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Question: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 9.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
A.16.5 %.
B.8 %.
C.35 %.
D.55 %.
e ) 65 %B.
"the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.095 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 95 f - - > s = f - - > f / s = 1 / 12 - - > f / ( s + f ) = 1 / ( 1 + 12 ) = 1 / 13 = 0.08 . answer : b ." | null |
Question: how many of the positive divisors of 720 are also multiples of 4 not including 720 ?
A.11.
B.12.
C.17.
D.18.
e ) 24C.
"720 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 ^ 2 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 2 , and 1 . there are ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 720 . the answer is c ." | null |
Question: ( p / q - q / p ) = 21 / 10 . then find 4 p / q + 4 q / p ?
A.58 / 9.
B.58 / 5.
C.58 / 7.
D.58 / 2.
e ) 58 / 1B.
let p / q = a , then ( a - 1 / a ) = 21 / 10 ⇒ a 2 − 1 = a . 2110 ⇒ a 2 − 1 = a . 2110 ⇒ 10 a 2 − 21 a − 10 ⇒ 10 a 2 − 21 a − 10 = 0 roots of the equation = − b ± b 2 − 4 ac − − − − − − − √ 2 a − b ± b 2 − 4 ac 2 a a = 21 ± 441 + 400 − − − − − − − − √ 2021 ± 441 + 40020 a = 21 ± 292021 ± 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b | null |
Question: a jar was full with honey . a person used to draw out 20 % of the honey from the jar and replaced it with sugar solution . he has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar , the rest part of the jar was filled with the sugar solution . the initial amount of honey in the jar was filled with the sugar solution . the initial amount of honey in the jar was :
A.1.25 kg.
B.1.29 kg.
C.1.85 kg.
D.3.25 kg.
e ) 1.23 kgA.
answer : a ) 1.25 kg | null |
Question: a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
A.30.
B.80.
C.20.
D.25.
e ) 26B.
"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b" | null |
Question: carl is facing very difficult financial times and can only pay the interest on a $ 8,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
A.$ 1200.
B.$ 2000.
C.$ 2150.
D.$ 2500.
e ) $ 1600E.
"usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 8,000 = $ 1600 as our answer . but since , the interest is compounded , it will be a bit more than $ 1600 . option ( e ) looks correct ." | null |
Question: the ratio of two numbers is 2 / 3 , and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1 / 2 , then the numbers are .
A.6 and 9.
B.6 and 10.
C.6 and 8.
D.6 and 7.
e ) 6 and 11A.
a : b = 2 : 3 b = 3 / 2 a a - 1 / b + 1 = 1 / 2 solving this we get a = 6 and b = 9 answer : a | null |
Question: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
A.276.
B.280.
C.322.
D.345.
e ) 354B.
"clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b" | null |
Question: two cubes of their volumes in the ratio 64 : 125 . the ratio of their surface area is :
A.1.5 : 5.
B.2 : 5.
C.3 : 5.
D.1 : 5.
e ) 4 : 5E.
"the ratio of their surface area is 64 : 125 4 : 5 answer is e ." | null |
Question: if the average of 16 x and 8 y is greater than 80 , and x is twice y , what is the least integer value of x ?
A.8.
B.9.
C.10.
D.11.
e ) 12A.
"substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 16 x and 4 x is greater than 80 . average of 16 x and 4 x is 10 x . so , 10 x > 80 x > 8 answer : a" | null |
Question: what is the square root of 168,921 ?
A.476.
B.389.
C.497.
D.411.
e ) 524D.
"1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) b = 389 ^ 2 and d = 411 ^ 2 b = ( 400 - 11 ) ^ 2 and d = ( 400 + 11 ) ^ 2 since we need the answer less than 160000 = > b is out . thus we have d as the ans ." | null |
Question: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?
A.20.
B.10.
C.30.
D.24.
e ) 5D.
"arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d" | null |
Question: a man is 28 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 ?
A.16.
B.19.
C.15.
D.26.
e ) 10D.
