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mathematics
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation s of the mean, what percent of the distribution is less than m+s?
[ "16%", "32%", "48%", "84%", "92%" ]
16% ________________________________________________ m+s 34% ________________________________________________ m 34% ________________________________________________ m-s 16% since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m. thus 16% lie below m-s and 16% lie above m+s now below m+s = 16+34+34 = 84% hence D The answer is: D
D
mathematics
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
[ "7", "6", "8", "9", "5" ]
1/10 + 1/15 - 1/x = 1/18 x = 9 Answer:D The answer is: D
D
mathematics
1/2-[(2/7*7/32)+1]+9/16=
[ "29/16", "19/16", "15/16", "9/13", "0" ]
1/2 - [(2/7*7/32) + 1] + 9/16 = 1/2 - [(1/16) + 1] + 9/16 = 1/2 - [17/16] + 9/16 = 8/16 - 17/16 + 9/16 = 0 The answer is E. The answer is: E
E
mathematics
The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
[ "80,70 kmph", "80,40 kmph", "10,40 kmph", "80,80 kmph", "90,30 kmph" ]
Speed downstream = 60 + 30 = 90 kmph Speed upstream = 60 - 30 = 30 kmph Answer: E The answer is: E
E
mathematics
Find the average of all the numbers between 6 and 34 which are divisible by 5.
[ "15", "18", "20", "22", "None" ]
Sol. Average = (10 + 15 + 20 + 25 + 30 / 5) = 100 / 5 = 20. Answer C The answer is: C
C
mathematics
How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
[ "65 sec", "88 sec", "25 sec", "88 sec", "55 sec" ]
D = 100 + 150 = 250 S = 36 * 5/18 = 10 mps T = 250/10 = 25 sec Answer: C The answer is: C
C
mathematics
A students was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
[ "3", "7", "17", "31", "10" ]
Solution Clearly, we have (3+11+7+9+15+13+8+19+17+21+14+x/12) =12 Number in place of x is 137+x=144 x= 144-137 x= 7. Answer B The answer is: B
B
mathematics
There are three guys who have equal number of bullets. All of them shoot 6 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
[ "18", "19", "20", "21", "27" ]
let initially each was having x bullets they shot 6 bullets so 3x-18=x x=9 so each was having 9 bullets. total was 27 ANSWER:E The answer is: E
E
mathematics
A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 472. What is the sum of the last 8 of the even integers?
[ "588", "594", "600", "606", "612" ]
The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 472 The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) = 472 + 8(16) = 472 + 128 = 600 The answer is C. The answer is: C
C
mathematics
The sum of the ages of 4 children is 52 years. The age of the youngest child is 4. If the intervals of years each born is same find the interval?
[ "4", "8", "10", "6", "Cannot be determined" ]
Explanation: Let the interval is x .The youngest child's age is 4. Each of the other 3 children will then be 4+x, 4+2x, 4+3x We know that the sum of their ages is 52 . so, 4+(4+x)+(4+2x)+(4+3x) = 52 x= 6 Answer: D The answer is: D
D
mathematics
Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?
[ "50%", "90%", "112.5%", "210%", "212.5%" ]
Let's take the original output to be 100 and the new output to be 170% or 170. Let's take the original work hours to be 100 hours and the new work hours to be 80% or 80 hours. The old output per work hour = 100/100 hours or 1. The new output per work hour = 170/80 or 2.125. So the resulting increase is actually new minus old or 1.125 or 112.5%. Choice C The answer is: C
C
mathematics
In 1990 a total of u earthquakes occurred worldwide, some but not all of which occurred in Asia. If v o f these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
[ "u/v", "v/u", "v/(u-v)", "u/(u-v)", "1- (v/u)" ]
We're given a couple of facts to work with: 1) There were a total of u earthquakes 2) Of those earthquakes, v of them occurred in Asia We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia. Let's TEST VALUES u = 5 total earthquakes v = 2 occurred in Asia Thus, there were 3 earthquakes that DID NOT occur in Asia.... The answer to the question is 2:3 We just need to plug in the values for u and v and find the match... Answer A: u/v = 5/2 NOT a match Answer B: v/u = 2/5 NOT a match Answer C: v/(u-v) = 2/(5-2) = 2/3 This IS a match Answer D: u/(u-v) = 5/(5-2) = 5/3 NOT a match Answer E: 1 - (v/u) = 1-2/5 = 3/5 NOT a match C The answer is: C
C
mathematics
What is the remainder when 1201 × 1202 ×1203 × 1204 is divided by 6?
