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mathematics

A bag consists of 1 rupee, 50 paise and 25p coins and their total value in rupees is Rs 1120 .These three types of coins are in the ratio 3:20:4. How may 25 paisa coins are there?

The ratio is 100p: 50 p : 25 p =4 : 2: 1 The coins are in the ratio = 3 :20: 4 The ratio of their values in rupees=> 12 :40 :4 The value of 25 p coins in total Rs 1120 = 1120 x 4/56= 80 rupees Number of 25 p coins are = 80x4 = 320 coins Answer:C The answer is: C

C

mathematics

16.02 × 0.001 = ?

16.02 × 0.001 = ? or,? = 0.01602 Answer D The answer is: D

D

mathematics

A train 200 m long running at 54 kmph crosses a platform in 25 sec. What is the length of the platform?

Length of the platform= 54 * 5/18 * 25 = 375 – 200 = 175 Answer:A The answer is: A

A

mathematics

x - y =2 2x = 2y + 4 The system of equations above has how many solutions?

x-y=2 ---------------1 2x=2y+4 ---------------2 Divide equation 2 by 2: 2x/2=(2y+4)/2 x=y+2 x-y=2----------------3 Equation 1 and 3 are equal and thus have infinitely many solutions: x-y=2 x=4, y=2 x=6, y=4 x=7, y=5 Ans:D The answer is: D

D

mathematics

Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?

Let the amount lent at 7% be Rs. x Amount lent at 10% is Rs. (6000 - x) Total interest for one year on the two sums lent = 7/100 x + 10/100 (6000 - x) = 600 - 3x/100 => 600 - 3/100 x = 450 => x = 5000 Amount lent at 10% = 1000 Required ratio = 5000 : 1000 = 5 : 1 Answer:A The answer is: A

A

mathematics

There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number?

Let the two positive numbers be 5x and 8x respectively. 8x - 5x = 36 3x = 36 => x = 12 => Smaller number = 5x = 60. Answer: D The answer is: D

D

mathematics

Guna has 8 flavors of ice cream in him parlor. How many options are there for Thilak to pick a one-flavor, two-flavor, three-flavor, four-flavor, five-flavor, six-flavor,seven-flavor or eight-flavor order?

8C1 + 8C2+ 8C3+8C4+8C5+8C6+8C7+8C8 = 395. Answer: B The answer is: B

B

mathematics

City A to city B, Andrew drove for 1hr at 48 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?

The total distance is 1×48+3×60=228 And the total time is 4 hours. Hence, Average Speed=(Total Distance/Total Time) =228/4=57 A The answer is: A

A

mathematics

How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 -> 9 (X) 2343 -> 12 (/) 3474 -> 18 (X) 4131 -> 9 (X) 5286 ->21 (/) 5340 -> 12 (/) 6336 -> 18 (X) 7347 -> 21 (/) 8115 -> 15 (/) 9276 -> 24 (/) Required number of numbers = 6. ANSWER IS B The answer is: B

B

mathematics

What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards, it contains all Queens?

nCr = n!/(n-r)!r! Total number of possible hands = 52C5 52C5 = 2274090 Number of hands with 4 Queens = 4C4 × 48C1 4C4 = 24 48C1 = 48 (other 1 card must be chosen from the rest 48 cards) Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015. Option is B The answer is: B

B

mathematics

A man is standing on a railway bridge which is 165 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.

If length of train is l and speed of train is s, then l/s = 8 (l+165)/s = 20 (l+165)/l = 20/8 =5/2 2l+330 =5*l 3*l= 330 l=110 mtrs s= l/8 = 110/8 = 13.75 m/sec ANSWER:B The answer is: B

B

mathematics

A bag contains 12 white &18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?

The probability that first ball is white: =12C130C1=12C130C1 =1230=1230 =25=25 Since, the ball is not replaced; hence the number of balls left in bag is 29. Hence, the probability the second ball is black: =18C129C1=18C129C1 =1829=1829 Required probability, =(25)×(1829)=(25)×(1829) =36/145 B The answer is: B

B

mathematics

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, then how old is B?

