 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 6.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 18 + 6 ) = 12 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 18 - 6 ) = 1 / 2 ( 12 ) = 6 kmph answer is b ."
Answer: b
Problem: the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 20 inclusive ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the average of the even numbers from 0 to 20 is 20 / 2 = 10 the answer is c ."
Answer: c
Problem: what is the smallest number h which when increased by 5 is completely divisible by 8 , 11 and 24 ?
Options: a ) 264 , b ) 259 , c ) 269 , d ) 270 , e ) 282
Rationale: this question includes a number of great number property shortcuts that you can take advantage of : 1 ) the question asks for the smallest number that , when increased by 5 is divisible by 8 , 11 and 24 . since the answers are numbers , we can test the answers . 2 ) any number that is divisible by 24 is also divisible by 8 , so we really just need to consider the 11 and the 24 . 3 ) to be divisible by 24 , the end number must be even . since we ' re adding 5 to get to that end number , the starting number must be odd . the last shortcut allows us to eliminate answers a , d and e . between answers b and c , testing b first will prove that , when increased by 5 , the end sum is divisible by both 11 and 24 . final answer : b
Answer: b
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1290 , find the loss % ?
Options: a ) 14 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 210 100 - - - - ? = > 14 % answer : a"
Answer: a
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 900 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 900 20 x / 100 = 900 x = 900 * 100 / 20 = 4500 answer is a"
Answer: a
Problem: ( 17 ) 3.75 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 3.75 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.75 + x = 8 ⇔ x = ( 8 - 3.75 ) ⇔ x = 4.25 answer c"
Answer: c
Problem: the speed of a boat in still water in 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 1.2 km , b ) 2.4 km , c ) 3.2 km , d ) 3.6 km , e ) 4.6 km
Rationale: "speed downstream = ( 15 + 3 ) kmph = 18 kmph . distance travelled = 18 x 12 / 60 km = 3.6 km . answer : d"
Answer: d
Problem: if 1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 0.01 , e ) 0.0001
Rationale: "1000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 1000 microns = 1 , 000,000 angstroms 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : b"
Answer: b
Problem: 10 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 15 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the number of hours required to complete the work is 10 * 7 * 18 = 1260 15 × 12 × ( x ) = 1260 x = 7 the answer is b .
Answer: b
Problem: calculate the value of n from the below equation : y ^ 4 â ˆ ’ 20 y + 1 = 22
Options: a ) 5 , b ) 3 , c ) 6 , d ) 2 , e ) 1
Rationale: use elimination method to find the correct option . you find that of all the options 3 is the correct value for y answer : b
Answer: b
Problem: the average of first five prime numbers greater than 37 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 42.3 , d ) 48.6 , e ) 32.4
Rationale: "41 + 43 + 47 + 53 + 59 = 243 / 5 = 48.6 answer : d"
Answer: d
Problem: a bag contains 6 black and 6 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 6 ) = 12 . number of white balls = 6 . p ( drawing a white ball ) = 6 / 12 = 1 / 2 . option b ."
Answer: b
Problem: the list price of an article is rs . 67 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.86 % , b ) 4.86 % , c ) 5.86 % , d ) 6.86 % , e ) 7.86 %
Rationale: 67 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 6.86 % answer : d
Answer: d
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many w miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him w : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 3 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 4 / 9 , b ) 2 / 3 , c ) 3 / 2 , d ) 9 / 2 , e ) 9 / 4
Rationale: "the area of rectangle a is ab . c = 3 a / 2 and d = 3 b / 2 . the area of rectangle b is cd = 9 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 9 ab / 4 ) = 4 / 9 . the answer is a ."
Answer: a
Problem: the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.8 , what is the probability that event b will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.65
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.8 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.65 ans : e"
Answer: e
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 1 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 14 / 17 , e ) 1 / 2
Rationale: let the total # of cups be 10 . # of small cups sold 1 / 5 * 10 = 2 ; # of large cups sold 10 - 2 = 8 ; let the price of small cup be $ 6 , then the price of larges cup would be 7 / 6 * 6 = $ 7 ; revenue from small cups : 2 * $ 6 = $ 12 ; revenue from large cups cups : 8 * $ 7 = $ 56 ; fraction of total revenue from large cups : 56 / ( 56 + 12 ) = 14 / 17 . answer : d .
Answer: d
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 14,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 120,500 , e ) 100,000
Rationale: answer equals d in 48 years . i thought by 50 th year it would reach 120,500 . options should have been separated more widely for clarity .
Answer: d
Problem: 12 is 4 % of a , and 4 is 12 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: "4 a / 100 = 12 a = 300 12 b / 100 = 4 b = 100 / 3 c = b / a = 100 / ( 3 * 300 ) = 1 / 9 the answer is d ."