[ "0", "1", "2", "3", "4" ]
The remainders when dividing each number by six are: 1, 2, 3, and 4. The product is 1*2*3*4 = 24 The remainder when dividing 24 by 6 is 0. The answer is A. The answer is: A
A
mathematics
The profits of QRS company rose 35% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
[ "15%", "32%", "40%", "62%", "80%" ]
Assume 100 in march , then 135 in April as 35% increase , Then 108 in may as 20% decrease from April , and then 162 in june which is 150% of 108 . So overall increase is from 100 to 162 is 62% Answer D The answer is: D
D
mathematics
If you roll a fair-sided die twice, what is the probability of getting a (2 ,2)?
[ "1/4!", "1/3!", "1/2!", "1/36", "1/24" ]
total no. in two dice (1,1) ,(2,2) .....(6,) Total number of events= 6*6 Total events of getting same pair(2, 2) = 6 Probability= 6/6*6= 1/6=1/3! B The answer is: B
B
mathematics
A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 25 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
[ "300.", "412.", "432.", "502.", "522." ]
Pastry is divided in 25 customers equally. So,total number of pastry must be a multiple of 25 Only option A satisfies the condition, and hence is the answer The answer is: A
A
mathematics
The cost of paint is 60 per kilograme. A kilogram paint covers 20 square feet. How much will it cost to paint the outside of a cube having each side 10 feet?
[ "3000", "900", "1800", "360", "None of these" ]
Area of cube = 6× (side)2 = 6 × 10 × 10 = 600 square feet. Cost to paint outside of the cube = 600⁄20 × 60 = 1800 Answer C The answer is: C
C
mathematics
Nobel buys an old car for $1000 and spends $1000 on its repairs. If he sells the scooter for $2500, his gain percent is?
[ "10%", "15%", "25%", "20%", "30%" ]
C.P. = 1000+1000 = $2000 S.P. = $2500 Gain = 2500-2000 = $500 Gain% = 500/2000 * 100 =25% Answer is C The answer is: C
C
mathematics
A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
[ "53", "54", "55", "56", "57" ]
12.4*x+26=(4+x)12 solve equation x=55 ANSWER:C The answer is: C
C
mathematics
The list price of an article is Rs.68. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
[ "3.23%", "4.23%", "5.23%", "7.23%", "8.23%" ]
68*(90/100)*((100-x)/100) = 56.16 x = 8.23% ANSWER:E The answer is: E
E
mathematics
The average of six number is 3.99. The average of two of them is 3.4, while the average of the other two is 3.85. what is the average of the remaining two number ?
[ "4.5", "4.6", "4.72", "4.8", "None of these" ]
solution: Sum of the remaining two numbers = (3.99 × 6) - [(3.4 × 2) + (3.85 ×2)] =23.94 -(6.8 + 7.7) = 23.94 - 14.5 = 9.44. ∴ Required average =9.44/2 = 4.72 Answer C The answer is: C
C
mathematics
If there are 4 peanuts in a box and Mary puts 8 more peanuts inside, how many peanuts are in the box?
[ "8", "9", "10", "11", "12" ]
8+4=12 correct answer is E)12 The answer is: E
E
mathematics
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 11 minutes 20 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
[ "3%", "5%", "8%", "10%", "15%" ]
Bob's time = 680 secs. His sis' time = 576 secs. Percent increase needed = (680-576/680) * 100 = 104/640 * 100 = 15%. Ans (E). The answer is: E
E
mathematics
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
[ "45", "60", "75", "90", "None" ]
Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. Answer D The answer is: D
D
mathematics
If x^2 + 9/x^2 = 10, what is the value of x - 3/x
[ "36", "25", "2", "5", "3" ]
To find : x-3/x. Let it be t. => x-3/x = t => (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides). => (10) - 2*3 = 4 => t^2 = 4. Thus t=2 or t=-2. Answer C The answer is: C
C
mathematics
A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
[ "8 PM", "4 PM", "7 PM", "5 PM", "2 PM" ]
1 to 2 = 1/4 2 to 3 = 1/4 + 1/5 = 9/20 After 3 AM = 1/4 + 1/5 - 1/2 = -1/20 1/4 + 9/20 = 14/20 1 h ---- 1/20 ? ----- 14/20 14 hours ==> 5 PM Answer: D The answer is: D
D
mathematics
An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
[ "196", "400", "441", "484", "900" ]
441 = 3^2*7^2 so it can not be the square of an even number multiplied by an odd number. The answer is C. The answer is: C
C
mathematics
15 times a number gives 150. The number is
[ "11", "15", "13", "14", "Cannot be determined" ]
Explanation: Let the number be 'N' 15×N=150⇒N=10 Correct Option: B The answer is: B
B
mathematics
The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
[ "38 cm2", "85 cm2", "65 cm2", "40 cm2", "35 cm2" ]
Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 32/2 = 40 cm2 Answer:D The answer is: D
D
mathematics