"let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d" | null |
Question: in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :
A.23.
B.37.
C.56.
D.40.
e ) 81C.
"explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 30 + 42 â € “ 28 = 44 therefore students who passed = 100 â € “ 44 = 56 . answer : c" | null |
Question: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is : ?
A.40.
B.60.
C.80.
D.67.
e ) 30C.
"let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c" | null |
Question: two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1 / 2 minute . if the length of the first train is 125 m , what is the length of the second train ?
A.300 m.
B.287 m.
C.125 m.
D.250 m.
e ) 167 mC.
rs = 50 â € “ 40 = 10 * 5 / 18 = 25 / 9 mps t = 90 sec d = 25 / 9 * 90 = 250 m 125 - - - - - - - - 125 m answer : c | null |
Question: a man can row upstream at 25 kmph and downstream at 31 kmph , and then find the speed of the man in still water ?
A.22.
B.28.
C.30.
D.27.
e ) 18B.
"us = 25 ds = 31 m = ( 31 + 25 ) / 2 = 28 answer : b" | null |
Question: a , b , c can complete a piece of work in 24 , 8,12 days . working together , they complete the same work in how many days ?
A.4.
B.4 / 5.
C.7 / 9.
D.10.
e ) 24 / 7A.
"a + b + c 1 day work = 1 / 24 + 1 / 8 + 1 / 12 = 6 / 24 = 1 / 4 a , b , c together will complete the job in 4 days answer is a" | null |
Question: a cricket player whose bowling average was 23.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?
A.64.
B.72.
C.131.
D.456.
e ) 108C.
"average = total runs / total wickets total runs after last match = 23.5 w + 52 total wickets after last match = w + 5 ( 23.5 w + 52 ) / ( w + 5 ) = 23.5 - 0.5 = 23 w = 126 so total wickets aftr last match = w + 5 = 131 answer : c" | null |
Question: on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?
A.1.
B.3.
C.5.
D.7.
e ) 9B.
"d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )" | null |
Question: how many different positive integers are factors of 20 ?
A.6.
B.8.
C.4.
D.10.
e ) 12C.
"2 * 10 4 * 5 answer : c" | null |
Question: jim â € ™ s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
A.$ 3.15.
B.$ 4.45.
C.$ 4.80.
D.$ 5.65.
e ) $ 5.40D.
"let the fixed charge of jim â € ™ s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d" | null |
Question: if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?
['A.225 square inches', 'B.45 square inches', 'C.25 square inches', 'D.15 square inches', 'e ) 10 square inches']D.
definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d | null |
Question: at a certain university , 66 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
A.25.
B.37.5.
C.60.
D.62.5.
e ) 75C.
"answer is 75 % total women = 66 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 24 % but question wants to know the percent of men that are tenured 24 % / 40 % = 60 % c" | null |
Question: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 50 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
A.$ 37.80.
B.$ 49.
C.$ 39.20.
D.$ 39.50.
e ) $ 40.60B.
a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.5 = $ 14 - - > x = $ 28 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 28 + 21 = $ 49 . answer : b . | null |
Question: excluding stoppages , the speed of a bus is 58 kmph and including stoppages , it is 40 kmph . for how many minutes does the bus stop per hour ?
A.19.
B.19.13.
C.10.5.
D.11.35.
e ) none of theseA.
"due to stoppages , it covers 18 km less . time taken to cover 18 km = ( ( 18 / 58 ) ã — 60 ) = 19 min . option ( a ) is correct" | null |
Question: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
A.400.
B.465.
C.430.
D.450.
e ) 510B.
"let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b" | null |
Question: what is the 149 th digit to the right of the decimal point in the decimal form of 30 / 33 ?
A.5.
B.6.
C.9.
D.0.
e ) 1C.
to solve , we first have to use some long division . long division allows us to get 30 / 33 in decimal form , which is 0.909090 … where “ 90 ” is repeating . we see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 9 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 0 . in other words , each odd - positioned digit is a 9 , and each even - positioned digit is a 0 . then the 149 th digit to the right of the decimal point and we see that 149 is odd , then 149 th digit is a 9 . answer c . | null |
Question: the salary of a person was reduced by 14 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
A.10 %.