Answer: d
Problem: a contractor undertook to make 15 km of roadway in 40 weeks . in 10 weeks , 3 km was complete by 180 men working 8 hours a day . the men then agreed to work 1 hour a day overtime , and some boys were engaged to assist them , the work was finished in the stipulated time ( 40 weeks ) . how many boys were employed , if the work of 3 boys is equal to that of 2 men ?
Options: a ) 48 , b ) 50 , c ) 22 , d ) 27 , e ) 221
Rationale: explanation : let the capacity of man = 3 units , and boy = 2 units per hour . now total work = 3 × 180 × 8 × 7 × 10 = 3 km . - - - - - - - ( 1 ) let k boys were recruited . now total work = ( 3 × 180 + 2 × k ) × 9 × 7 × 30 = 12 km . - - - - - - ( 2 ) by dividing 2 nd equation by 1 st , ⇒ ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ⇒ k = 50 answer : b
Answer: b
Problem: a man can row 7 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.3 , b ) 3.4 , c ) 3.5 , d ) 3.6 , e ) 3.7
Rationale: "m = 7 s = 1.2 ds = 7 + 1.2 = 8.2 us = 7 - 1.2 = 5.8 x / 8.2 + x / 5.8 = 1 x = 3.40 . answer : b"
Answer: b
Problem: find the least number of complete years in which a sum of money put out at 33.3 % compound interest will be more than double of itself ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 years answer : a"
Answer: a
Problem: the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is
Options: a ) 15 , b ) 20 , c ) 25 , d ) 35 , e ) 45
Rationale: "explanation : let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 x 131 = 400 = > ( a + b + c ) = 400 − − − √ = 20 . option b"
Answer: b
Problem: by selling a book for 290 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 241 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 290 × 100 / 120 = 241 option ' b '"
Answer: b
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability w that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins .
Answer: d
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 170 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 650 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 170 = 1700 3 * 100 + 5 * 150 = 1050 1700 – 1050 = 650 b"
Answer: b
Problem: a grocer has a sale of rs . 5266 , rs . 5768 , rs . 5922 , rs . 5678 and rs . 6029 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) 4637 , b ) 4737 , c ) 4937 , d ) 5937 , e ) 5978
Rationale: "total sale for 5 months = rs . ( 5266 + 5768 + 5922 + 5678 + 6029 ) = rs . 28663 . required sale = rs . [ ( 5600 x 6 ) - 28663 ] = rs . ( 33600 - 28663 ) = rs . 4937 . answer : c"
Answer: c
Problem: in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 800 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 40 * 100 = 5 % . we are told that 5 % approximates the percent of tagged fish in the pond . since there are 40 tagged fish , then we have 0.05 x = 40 - - > x = 800 . answer : b ."
Answer: b
Problem: the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e .
Answer: e
Problem: a report consists of 20 sheets each of 55 lines and each such line consist of 65 characters . this report is retyped into sheets each of 65 lines such that each line consists of 70 characters . the percentage reduction in number of sheets is closest to
Options: a ) 20 , b ) 5 , c ) 30 , d ) 35 , e ) 67
Rationale: explanation : total no of characters = 20 * 55 * 65 . from the problem it is clear that 20 * 55 * 65 = x * 65 * 70 . we get x = 15.6 ∼ 16 because these are sheets . therefore 4 less sheets . hencde , there is 20 % decrease in number of sheets . answer : a
Answer: a
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio q of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) q = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Problem: 8 / 4 / 2 = ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 4 , e ) 1
Rationale: "8 / 4 / 2 = ( 8 / 4 ) / 2 = 2 / 2 = 1 answer is e ."
Answer: e
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.00 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is c ."
Answer: c
Problem: by weight , liquid x makes up 0.7 percent of solution p and 1.2 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.2 % , b ) 1.1 % , c ) 1.0 % , d ) 0.9 % , e ) 0.8 %
Rationale: "the number of grams of liquid x is 0.7 ( 200 ) / 100 + 1.2 ( 800 ) / 100 = 1.4 + 9.6 = 11 grams . 11 / 1000 = 1.1 % the answer is b ."
Answer: b
Problem: a courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 16000 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2000 × 1600 / 20 × 10 ) = 16000 answer : a"
Answer: a
Problem: a car takes 4 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 92 kmph , b ) 98 kmph , c ) 90 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "time = 4 distence = 540 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 540 / 6 = 90 kmph c )"
Answer: c
Problem: 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275
Options: a ) 107 , b ) 147 , c ) 10 , d ) 296 , e ) none of these
Rationale: "explanation : let 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275 then , 63 * 15 / 5 + x = 61 + 275 63 * 3 + x = 336 189 + x = 336 x = 147 answer b"
Answer: b
Problem: 36 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 44 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 37
Rationale: "( 36 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 80 80 – 36 = 44 answer : a"
Answer: a
Problem: square a has an area of 121 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 121 , d ) 105 / 121 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 121 - 16 = 105 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 105 / 121 . answer : d ."