A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 1/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
[ "300", "200", "250", "150", "160" ]
Basically, this question is asking you to figure out how many students are being double-counted. A-Club has 200 members (1/2 of 400) B-Club has 250 members (5/8 of 400) C-Club has 300 members (3/4 of 400) We can create an equation to solve this: 200+250+300 = n + x + 2y where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs. The question provides y for us (50). 750 = 400 + x + 100 x =250 C The answer is: C
C
mathematics
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
[ "2500", "2700", "2900", "3100", "3500" ]
Explanation: Total number of votes = 7500 Given that 20% of Percentage votes were invalid => Valid votes = 80% Total valid votes = 7500 X80/100 1st candidate got 55% of the total valid votes. Hence the 2nd candidate should have got 45% of the total valid votes => Valid votes that 2nd candidate got = total valid votes x 45/100 =7500 X 80/100 X 45/100 =2700 ANSWER IS B The answer is: B
B
mathematics
In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
[ "100 cu.m", "1000 cu.m", "10000 cu.m", "2000 cu.m", "4000 cu.m" ]
20 * 10 * 5 = 1000 ANSWER:B The answer is: B
B
mathematics
Three printing presses, E, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take E, working alone at its constant rate, to do the same job?
[ "8", "10", "12", "15", "20" ]
=1/4-1/5=1/20 E can do 1/20 job in 1 hour E can do the whole job in 20 hours=E The answer is: E
E
mathematics
If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is Q:
[ "Q=1", "Q=2", "Q=3", "Q=4", "Q=5" ]
10p/96 should resolve to a integer => 5p/48 should resolve to an integer. Hence p/48 should resolve to a integer. 48 -- > 2^4 * 3. Hence p should have atleast 2^4*3 for p/48 to resolve to a int. The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2). The answer is: B
B
mathematics
A family pays $800 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
[ "$1,000", "$1,200", "$1,400", "$1,800", "$2,200" ]
Upfront payment for insurance plan = 800$ Family needs to pay 30 % of first 1000 $ in expense = 300$ Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 300 = 1100 $ Total amount paid by insurance plan for first 1000 $ = 800 $ Total amount paid by family will equal amount paid by plan when medical expense = 1400 $ (Since insurance plan will pay 100% of amount that exceeds 1100$ ) Answer C The answer is: C
C
mathematics
A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?
[ "44%", "48%", "52%", "42%", "46%" ]
First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race. Then Add the remaining distance as head start for B to win the race. Its best to apply Ratios concept here. Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A Distance covered by B = speed x time = (13/15) x (0.6) = 0.52% (Which means B would have covered 0.52 of the race length during the time in which A has covered 0.6 of the race length. Therefore to win, B needs a headstart of (1 - 0.52 = ) 0.48 of the race length. So the answer is B The answer is: B
B
mathematics
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98 The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?
[ "0.5%", "1%", "1.25%", "3%", "4%" ]
Required percentage = [ (3.00 + 2.52 + 3.84 + 3.68 + 3.96) x 100 ] % (288 + 342 + 324 + 336 + 420) = [ 17 x 100 ] % 1710 ~= 1%. B) The answer is: B
B
mathematics
In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
[ "150", "750", "1,250", "1,500", "2,500" ]
Given 150 deers were caught and they are tagged in the first slot. In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged. Given this 10% approximates the percentage of tagged deer in the forest..here number is 150.. then 100% is 1500.. is the number of deers population in the forest.. Answer: D is correct answer.. The answer is: D
D
mathematics
A person buys an article at $1200. At what price should he sell the article so as to make a profit of 40%?
[ "1670", "1600", "1680", "1900", "1230" ]
C 1680 Cost price = $1200 profit = 40% of 1200 = $480 Selling price = Cost price + Profit = 1200 + 480 = 1680 The answer is: C
C
mathematics
6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is
[ "Rs. 150", "Rs. 170", "Rs. 180", "Rs. 190", "None of these" ]
Explanation: Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2 = 24 : 24 : 12 = 2 : 2 : 1 Money earned by children = 950 x (1/5) = Rs. 190 Answer: Option D The answer is: D
D
mathematics
A girl swims downstream 40 km and upstream 16 km taking 4 hours each time, what is the speed of the girl in still water?