B.16.3 %.
C.13.7 %.
D.15.1 %.
e ) 12.3 %B.
let the original salary be $ 100 new salary = $ 86 increase on 86 = 14 increase on 100 = 14 / 86 * 100 = 16.3 % answer is b | null |
Question: 11 times a number gives 132 . the number is
A.11.
B.12.
C.13.2.
D.none.
e ) can not be determinedB.
"explanation : let the number be ' n ' 11 × n = 132 ⇒ n = 12 correct option : b" | null |
Question: a bullet train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the bullet train must run to reduce the time of journey to 40 min will be .
A.80 kmph.
B.40 kmph.
C.60 kmph.
D.90 kmph.
e ) 30 kmphC.
c 60 kmph time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph | null |
Question: the area of a triangle is with base 12 m and height 5 m ?
A.88 m 2.
B.30 m 2.
C.66 m 2.
D.77 m 2.
e ) 31 m 2B.
"1 / 2 * 12 * 5 = 30 m 2 answer : b" | null |
Question: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ?
A.3 / 10.
B.2 / 5.
C.2 / 7.
D.10 / 21.
e ) 5 / 11C.
from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 7 . the answer is c . | null |
Question: one half of a two digit number exceeds its one third by 9 . what is the sum of the digits of the number ?
A.A.3.
B.B.5.
C.C.7.
D.D.9.
e ) e ) 11D.
"x / 2 – x / 3 = 9 = > x = 54 5 + 4 = 9 answer : d" | null |
Question: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 360 per week . how much does she earn in dollars per hour ?
A.11.
B.10.
C.9.
D.8.
e ) 7B.
"let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 360 per week 36 x = 360 x = 10 correct option : b" | null |
Question: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 15 and 12 . the larger of the two numbers is
A.476.
B.399.
C.450.
D.322.
e ) noneC.
"solution clearly , the numbers are ( 30 x 15 ) and ( 30 x 12 ) . larger number = ( 30 x 15 ) = 450 . answer c" | null |
Question: the difference between the place values of two nines in the numerical 62039295 is
A.89.
B.891.
C.8910.
D.0.
e ) none of themC.
"required difference = ( 9000 - 90 ) = 8910 . answer is c" | null |
Question: dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
A.67.
B.26.
C.88.
D.90.
e ) 75C.
"average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c" | null |
Question: in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?
A.159.
B.194.
C.210.
D.209.
e ) 166C.
"out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students ." | null |
Question: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
['A.96', 'B.108', 'C.120', 'D.132', 'e ) 140']A.
the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a . | null |
Question: the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?
A.5 years.
B.4 years.
C.6 years.
D.7 years.
e ) 8 yearsA.
"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . age of the youngest child = x = 5 years . a )" | null |
Question: a man invested rs . 14,400 in rs . 100 shares of a company at 25 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?
A.rs . 576.
B.rs . 600.
C.rs . 650.
D.rs . 720.
e ) noneA.
"solution number of shares = ( 14400 / 125 ) = 115.2 . face value = rs . ( 100 x 115.2 ) = rs . 11520 . annual income = rs . ( 5 / 100 x 11520 ) = rs . 576 . answer a" | null |
Question: a ladder 22 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 7 feet from the base of the wall . if the top of the ladder slips down 3 feet , how many feet will the bottom of the ladder slip ?
A.12.86.
B.15.
C.18.
D.19.
e ) 25A.
"22 ^ 2 - 7 ^ 2 = 435 it means that the height is equal to 20.85 . since the top of the ladder slips down 4 feet , then the height of the wall = 20.85 - 3 = 17.85 the bottom = sqrt ( 22 ^ 2 - 17.85 ^ 2 ) = sqrt ( 484 - 318.62 ) = 12.86 ans is a" | null |
Question: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?
A.7.
B.9.
C.11.
D.13.
e ) 15D.