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 47 5x = 45 => x = 9 Hence, B's age = 2x = 18 years. Answer: C The answer is: C

C

mathematics

A can do a certain job in 18 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

Ratio of times taken by A and B = 160 : 100 = 8 : 5. Suppose B alone takes x days to do the job. Then, 8 : 5 :: 18 : x = 8x = 5 x 18 =x = 11 1/4 days. Answer is A. The answer is: A

A

mathematics

A sun is divided among X, Y and Z in such a way that for each three rupees X gets, Y gets two rupees and Z gets 80 paisa. If the share of Y is RS. 55, what is the total amount of X and Y?

x:y:z = 300:200:80 15:10:4 10 --- 55 19 --- ? => 104.5 Answer: C The answer is: C

C

mathematics

Exactly 36% of the numbers in set W are even multiples of 3. If 40% of the even integers in set W are not multiples of 3, what percent of the numbers in set W are not even integers?

Everything is correct except the red part with a typo: it should be N=0.6W --> even numbers are 60% of W --> 40% of W are not even integers. Answer: D. The answer is: D

D

mathematics

A, Band C can do a piece of work in 11 days, 20 days and 20 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?

(A+B)'s 1 day's work = 1/11+1/20 = 31/220 (A+C)'s 1 day's work = 1/11+1/20 = 31/220 work done in 2 day's = 31/220+31/220= 31/110 31/110th work done in 2 days work done= 110/31*2 = 7 days (approx) ANSWER:A The answer is: A

A

mathematics

Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $28 more. What was his original selling price?

Let P be the original purchase price of the product. Bill originally sold the product for 1.1*P. In the second scenario, the purchase price is 0.9*P. A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P Thus, according to the information in the question, 1.17P - 1.1P = 28 0.07 = 28 P = 400 The original selling price was 400*1.1 = 440. The correct answer is E. The answer is: E

E

mathematics

I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?

x*(85/100) = (480 - x)119/100 x = 280 Answer:B The answer is: B

B

mathematics

The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

Total no of ways arranging 5 letter with one letter redundant is 5!/2!=60 No of ways two I's can be together 4!=24 no of ways at least one alpha is between two I's =60-24=36 ANS:D The answer is: D

D

mathematics

The sides of a square region, measured to the nearest centimeter, are 10 centimeters long. The least possible value of the actual area of the square region is

Though there might be some technicalities concerning the termnearest(as 9.5 is equidistant from both 9 and 10) the answer still should be : 9.5^2=90.25. Answer: E The answer is: E

E

mathematics

A monkey ascends a greased pole 22 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?

The money is climbing 1meter in 2min. This pattern will go on till he reaches 20meters. I mean this will continue for first 20*2=40mins. he would have reached 20meters. After that he will climb 2meters and he will reach the pole. So total time taken = 40 + 1 = 41mins. So, asnwer will be B The answer is: B

B

mathematics

In an office, totally there are 5200 employees and 45% of the total employees are males. 50% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?

Number of male employees = 5200* 45/100 = 2340 Required number of male employees who are less than 50 years old = 4160 * (100 - 50)% = 2340* 50/100 = 1170. ANSWER:B The answer is: B

B

mathematics

The value of (9x10^8)(5x10^9) is closest to which of the following?

multiplying these we get, 45 x 10^8 x 10^9 = 4.5 x 10^18 which is closer to 10^19 Answer: A The answer is: A

A

mathematics

Virginia, Adrienne, and Dennis have taught history for a combined total of 102 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?

Let number of years taught by Virginia = V number of years taught by Adrienne = A number of years taught by Dennis = D V+A+D = 96 V= A+9 =>A = V-9 V= D-9 => A = (D-9)-9 = D-18 D-9 + D-18 + D =102 => 3D = 102 + 27 = 129 => D = 43 Answer D The answer is: D

D

mathematics

Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is

Solution Relative Speed = (36 + 45) km/hr = (81 x 5/18) m/sec = (45/2) m/sec Length of the train = (45 / 2 x 8) m = 180 m. Answer D The answer is: D

D

mathematics

Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer D)$147 The answer is: D

D

mathematics

If fy > 0 and yz < 0, which of the following must be negative:

fy > 0 means that fy is positive. yz < 0 means that yz is negative. f(y^2)z = (fy)(yz) = positive*negative = negative. Thus option C is always negative. The answer is: C

C

mathematics

A car covers a distance of 660 km in 6 hours. Find its speed?