Answer: d
Problem: the end of a blade on an airplane propeller is 15 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 450 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 15 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 15 / 5280 = 450 π d is the answer"
Answer: d
Problem: a man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph , find his average speed for the total journey ?
Options: a ) 5 , b ) 4 , c ) 4.5 , d ) 3.75 , e ) 3
Rationale: "m = 4 s = 1 ds = 5 us = 3 as = ( 2 * 5 * 3 ) / 8 = 3.75 answer : d"
Answer: d
Problem: 20 % of a number is more than 40 % of 140 by 80 . find the number ?
Options: a ) 680 , b ) 620 , c ) 652 , d ) 520 , e ) 458
Rationale: "( 20 / 100 ) * x – ( 40 / 100 ) * 140 = 80 1 / 5 x = 136 x = 680 answer : a"
Answer: a
Problem: a certain machine produces 550 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 5 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 66,000 , d ) 100,000 , e ) 168,000
Rationale: "since 5 days consist of 24 * 5 hours the total is 120 hours . since every hour the machine produces 550 units of product p the total product during 120 hours is 120 * 550 = 66,000 . correct option : c"
Answer: c
Problem: the average salary / head of all the workers ina workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 25
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c
Answer: c
Problem: if the sides of a square are multiplied by sqrt ( 20 ) , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 2 % , b ) 5 % , c ) 20 % , d ) 50 % , e ) 150 %
Rationale: "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt ( 20 ) * x , so the area is 20 x ^ 2 . the area of the original square is 1 / 20 = 5 % times the area of the new square . the answer is b ."
Answer: b
Problem: the average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 3 kg = > ( 80 - x ) / 6 = 3 = > x = 62 answer : a"
Answer: a
Problem: if 20 honey bees make 20 grams of honey in 20 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 30
Rationale: explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 20 : : 20 : x honey 20 : 1 = > 1 x 20 x x = 20 x 1 x 20 = > x = 20 . answer : c
Answer: c
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 60 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 7 : 15 , b ) 7 : 10 , c ) 7 : 8 , d ) 7 : 4 , e ) 7 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 60 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.60 = $ 36 cost = 36 / 1.6 = $ 22.5 if he wants a 60 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 22.5 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 22.5 / 33 = 15 / 22 of a liter . if milk is 15 / 22 of the liter , then water is 7 / 22 of the liter , and the ratio of water to milk is 7 : 15 . answer choice ( a )"
Answer: a
Problem: in town x , 65 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 27 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 65 % , out of which 48 are employed males , hence 17 % are employed females . ( employed females ) / ( total employed people ) = 17 / 64 = 27 % answer : b ."
Answer: b
Problem: out of 3 consecutive odd numbers 9 times the first number is equal to addition of twice the third number and adding 9 to twice the second . what is the first number ?
Options: a ) 20 / 21 , b ) 23 / 25 , c ) 24 / 23 , d ) 22 / 5 , e ) 21 / 5
Rationale: description : = > 9 x = 2 ( x + 2 ) + 9 + 2 ( x + 4 ) = > 9 x = 4 x + 21 = > 5 x = 21 x = 21 / 5 answer e
Answer: e
Problem: find the lcm of 23 , 46,827
Options: a ) 227 , b ) 83 , c ) 23 , d ) 827 , e ) none of these
Rationale: explanation : whenever we have to solve this sort of question , remember the formula . lcm = \ \ begin { aligned } \ \ frac { hcf of denominators } { lcm of numerators } \ \ end { aligned } so answers will be option 2 , please also give attention to the difference in formula of hcf and lcm answer : option b
Answer: b
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 42 liters of forest green to change it to verdant green ?
Options: a ) 14 , b ) 12 , c ) 15 , d ) 11 , e ) 10
Rationale: "42 liter of forset green have 24 liter of blue and 18 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 24 / ( 18 + x ) = ¾ 54 + 3 x = 96 = > x = 14 answer : a"
Answer: a
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 300,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,250 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 300000 [ 1 ] 0.04 x = 0.80 * 300000 = 240000 [ 2 ] 240000 + 0.09 y = 300000 - - > 0.09 y = 60000 [ 3 ] 240000 / 12 = 20000 [ 4 ] 60000 / 12 = 5000 [ 5 ] adding [ 4,5 ] we get : 25000 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.25 , ans a"
Answer: a