( 2 / 18 ) * 117 = 13 grams the answer is d . | null |
Question: if a tire rotates at 400 revolutions per minute when the car is traveling 24 km / h , what is the circumference of the tire ?
A.1 meters.
B.6 meters.
C.5 meters.
D.3 meters.
e ) 7 metersA.
"400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 24,000 m : c is the circumference c = 1 meters correct answer a" | null |
Question: a can do a work in 15 days and b in 20 days . if they work on it together for 7 days , then the fraction of the work that is left is
A.8 / 17.
B.7 / 15.
C.3 / 15.
D.8 / 15.
e ) 11 / 60E.
"person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 7 = 245 remaining work is 300 - 245 = 55 remaining fraction of work is = 55 / 300 = 11 / 60 answer e" | null |
Question: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?
A.220.
B.230.
C.500.
D.1500.
e ) 590D.
n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d | null |
Question: 40 % of a number is added to 60 , the result is the same number . find the number ?
A.300.
B.288.
C.270.
D.100.
e ) 281D.
"( 40 / 100 ) * x + 60 = x 4 x + 600 = 10 x 6 x = 600 x = 100 answer : d" | null |
Question: in right triangle abc , ac is the hypotenuse . if ac is 35 and ab + bc = 55 , what is the area of the triangle abc ?
A.225.
B.450.
C.25 √ 2.
D.200.
e ) 200 √ 2B.
"square ab + bc = 55 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3025 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 35 ^ 2 = 1225 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1225 + 2 * ab * bc = 3025 . 1225 + 2 * ab * bc = 3025 . ab * bc = 900 . the area = 1 / 2 * ab * bc = 450 . answer : b ." | null |
Question: what is the smallest integer that is multiple of 5 , 711
A.A.70.
B.B.35.
C.C.385.
D.D.280.
e ) e ) 140C.
it is the lcm of 5 , 7 and 11 which is 385 . the answer is c . | null |
Question: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 7 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
A.14 / 15.
B.15 / 14.
C.5 / 5.
D.5 / 4.
e ) can not be determinedC.
"average speed of jack = distance / time = 42 / 7 = 6 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = 6 / 10 = 3 / 5 answer c" | null |
Question: the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
A.23 kg.
B.43 kg.
C.21 kg.
D.31 kg.
e ) 43 kgD.
sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d | null |
Question: a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is
A.12.
B.24.
C.18.
D.27.
e ) 25B.
if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b | null |
Question: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 40 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
A.$ 15,360.
B.$ 17,360.
C.$ 18,000.
D.$ 21,360.
e ) $ 30,960E.
"for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 40 % of the benefit ; benefit received = 12000 - 0.4 * 12000 = 12000 - 4800 x = 7200 earning becomes 9360 + 3 x = 9360 + 3 * 7200 = 30960 ans : e" | null |
Question: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?
A.s . 43000.
B.s . 50000.
C.s . 57000.
D.s . 38000.
e ) s . 62000D.
"length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d" | null |
Question: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses e at the restaurant ? ( assume that all boxes are filled to capacity . )
A.96.
B.240.
C.e = 256.
D.e = 384.
e ) e = 480E.
"most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e" | null |
Question: rajani has to read a book of 445 pages . she has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book ?
A.25 days.
B.20 days.
C.46 days.
D.21 days.
e ) none of theseE.
remaining pages to read = 445 – 157 = 288 ∴ reqd . number of days = 288 ⁄ 24 = 12 answer e | null |
Question: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 21 ?
A.2.
B.4.
C.6.
D.8.
e ) 10A.
"n = 3 p + 1 = 7 q + 5 n + 2 = 3 p + 3 = 7 q + 7 n + 2 is a multiple of 3 and 7 , so it is a multiple of 21 . the answer is a ." | null |
Question: a sum of money becomes 7 / 6 of itself in 7 years at a certain rate of simple interest . the rate per annum is ?
A.50 / 13.
B.50 / 17.
C.50 / 19.
D.50 / 21.
e ) 50 / 23D.