660/6 = 110 kmph Answer:D The answer is: D

D

mathematics

Find the value of (70+ 28/100) × 100

(7000 +28)/100 * 100 = 7028 Answer : A The answer is: A

A

mathematics

In a queue if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?

Sol. Required number = 16 *^30 = 20 B The answer is: B

B

mathematics

In how many ways can the letters of the word 'LEADER' be arranged?

Explanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. Required number of ways = 6! / (1!)(2!)(1!)(1!)(1!) =360. ANSWER IS C The answer is: C

C

mathematics

If 144/0.144 = 14.4/x, then the value of x is:

Given Expression =[a(Power2) - b(Power 2)]/(a + b)(a - b) =[a(Power 2 - b(Power 2)]/[a(Power 2) - b(Power 2)] = 1. Answer is B. The answer is: B

B

mathematics

A and B can do a work in 6 days, B and C in 2 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together?

One day work of A and B = 1/6 One day work of B and C = 1/2 One day work of C and A = 1/8 2(A + B + C) = 1/6 + 1/2 + 1/8 2(A + B + C) = 19/24 (A + B + C) = 19/48 Number of days required = 48/19 days. Answer: D The answer is: D

D

mathematics

The length of the longest rod that can fit in a cubical room of 4 m side is?

100% Answer:A The answer is: A

A

mathematics

Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?

Explanation: When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years. Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32. Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years. Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23. Answer: A) 32 years, 23 years The answer is: A

A

mathematics

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?

Explanation: i) Let the ages of the five members at present be a, b, c, d & e years. And the age of the new member be f years. ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1) iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2) ==> a + b + c + d + e = 5x + 15 ==> a + b + c + d = 5x + 15 - e ------ (3) iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above, The new average is: (5x + 15 - e + f)/5 Equating this to the average age of x years, 3 yrs, ago as in (2) above, (5x + 15 - e + f)/5 = x ==> (5x + 15 - e + f) = 5x Solving e - f = 15 years. Thus the difference of ages between replaced and new member = 15 years. Answer: D The answer is: D

D

mathematics

A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.238 where as B does not. In what ratio should they divide the second year's profit?

Explanation: 3: 4 A = 3/7*238 = 102 402: 400 201:200 Answer:B The answer is: B

B

mathematics

A train of length 250 metres takes 45 seconds to cross a tunnel of length 350metres. What is the speed of the train in km/hr?

Sol. Speed = [250 + 350/ 45] m/sec = [600 / 45 * 18/5] km/hr = 24 km/hr. Answer D The answer is: D

D

mathematics

After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5130. What was the number of original inhabitants?

Let the total number of original inhabitants be x. (75/100) * (90/100) * x = 5130 (27/40) * x = 5130 x = 5130 * 40 / 27 = 7600 The answer is B. The answer is: B

B

mathematics

When x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?

When x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1. When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6. Equate those two: 3y + 1 = 5z + 6; y = (5z + 5)/3. Answer: D. The answer is: D

D

mathematics

A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 72 km downstream?

Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 72/26 = 36/13 hours. Answer:B The answer is: B

B

mathematics

The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?

C 12 (X + Y) – (Y + Z) = 12 X – Z = 12 The answer is: C

C

mathematics

Twelve years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages

Explanation: Let the present age of P and Q be 3x and 4x respectively. Twelve years ago, P was half of Q in age => 2(3x – 12) = (4x – 12) => 6x – 24 = 4x – 12 => 2x = 12 => x = 6 7x = 7*6 = 42 Answer: Option C The answer is: C

C

mathematics

10 friends went to a hotel and decided to pay the bill amount equally. But 9 of them could pay Rs. 50 each as a result 10th has to pay Rs. 180 extra than his share. Find the amount paid by him.