[ "3", "4", "5", "6", "7" ]
40 --- 4 DS = 10 ? ---- 1 16 ---- 4 US = 4 ? ---- 1 M = ? M = (10 + 4)/2 = 7 Answer:E The answer is: E
E
mathematics
The sum of all solutions for x in the equation x^2 – 8x + 21 = |x – 5|+ 4 is equal to:
[ "–7", "7", "20", "12", "14" ]
x^2 - 8x + 17 = |x-5| RHS can be -ve or +ve x^2 - 9x + 22 = 0 x^2 - 7x + 12 = 0 x= 11,4,3,2 We test all 3 values in original equation, all ok. Thus, Sum = 11 + 4 +3 + 2= 20 Ans (C) The answer is: C
C
mathematics
If x−log48+3log2=log125/3−log3, what is the value of x?
[ "2", "1", "3", "5", "8" ]
Explanation: 1/3 log 125= log (125^1/3) = log 5 3 log 2= log (2^3)= log 8 log a + log b= log (a*b) Utilizing the same, LHS= x -log 48 +log 8= x - log 6 - log 8 + log 8 = x - log 6 RHS= log 5 - log 3 => x= log 5 - log 3 + log 6 = log 5 - log 3 + log 2 + log 3 => x= log 10 = 1 Answer B The answer is: B
B
mathematics
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 10 minutes, then the area of the park (in sq. m) is
[ "153200", "240000", "153600", "154000", "154200" ]
Perimeter = Distance covered in 10 min. = 12000 x 10 m = 2000 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 2000 or x = 200. Length = 600 m and Breadth = 400 m. Area = (600 x 400) m2 = 240000 m2. B The answer is: B
B
mathematics
Find the length ofa rectangle is decreased by 40cm & the width is increased by 5cm, a square with the same area asthe original rectangle result. Find the perimeter ofthe original rectangle?
[ "30 cm", "40 cm", "50 cm", "60 cm", "70 cm" ]
Let x and y be the length and breadth of the rectangle respectively. Then, x - 4 = y + 3 or x - y = 7 ----(1) Area of the rectangle =xy; Area of the square = (x - 4) (y + 3) (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2) Solving 1 & 2 , we get x = 16 and y = 9. Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm. C The answer is: C
C
mathematics
In how many years does a sum of Rs. 4000 yield a simple interest of Rs. 16500 at 15% p.a.?
[ "27.5 years", "26.5 years", "25.5 years", "28.5 years", "29.5 years" ]
T = (100 * 16500)/(15 * 4000) = 27.5 years ANSWER:A The answer is: A
A
mathematics
If x is a number such that x^2 + 4x - 5 = 0 and x^2 - 5x + 4 = 0, then x =
[ "5", "4", "1", "-4", "-5" ]
x^2 + 4x - 5 = (x+5)(x-1) = 0 Then x=-5 or x=1. x^2 - 5x + 4 = (x-4)(x-1) = 0 Then x=4 or x=1. Thus x=1. The answer is C. The answer is: C
C
mathematics
In a 100 m sprint race Kelly was given a 3 m head start by Abel. If Abel lost the race to Kelly by a distance of 0.50 m, how many meters more would Abel need to overtake Kelly?
[ "20.5", "18.4", "17.5", "19.9", "21.5" ]
Distance Abel ran before completion of race---100 m-0.50m=99.5m Distance gained on Kelly over 99.5m---3m-0.50m=2.50m then Abel gains 99.5m/2.50m = 1m on Kelly every 39.8 meters. Therefore 39.8 divided by half a meter ( i.e the 0.50 m Abel was defeated with) ANSWER: D. 19.9m The answer is: D
D
mathematics
Shaquan has 5 playing cards, each one is ordered by the number on it, but one card is flipped over. They are numbered 8, 16, 24, x , 40. If X is the card flipped over, what number will be on the other side?
[ "22", "30", "32", "26", "28" ]
The answer is C) 32 because the cards are numbered by multipliers of 8. 8x2 is 16, 8x3 is 24, 8x4 is 32, and 8x5 is 40. The answer is: C
C
mathematics
In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 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?