"let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 7 years . rate = ( 100 * x ) / ( x * 6 * 7 ) = 50 / 21 % . answer : d" | null |
Question: a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .
A.10.5.
B.11.
C.12.
D.13.
e ) 15A.
leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a | null |
Question: a library has an average of 600 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 :
A.250.
B.260.
C.300.
D.285.
e ) noneC.
"since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c" | null |
Question: the lcm of two numbers is 2310 and hcf is 30 . if one of the numbers is 210 . then what is the other number ?
A.715.
B.825.
C.330.
D.582.
e ) 465C.
"first number * second number = lcm * hcf other number = 2310 * 30 / 210 = 11 * 30 = 330 answer : c" | null |
Question: a small college reduced its faculty by approximately 15 percent to 195 professors . what was the original number of faculty members ?
A.182.
B.208.
C.224.
D.229.
e ) 302D.
"if x is the original number of faculty members , then after 15 % reduction in faculty members number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of faculty members is 229 correct answer - d" | null |
Question: how many seconds will a train 60 meters long take to cross a bridge 120 meters long if the speed of the train is 30 m / sec ?
A.6 sec.
B.8 sec.
C.15 sec.
D.3 sec.
e ) 5 secA.
"d = 60 + 120 = 180 s = 30 mps t = 180 / 30 = 6 sec a ) 6 sec" | null |
Question: if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?
A.38.25 %.
B.40.25 %.
C.82.25 %.
D.50 %.
e ) 65 %C.
if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c | null |
Question: the length of the bridge , which a train 120 m long and traveling at 45 km / hr can cross in 30 sec is ?
A.235.
B.240.
C.245.
D.250.
e ) 255E.
"speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 x = 255 m . answer : option e" | null |
Question: 4 , 12 , 48 , 240 , 1440 , 10080,80640 ( . . . )
A.7620.
B.10080.
C.6200.
D.10020.
e ) 725760E.
"explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 , 8,9 answer : option e" | null |
Question: if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?
A.40 km.
B.76 km.
C.18 km.
D.16 km.
e ) 97 kmA.
"let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a" | null |
Question: there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
A.75.
B.100.
C.125.
D.140.
e ) 225D.
"let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d" | null |
Question: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?
A.44 %.
B.45 %.
C.50 %.
D.55 %.
e ) 60 %A.
"let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )" | null |
Question: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?
A.65 degrees.
B.32 degrees.
C.37 degrees.
D.34 degrees.
e ) 74 degreesB.
"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 – 152 = 32 answer : b" | null |
Question: difference between the length & breadth of a rectangle is 30 m . if its perimeter is 300 m , then its area is ? ? we have : ( l - b ) = 30 and 2 ( l + b ) = 300 or ( l + b ) = 150 ?
A.3 : 5.
B.2 : 3.
C.3 : 6.
D.3 : 4.
e ) 3 : 2E.
solving the two equations , we get : l = 90 and b = 60 . the ratio of length and breath is 90 : 60 = 3 : 2 e | null |
Question: what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
['A.36', 'B.32', 'C.24', 'D.21', 'e ) 15']C.
27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c | null |
Question: if the area of a circle is 16 pi square feet , find its circumference .
A.8 pi feet.
B.28 pi feet.
C.38 pi feet.
D.48 pi feet.
e ) 58 pi feetA.
"the area is given by pi * r * r . hence pi * r * r = 16 pi r * r = 16 ; hence r = 16 feet the circumference is given by 2 * pi * r = 2 * pi * 4 = 8 pi feet correct answer a" | null |
Question: 892.7 – 573.07 – 95.007 = ?
A.224.623.
B.224.777.
C.233.523.
D.414.637.
e ) none of theseA.
"solution given expression = 892.7 - ( 573.07 + 95.007 ) = 892.7 - 668.077 = 224.623 . answer a" | null |
Question: find k if 64 / k = 4 .
A.16.
B.17.
C.18.
D.14.
e ) 13A.
since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a | null |
Question: if 1 + 3 = 10 ; 3 + 5 = 52 ; 5 + 7 = 174 then 7 + 11 = ?