Explanation: Average amount paid by 9 persons = Rs. 50 Increase in average due to Rs. 50 paid extra by the 10th men = Rs. 180/9= Rs. 20 Therefore, Average expenditure of 10 friends = Rs. 50 + Rs. 20 = Rs. 70 Therefore, Amount paid by the 10th men = Rs. 70 + Rs. 50 = Rs. 120 Correct Option: D The answer is: D

D

mathematics

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?

Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years. Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years. Husband's present age (90 - 50) = 40 years. Answer:B The answer is: B

B

mathematics

Two pipes A and B can separately fill a tank in 20 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?

4/20 + x/15 = 1 x = 12 ANSWER:A The answer is: A

A

mathematics

A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 35% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?

1st year Income= I 1st year savings= S 1st year Expense= E1 2nd year Income = 1.35I 2nd year savings= 2S (100% increase) 2nd Year expense= E2 E1+ E2= 2E1 E2=E1 That means Expenses are same during both years. With increase of 35% income the savings increased by 100%. or S= .35I or S= 35% of Income E is the answer The answer is: E

E

mathematics

x+(1/x) = 4 find x^2 + (1/x^2)

squaring on both sides (x+1/x)^2=4^2 x^2+1/X^2=16-2 x^2+1/X^2=14 ANSWER:D The answer is: D

D

mathematics

During a clearance sale, a retailer discounted the original price of its TVs by 24% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?

VERITAS PREPOFFICIAL SOLUTION: D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 62%. E The answer is: E

E

mathematics

If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

29.94/ 1.45 = 299.4/14.5 = (2994/14.5) x 1/10) [ Here, Substitute 172 in the place of 2994/14.5 ] = 172/10 = 17.2 Answer is A. The answer is: A

A

mathematics

What is the solution of the equations x - y = 0.1 and 1(x + y)-1 = 2 ?

Answer x - y = 0.1 ...(i) and 1(x + y)-1=2 ⇒ 1/ (x + y) = 2 ⇒ 2(x + y) =1 ⇒ x + y = 1/2 ...(ii) On solving Eqs.(i) and (ii),we get x = 0.3 and y = -0.2 Correct Option: A The answer is: A

A

mathematics

Carrie likes to buy t-shirts at the local clothing store. They cost $8.75 each. One day, she bought 18 t-shirts. How much money did she spend?

$8.75*18=$70. Answer is B. The answer is: B

B

mathematics

How many words can be formed using the letters of the word “CORPORBTION”?

In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN (OOAIO). This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different. Number of ways arranging these letters = 7! = 2520. 2! Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5! = 20 ways. 3! Required number of ways = (2520 x 20) = 50400. E The answer is: E

E

mathematics

A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?

Typical dosage is Dose : weight :: 2: 15. Now if weight is 75 :(75/15)) then typical dosage would be 2 *5 = 10 cc. Dosage = 18 cc. Dosage is greater by 2 cc. % dosage is greater: (2 / 10)*100 = 20 % E is the answer. The answer is: E

E

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 35 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?

Pastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35 Only option A satisfies the condition, and hence is the answer The answer is: A

A

mathematics

If a and b are nonzero integers such that 2a+1 = 5b+1, then each of the following must be true EXCEPT

This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though. We're told that A and B are NONZERO INTEGERS and that 2a+1 = 5b+1 or 2A = 5b. We're told that each of the answer is always true EXCEPT for one of them... Before we get to the actual work, it's important to note a few details: 1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE... 2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question. Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time... A = 5 B = 2 AND A = -5 B = -2 Answer A: 0 < B/A < 1 2/5 and -2/-5 both = 2/5. Answer A appears true. Answer B: AB is positive (2)(5) and (-2)(-5) both = +10. Answer B appears true. Answer C: B is between 0 and A on the number line 0....2....5 -5....-2....0 Answer C appears true. Answer D: A/B = 10/4 5/2 = -5/-2 10/4 = 5/2 Answer D appears true. Answer E: A - B is positive 5 - 2 = 3 -5 - (-2) = -3 *****This is NOT always true. Final Answer: E The answer is: E

E

mathematics

January 1, 2008 is Saturday. What day of the week lies on Jan 1, 2009?