[ "400", "625", "1250", "2500", "10 000" ]
If x is total number of fish in the pond : 4 = 50/x * 100 => x = 1250 So answer is C The answer is: C
C
mathematics
Avg cost of 6 pencils and 8 pens is Rs. 70.The avg cost of 8 pencils and 10 pens is Rs.90. Find the total cost of 25 pencils and 25 pens?
[ "100", "125", "130", "80", "90" ]
Avg cost of 6 pencils and 8 pens is Rs. 70 (6 pencil + 8 pens) 14=70 therefore 1 pencil cost is 70/14=5, so 6 pencil cost is 6x5=30 and 8 pens cost is 8x5=40 Again, avg cost of 8 pencils and 10 pens is Rs.90 (8 pencil + 10 pens) 18=90 therefore 1 pencil cost is 90/18=5, so 8 pencil cost is 8x5=40 and 10 pens cost is 10x5=50 So 25 pencil cost is (25/a)=125 and 25 pens cost is (25x5)=125 ANSWER:B The answer is: B
B
mathematics
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
[ "2", "5", "6", "1", "0" ]
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2. Thus, when 2n is divided by 4, the remainder is 2. ANSWER A The answer is: A
A
mathematics
A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
[ "21 years", "22 years", "20 years", "24 years", "26 years" ]
Explanation: Let's Son age is x, then Father age is x+22. => 2(x+2) = (x+22+2) => 2x+4 = x+24 => x = 20 years Option C The answer is: C
C
mathematics
Today is Monday. After 61 days, it will be
[ "Sunday", "Saturday", "Monday", "Thursday", "Wednesday" ]
61 days = 8 weeks 5 days = 5 odd days Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days) = Saturday Answer is B The answer is: B
B
mathematics
If f(x)=4x−1 and g(x)=2x+2 for all integers, which of the following is a possible value of g(f(x))?
[ "-23", "-17", "2", "16", "20" ]
g(f(x)) = 2*f(x)+2 = 2*(4x-1)+2 = 8x Of these five options, only 16 has the form 8x. The answer is D. The answer is: D
D
mathematics
A train running at the speed of 126 km/hr crosses a pole in 9 seconds. Find the length of the train.
[ "150 meter", "286 meter", "186 meter", "315 meter", "265 meter" ]
Speed = 126*(5/18) m/sec = 35 m/sec Length of Train (Distance) = Speed * Time (35) * 9 = 315 meter Answer:D The answer is: D
D
mathematics
(3080 + 6160) / 28
[ "380", "350", "330", "310", "None of these" ]
Explanation: As per BODMAS rule, first we will solve the equation in bracket then we will go for division = (9240)/28 = 330 Option C The answer is: C
C
mathematics
5 - [5 - {5 - 5(5 + 5)}] = ?
[ "5", "-45", "45", "50", "60" ]
Explanation: => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)] = 5 - (50) = - 45 Answer: Option B The answer is: B
B
mathematics
A and B invests Rs.5000 and Rs.6000 in a business. After 6 months, A withdraws two-fifth of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
[ "3:5", "7:8", "5:6", "3:4", "7:9" ]
A : B (5000*6)+(3000*6) : (6000*8)+(4000*4) 48000 : 64000 3 : 4 Answer: D The answer is: D
D
mathematics
The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
[ "1/2", "1", "3/4", "3/5", "3/7" ]
Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2 Ans.(A) The answer is: A
A
mathematics
The original price of a suit is $200. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?
[ "$178.50", "$182.50", "$185.50", "$187.50", "$200" ]
0.75*(1.25*200) = $187.50 The answer is D. The answer is: D
D
mathematics
Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'?
[ "4", "5", "6", "8", "7" ]
If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles. V - x = A + x --- (1) If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles. V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2) From (1) we have V - A = 2x Substituting V - A = 2x in (2) 6x = 30 => x = 5. ANSWER:B The answer is: B
B
mathematics
A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
[ "23.75", "22", "20", "19.2", "None of these" ]
C.P. of mixture = 80×15+20×20 /80+20=16 ∴ S.P. = (100+25)/100×16=20 Answer C The answer is: C
C
mathematics
A certain car can travel 72 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
[ "52", "65", "117", "91", "104" ]
Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters Time = 5.7 hours 1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile Speed (km/hour)= D/T = 72 (km*) x 3.9 x 3.8 / 5.7 replace (km*) to miles ; multiply by 1/1.6 mile Speed (miles/hour)= 72x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour Ans :C PS :i felt the factors were easy to cancel out ,so didn't require much rounding off = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 117 C The answer is: C
C
mathematics
Which of the following fractions is greater than 1/7?