A.354.
B.225.
C.654.
D.741.
e ) 464E.
"1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e" | null |
Question: 10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?
A.30.
B.35.
C.38.
D.40.
e ) 45D.
10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d | null |
Question: 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish
A.1 day.
B.2 days.
C.3 days.
D.4 days.
e ) 5 daysB.
14 men make toy in 5 days after 1 day 14 more worker join m 1 / m 2 = d 2 / d 1 14 / 28 = d 2 / 4 = 2 day answer : b | null |
Question: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19.50 ?
A.10 : 7.
B.9 : 8.
C.11 : 7.
D.13 : 11.
e ) 14 : 8C.
"correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5.50 : 3.50 = 11 : 7" | null |
Question: a sum of rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months , the total amount of rs 500 is received . find the rate of interest ?
A.3 %.
B.4 %.
C.5 %.
D.6 %.
e ) 7 %B.
here p = 468.75 which is the principle . amount = rs 500 amount = si + p 500 = [ 468.75 * ( 20 / 12 ) * r ] / 100 + 468.75 31.25 = 156.25 * 5 r / 100 r = 4 % answer : b | null |
Question: how many positive integers less than 5,000 are evenly divisible by neither 14 nor 21 ?
A.4,514.
B.4,475.
C.4,521.
D.4,428.
e ) 4,349E.
"integers less than 5000 divisible by 14 5000 / 14 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 14 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 14 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ." | null |
Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?
A.123.
B.267.
C.277.
D.124.
e ) 120D.
"let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 110 x = 124 answer : d" | null |
Question: a solid yellow stripe is to be painted in the middle of a certain highway . if 1 gallon of paint covers an area of q square feet of highway , how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
['A.( 5,280 mt ) / 12 q', 'B.( 5,280 pt ) / 12 m', 'C.( 5,280 pmt ) / 12', 'D.( 5,280 ) ( 12 m ) / pt', 'e ) ( 5,280 ) ( 12 p ) / mt']A.
given that : 1 gallon of paint covers an area ofqsquare feet . question : how many gallonsof paint will be needed . . . in any case you will have : ( total area in square feet ) / ( gallons per feet ) = ( total area in square feet ) / q , so q must be in the denominator : eliminate all but a and d . now , lets see where should be t : ( area in square feet ) = ( width in feet ) * ( length in feet ) - - > width = tinchesas 1 feet = 12 inchesthent inches = t / 12 feet , so ( area in square feet ) = ( t / 12 ) * ( length in feet ) , so t must be in the nominator : only a is left . answer : a . | null |
Question: a man buys 20 lts of liquid which contains 30 % of the liquid and the rest is water . he then mixes it with 20 lts of another mixture with 20 % of liquid . what is the % of water in the new mixture ?
A.59.
B.95.
C.80.
D.75.
e ) 65D.
"30 % in 20 lts is 6 . so water = 20 - 6 = 14 lts . 20 % of 20 lts = 4 . so water in 2 nd mixture = 20 - 4 = 16 lts . now total quantity = 20 + 20 = 40 lts . total water in it will be 14 + 16 = 30 lts . % of water = ( 100 * 30 ) / 40 = 75 . answer : d" | null |
Question: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is
A.3 cm.
B.4 cm.
C.6 cm.
D.7 cm.
e ) noneD.
"solution 4 î r 2 = 2 î 7 x 14 â ‡ ’ r 2 = ( 7 x 14 / 2 ) â ‡ ’ 49 â ‡ ’ r = 7 cm . answer d" | null |
Question: if 8 men or 12 women can do a piece of work in 30 days , in how many days can the same work be done by 6 men and 11 women ?
A.10 days.
B.11 days.
C.13 days.
D.15 days.
e ) 18 daysE.
"8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 30 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 30 = 1 / 360 so , 20 women work = 20 / 360 = 1 / 18 ans : 18 days answer : e" | null |
Question: how many positive integer solutions does the equation 8 x + 2 y = 100 have ?