Explanation: Number of odd days in 2008 = 2 (since it is a leap year) (we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008) Given that January 1, 2008 is Saturday. Hence January 1, 2009 = (Saturday+ 2 odd days) = Monday Answer: Option E The answer is: E

E

mathematics

Look at this series: 28, 25, 30, 27, 32, 29, ... What number should come next?

Explanation: In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on. Answer: Option B The answer is: B

B

mathematics

A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?

WC = 1:2 2x + x = 1/14 => x = 1/42 2x = 1/21 => 21 days Answer:B The answer is: B

B

mathematics

X can do a piece of work in 40 days; Y can do the same in 30 days. X started alone but left the work after 10 days, then Y worked at it for 10 days. Z finished the remaining work in 10 days. Z alone can do the whole work in?

Explanation: 10/40 + 10/30 + 10/x = 1 x = 24 days Answer: A The answer is: A

A

mathematics

Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?

A IV This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1. The answer is: A

A

mathematics

By selling 11 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?

70% --- 12 130% --- ? 70/130 * 11 = 6 Answer:D The answer is: D

D

mathematics

A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

Along one edge, the number of small cubes that can be cut = 100/10 = 10 Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000 Answer: C The answer is: C

C

mathematics

Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?

Number of ways to choose 2 colors among 5 - 5c2 Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4)) Now the order, the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4 [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this] Total number of combinations - 5c2 * 2* 7c4 = 700 ANS:C The answer is: C

C

mathematics

There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?

There are 18 balls in a jar. You take out 3 blue balls without putting 3 blue balls + 15 / 5 =6 Answer:E The answer is: E

E

mathematics

In a kilometer race, If Abhishek gives Bharti a 40 m start, Abhishek wins by 19 sec. But if Abhishek gives Bharti a 30 sec start, Bharti wins by 40 m. Find the time taken by Bharti to run 5,000 m?

If Abhishek takes x seconds and Bharti takes y seconds to run 1 km, then: =>y=150 sec and x=125 sec =>x+19=960y/1000 and =(960x/1000)+30=y =>y=150 sec and x=125 sec Answer =(150/1000)×500 = 750 sec Answer : B The answer is: B

B

mathematics

If n is a positive integer, which of the following is a possible value of |46 - 5n| ?

When 46>5n, then |46- 5n| = 46- 5n = (45-5n) + 1 = {multiple of 5} + 1 When 46<=5n, then |46- 5n| = -(46- 5n) = (5n-45) - 1 = {multiple of 5} - 1 So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits. Answer: C The answer is: C

C

mathematics

A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?

25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = 14000 Answer: D The answer is: D

D

mathematics

If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?

X * (120/100) ---------------- = 2/15 Y * (75/100) X/Y = 1/12 Answer: A The answer is: A

A

mathematics

16! is equal to which of the following?

After 4!, the units digit of every factorial is 0. 5!=120 6!=720 etc... The answer is B. The answer is: B

B

mathematics

6x – 5y + 3z = 23 4x + 8y – 11z = 7 5x – 6y + 2z = 11 Given the equations above, x + y + z = ?

(6x – 5y + 3z) - (5x – 6y + 2z ) = 23-11 or, x+y+z = 12 Option B is the ans The answer is: B

B

mathematics

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

The number of ways to select two men and three women = ⁵C₂ * ⁶C₃ = (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 200 Answer:B The answer is: B

B

mathematics

The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?

Let the present ages of A and B be 5x and 3x years respectively. Then, (5x - 4)/(3x + 4) = 1/1 2x = 8 => x = 4 Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1 ANSWER:C The answer is: C

C

mathematics

How many such letter-pairs are there in the word SERVANT having the same no. of letters left between them in the word as they have in the series?

1 pair is S & V 1 pair is N &S total 2 pair ANSWER: A The answer is: A

A

mathematics

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996?

A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2 The answer is: A

A

mathematics

If (x/y)=(7/5), find the value (x^2+y^2)/(x^2-y^2)

= (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(7/5)^2+1] / [(7/5)^2-1] = [(49/25)+1] / [(49/25)-1] = 37/12 Answer is A. The answer is: A

A

mathematics

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

Since first and second varieties are mixed in equal proportions. average price = 126+135/2 = 130.50 o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x - 153 = 22.50 x = 175.50 ANSWER A The answer is: A

A

mathematics

Find the smallest number that must be added to 1780 to make it a perfect square.