[ "1. 12/50", "2. 3/11", "3. 2/9", "4. 4/17", "5. 6/24" ]
1. 12/50 12.5/50 = 1/4 thus 12/50 < 1/4 2. 3/11 3/12 = 1/4 thus 3/11 > 1/4 3. 2/9 2/8 = 1/4 thus 2/9 < 1/4 4. 4/17 4/16 = 1/4 thus 4/17 < 1/4 5. 6/24 6/24 = 1/4 A The answer is: A
A
mathematics
Of the 3,600 employees of Company X, 1/4 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
[ "25%", "22.2%", "20%", "12.5%", "11.1%" ]
Welcome, just post the question and the choices Let's see, the way I did it was 1/4 are clerical out of 3600 so 900 are clerical 900 reduced by 1/3 is 900*1/3 so it reduced 300 people , so there is 600 clerical people left but since 600 people left, it also reduced from the total of 3600 so there are 3000 people total since 600 clerical left / 300 people total you get (A) 20% Answer : C The answer is: C
C
mathematics
If w and y are different prime numbers less than ten, what must be true about the sum of w and y?
[ "the sum is even", "the sum is odd", "the sum is less than ten", "the sum is greater than ten", "the sum is less than 13" ]
This has to be solved by checking for each option: Prime numbers less that 10 = 2, 3, 5, 7 A. the sum is even May or may not be true. w = 3, y, = 5 -> True. w = 2, y = 3 - True B. the sum is odd May or may not be true. w = 3, y, = 5 -> False. w = 2, y = 3 - True C. the sum is less than ten May or may not be true w= 5, y = 7, Sum = 12 w = 2, y = 3. Sum = 5 D. the sum is greater than ten May or may not be true w= 5, y = 7, Sum = 12 w = 2, y = 3. Sum = 5 E. the sum is less than 13 This will always be true. Maximum sum = 7 + 5 = 12. This is always less than 13. Correct Option: E The answer is: E
E
mathematics
It was 7:00 when Bill looked at the clock, he looks at the clock again 30 minutes later. What time is it now?
[ "7:30", "7:00", "8:00", "1:28", "2:40" ]
If it's 7:00 and 30 minutes pass buy, it will be 7:30 A The answer is: A
A
mathematics
What distance will be covered by a bus moving at 36 kmph in 30 seconds?
[ "287", "600", "289", "300", "207" ]
36 kmph = 36 * 5/18 = 10 mps D = Speed * time = 10 * 30 = 300 m. Answer:D The answer is: D
D
mathematics
Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
[ "12 : 15 :19", "12 : 15 :29", "12 : 15 :11", "12 : 15 :16", "12 : 15 :13" ]
Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16. Answer: D The answer is: D
D
mathematics
If f(x)= 2x^2- 3x+5 and g(y)= 2y-4, then g(f(x))
[ "7x^2+45x+9", "9x^2-15x+4", "4x^2-6x+6", "8x^2-9x+6", "9x^2+79x+78" ]
g(f(x)) = 2(f(x)) -4 =2(2x^2-3x+5)-4 =4x^2-6x+10-4 =4x^2-6x+6 the answer is C The answer is: C
C
mathematics
If 0 < x ≤ 3, then which one of the following is the maximum value of (x – 1)^2 + x ?
[ "–2", "–1", "7", "1", "2" ]
the maximum value of (x – 1)^2 + x for 0 < x ≤ 3 is when x=3 --> (x – 1)^2 + x =7 Answer C The answer is: C
C
mathematics
Excluding stoppages, the speed of a bus is 82 kmph and including stoppages, it is 75 kmph. For how many minutes does the bus stop per hour?
[ "5.12", "4.13", "6.15", "7.5", "None of these" ]
Due to stoppages, it covers 7 km less. Time taken to cover 7 km = ((7/82)×60) = 5.12 min. Option(A) is correct The answer is: A
A
mathematics
Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
[ "19.7", "19.9", "20.9", "21.9", "22" ]
Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 A) The answer is: A
A
mathematics
A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
[ "2:3:5", "3:4:7", "4:5:9", "6:5:9", "None of these" ]
A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12) = 144:192:336 = 3:4:7 ANSWER:B The answer is: B
B
mathematics
A reduction of 10% in the price of oil enables a house wife to obtain 6kgs more for Rs.900, what is the reduced price for kg?
[ "13", "15", "25", "17", "19" ]
900*(10/100) = 90 ---- 6 ? ---- 1 => Rs.15 Answer:B The answer is: B
B
mathematics
The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 6 ?