A.50.
B.84.
C.16.
D.35.
e ) 14B.
"formula : ( constant ) / ( lcm of two nos ) = 100 / ( 8 * 2 ) = 84 answer : b" | null |
Question: set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?
A.28.
B.32.
C.36.
D.40.
e ) 44D.
the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d . | null |
Question: the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .
A.1800.
B.2000.
C.1640.
D.2200.
e ) 2400B.
following the above formula , we have the total marks = 50 * 40 = 2000 answer is b | null |
Question: a man sitting in a train which is travelling at 64 kmph observes that a goods train travelling in a opposite direction , takes 18 seconds to pass him . if the goods train is 420 m long , find its speed .
A.32.
B.15.
C.18.
D.20.
e ) 25D.
"relative speed = ( 420 / 18 ) m / s = ( 420 / 18 ) * ( 18 / 5 ) = 84 kmph speed of goods train = 84 - 64 = 20 kmph answer is d" | null |
Question: the speed of a car is 95 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
A.76 kmph.
B.75 kmph.
C.77.5 kmph.
D.56 kmph.
e ) 86 kmphC.
"s = ( 95 + 60 ) / 2 = 77.5 kmph answer : c" | null |
Question: an article is bought for rs . 675 and sold for rs . 800 , find the gain percent ?
A.38 %.
B.28 %.
C.18 %.
D.22 %.
e ) 13 %C.
"675 - - - - 125 100 - - - - ? = > = 18 % answer : c" | null |
Question: a company recently conducted a survey and found that 40,000 of its customers live in rural areas . if the number of customers who live in urban areas is 137 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
A.90,000.
B.91,200.
C.92,400.
D.93,600.
e ) 94,800E.
the number of customers in urban areas is 40,000 + 1.37 * 40,000 = 94,800 . the answer is e . | null |
Question: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 30 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
A.7.5.
B.15.
C.17.5.
D.25.
e ) 32.5E.
"in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 30 = 2.5 km . the time it takes the hiker to complete this distance is 2.5 / 4 hours = 37.5 minutes the cyclist needs to wait 37.5 - 5 = 32.5 minutes the answer is e ." | null |
Question: 3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?
A.41.5 %.
B.42.75 %.
C.43 %.
D.45 %.
e ) 45.75 %B.
"we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 ã — 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 ã — 57 / 100 12 ã — 100 = 9 ã — 5710012 ã — 100 = 9 ã — 4.75 / 100 = 42.75 % b" | null |
Question: if x = 3 ^ 9 and x ^ x = 3 ^ k , what is k ?
A.3 ^ 11.
B.3 ^ 13.
C.3 ^ 25.
D.3 ^ 27.
e ) 3 ^ 81A.
solution : we know that x = 3 ^ 9 which implies x ^ x = ( 3 ^ 9 ) ^ ( 3 ^ 9 ) = 3 ^ ( 9 * 3 ^ 9 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 2 * 3 ^ 9 ) = 3 ^ ( 3 ^ ( 2 + 9 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 11 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 11 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 11 answer : a | null |
Question: carol spends 1 / 4 of her savings on a stereo and 1 / 2 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
A.1 / 4.
B.2 / 7.
C.5 / 12.
D.3 / 8.
e ) 7 / 12D.
"total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 2 ) ( 1 / 4 ) s = ( 1 / 2 ) * ( 1 / 4 ) * s = ( 1 / 8 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 8 ) / s = 3 / 8 answer : d" | null |
Question: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 11.00 ?
A.40.
B.60.
C.90.
D.132.
e ) 240D.
"cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 11 ( 1 / 12 ) * x = 11 x = 132 answer : d" | null |
Question: for all numbers a and b , the operation is defined by ab = ( a + 2 ) ( b – 3 ) . if 3 x = – 20 , then x =
A.– 15.
B.– 6.
C.3.
D.6.
e ) - 1E.
( 3 + 2 ) ( x - 3 ) = - 20 . . x - 3 = - 4 . . x = - 1 e | null |
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