[ "96", "106", "158", "116", "122" ]
Average = total runs / no.of innings = 32 So, total = Average x no.of innings = 32 * 20 = 640 Now increase in avg = 4 runs. So, new avg = 32+6 = 38 runs Total runs = new avg x new no. of innings = 38 * 21 = 798 Runs made in the 11th inning = 798-640 = 158 ANSWER:C The answer is: C
C
mathematics
R and S together can plough a field in 10 hours but by himself R requires 15 hours. How long would S take to plough the same field?
[ "24hours", "5 hours", "10hours", "15hours", "20hours" ]
f R and S together can do a piece of work in x days and R alone can do the same work in y days, then S alone can do the same work in x y/ y – x days. the No. of hours required by S= 10 × 20/ 20 – 10 = 200/10 = 20 hours E The answer is: E
E
mathematics
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
[ "8000", "80288", "2668", "2600", "2781" ]
Let the sum be Rs. x. Then, [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160 18x + 45x + 39x = (8160 * 100) 102x = 816000 => x = 8000. Answer:A The answer is: A
A
mathematics
The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
[ "Rs. 3096", "Rs. 4076", "Rs. 4085", "Rs. 4096", "Rs. 5023" ]
Explanation: Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096. ANSWER IS D The answer is: D
D
mathematics
If g(x) = ax^5 + bx^3 + 6, and g(5) = 10, then g(–5) =?
[ "– 10", "– 8", "– 6", "0", "2" ]
g(5) = 10 or, 5^5 a + 5^3 b + 6 = 10 or, 5^5 a + 5^3 b = 4 g(-5) = -5^5 a - 5^3 b + 6 = - (5^5 a + 5^3 b) + 6 = - 4 + 6 = 2 = (E) The answer is: E
E
mathematics
Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
[ "40%", "45%", "57%", "58%", "60%" ]
tot no of votes = (1136+7636+11628) = 20400 req = > (11628/20400 * 100) = > 57% ANSWER C The answer is: C
C
mathematics
If x is an odd integer and y = 2x + 8, which of the following CANNOT be a divisor of y?
[ "10", "14", "18", "21", "22" ]
x takes odd values as 1,3,5,7., y=2x+8 x is an odd term so 2x must be an even term when it adds with 8 so it must be a even integer 21 didn't follows this condition ans is D The answer is: D
D
mathematics
A student finds the sum 1 + 2 + 3 + ... as his patience runs out. He found the sum as 575. When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed?
[ "16", "18", "14", "20", "22" ]
Explanation : Sum of 1st 10 natural numbers (1 – 10) = 1 + 2 + …10 = 55. Sum of next 10 natural numbers (11 – 20) = 10 + 11 + 12 +…20 = 100 + 55 = 155. Sum of next 10 natural numbers (31 – 40) = 255. Sum of numbers from 31 – 40 = 355 and so on and on. So, we have here 55 + 155 + 255 = 465. If we add 355 to 465, it will be way more than 575. So, we can add one by one. 465 + 31 + 32 + 33 = 561. 465 + 31 + 32 + 33 +34 = 595. Thus, the sum should be 595 instead of 575, and the missing number is 20. Answer : D The answer is: D
D
mathematics
A pharmaceutical company received $4 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
[ "8%", "15%", "45%", "52%", "58%" ]
Solution: This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer. We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios. First 20 Million royalties/sales = 4/20= 1/5 Next 108 Million royalties/sales = 9/108 = 1/12 Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents. First 20 Million royalties/sales = (4/20) x 60 = 12 Next 108 Million royalties/sales = 9/108 = (1/12) x 60 = 5 We can plug 12 and 5 into our percent change formula: (new – old)/old x 100 [(5 – 12)/12] x 100 -175/3 x 100 At this point we can stop and consider the answer choices. Since we know that 175/3 is just a bit less than ½, we know that -175/3 x 100 is about a 58% decrease. Answer E. The answer is: E
E
mathematics
how many zeros are there in 50!
[ "10", "11", "12", "13", "14" ]
To find the number of trailing zeroes in 50! factorial we must find the number of integral values in : 50/5 + 50/5^2 + 50/5^3 +......... = 10+2+0+0.... =12 ANSWER:C The answer is: C
C
mathematics
A shopkeeper offers 2.5% discount on cash purchases. What cash amount would Rohan pay for a cycle the marked price of which is $650?
[ "$523.89", "$600.25", "$710.45", "$690.63", "$633.75" ]
S.P. = 97 1/2% of $650 = 195/2 * 1/100 * 650 = $633.75 Answer is E The answer is: E
E
mathematics
Points M(13,22) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN?
[ "(5,0)", "(0,5)", "(0, (136^(1/2))/2)", "(3/2,0)", "(9,15)" ]
The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:- The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints. So, x=(13+5)/2=9 and y=(22+8)/2=15 --> coordinates of the midpoint are (9, 15). Answer: E. The answer is: E
E
mathematics
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
[ "12:8", "8:16", "9:16", "8 :12", "16:9" ]
Water:soap = 3:2 Soap:Salt=12:8 => For 12 soap, salt = 8 => For 2 Soap, salt = (8/12)*2 = 16/12=4/3 So, water:soap:salt = 3:2:4/3 = 9:6:4 After open container, water:soap:salt = 2.25:6:4 So, water:salt = 2.25:4 = 9:16 ANSWER:C The answer is: C
C
mathematics
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 1 o'clock in the afternoon?
[ "180°", "154°", "160°", "170°", "150°" ]
The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour. In 5 hours, the angle traced by the hour hand is 5×30° = 150° The answer is E. The answer is: E
E
mathematics
If x is equal to the sum of the integers from 30 to 40, inclusive, and y is the number of EVEN integers from 30 to 40, inclusive, what is the value of x+y ?
[ "171", "281", "391", "591", "601" ]
sum s= n/2{2a+(n-1)d} = 11/2{2*30+ (11-1)*1} =11*35=385 =X number of even number =( 40-30)/2 +1 = 6= Y X+Y = 385+6 =391 C The answer is: C
C
mathematics
The unit digit in the product (224 * 607 * 214 * 863) is:
[ "2", "5", "6", "8", "10" ]
Explanation: Unit digit in the given product = Unit Digit in (4*7*4*3) = 6 ANSWER: C The answer is: C
C
mathematics
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
[ "36 1/3%", "37 1/3%", "33 1/3%", "33 1/8%", "31 1/3%" ]
1/4 CP = 210 SP = 21*(80/100) = 168 SP = 840*(120/100) = 1008 1008 - 168 = 840 3/4 SP = 630 Gain = 210 630 --- 210 100 --- ? => 33 1/3% Answer:C The answer is: C
C
mathematics
A man buy a book in Rs50 & sale it Rs70. What is the rate of profit ???
[ "10%", "40%", "30%", "25%", "28%" ]
cp=50 sp=70 profit=70-50=20 %=20/50*100=40% ANSWER:B The answer is: B
B
mathematics
How many prime numbers are between 51/13 and 89/9?
[ "0", "1", "2", "3", "4" ]
51/13= 4- 89/9= 10- Prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . Answer C The answer is: C
C
mathematics
Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 50 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?
[ "35", "36", "37", "38", "50" ]
Amount earned by James = 40*x + 10*2x =60x Therefore, Amount earned by James = 60x But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x [[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 60x]] So x*(1.5y -45 +30) = 60x Or x*(1.5y - 15) = 60x So 1.5y - 15 = 60 So 1.5y = 75 So y = 50 Answer is E The answer is: E
E
mathematics
If the sides of a triangle are 30 cm, 26 cm and 10 cm, what is its area?
[ "120", "110", "130", "140", "150" ]
The triangle with sides 30 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 30 cm. Area of the triangle = 1/2 * 26 * 10 = 130 cm2 Answer: Option C The answer is: C
C
mathematics
What percent of a day is 6 hours?
[ "6.25%", "20%", "25%", "12.5%", "10 %" ]
Total hours in a day = 24 Required percent =6×100=25% --- 24 Answer: Option C The answer is: C
C
mathematics
If 2x = 3√32, then x is equal to :
[ "3/5", "5/3", "15", "25", "NOne" ]
Sol. 2x = 3√32 ⇔ 2x = (32)1/3 = (25)1/3 = 25/3 ⇔ x = 5/3. Answer B The answer is: B
B
mathematics
If a,b and c are consecutive positive integers and a>b>c. What can be the value of (a^2-b^2)(b^2-c^2)?
[ "21", "79", "143", "231", "450" ]
Since a,b and c are consecutive positive integers and a>b>c, we can write them as (x + 1), x and (x - 1) respectively (a^2-b^2)(b^2-c^2) can be simplified into (2x + 1)(2x - 1) = 4x^2 - 1 using the options to find the product, only C. 143 satisfactorily gives us x as an integer ANSWER:C The answer is: C
C