4 1780 (42 16 82 180 164 16 Number to be added = (43)2 - 1780 = 1849 - 1780 = 69. ANSWER C 69 The answer is: C

C

mathematics

In a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal?

D 33 There is a meal for 200 children. 140 children have taken the meal. Remaining meal is to be catered to 60 children. Now, 200 children 110 men. 60 children = (110/200)x 60= 33 men. The answer is: D

D

mathematics

Set A: 3, e, 8, 10 Set B: 4, y, 9, 11 The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – e?

So we have even no. of elements in the Set So median is the average of Middle two numbers (e+8)/2= (y+9)/2 y - e= -1 Answer B The answer is: B

B

mathematics

A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?

round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 40% of 50% i.e 20%. so he completed 50 +20 =70 % of total trip C The answer is: C

C

mathematics

The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker’s discount is

Solution T.D =(B.G x 100 / R x T) = Rs.(270x100/12 x 3) = Rs.750. B.D =Rs(750 + 270) = Rs.1020. Answer C The answer is: C

C

mathematics

A certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

1C8*2C12 = 8*66 = 528 the answer is (D) The answer is: D

D

mathematics

If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true? 1. The slope of L is negative 2. Line L does pass the origin. 3. Line L must passes through the first quadrant

Slope of the given line= 3-n/n-3 Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative. 1) n<3 (n=2) 3-2/2-3= -1 2) n<3 (n= 0) 3-0/0-3= -1 3) n<3 (n=-3) 3+3/ -3-3= -2/3 4) n>3 3-4/4-3= -1 Answer A The answer is: A

A

mathematics

A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then ---------- (i) and ---------(ii) From eq.(i) and (ii) 3(R - A ) = 2 (R + K) R = 3A + 2K In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram = 1800 ( R - A) - 24 ( A + K) Time required = = (3600 - 24) = 3576 s E The answer is: E

E

mathematics

1/2+[(2/3*3/8)+4]-7/16=

1/2+[(2/3*3/8)+4]-7/16= 1/2+[(1/4)+4]-7/16= 1/2+[17/4]-7/16= 8/16 + 68/16 - 7/16 = 69/16 C The answer is: C

C

mathematics

What should come in the place of the question mark(?) in the following equation? 45(2)×27(2)/135(2)=?

? = 45×45×27×27 /135×135=81 Answer A The answer is: A

A

mathematics

Sides of a rectangular park are in the ratio 3: 2 and its area is 2460sq m, the cost of fencing it at 50 ps per meter is?

3x * 2x = 2460 => x = 20.24 2(79.76 + 50) = 259.52 m 259.52 * 1/2 = Rs.129.76 Answer:C The answer is: C

C

mathematics

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer: B The answer is: B

B

mathematics

A can finish a work in 48days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?

B+C 1day work = 1/9 + 1/12 = 7/36 work done by B and C in 3days = 7/36 * 3 = 7/12 Remaining work = 1 - 7/12 = 5/12 1/48 work is done by A in 1day 5/12 work is done by A in 48*5/12 = 20days Answer is D The answer is: D

D

mathematics

If the L.C.M of two numbers is 660 and their product is 18480, find the H.C.F of the numbers.

H.C.F = (Product of the numbers) / (Their L.C.M) = 18480/660 = 28. ANSWER:E The answer is: E

E

mathematics

A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?

Let the average after 7th inning = x Then average after 16th inning = x - 3 16(x-3)+87 = 17x x = 87 - 48 = 39 ANSWER=B The answer is: B

B

mathematics

Three cannons are firing at a target. If their individual probabilities to hit the target are 0.6, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire? prob. that all the cannons will hit the target = .06 prob. that none of the cannons will hit = 1 - .06 = .94

The probability that eachdoesn'thit is: 0.4, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities: .4*.3*.2 = 0.024. Option: C The answer is: C

C

mathematics

If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:

Explanation: Clearly, 4864 is divisible by 4. So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3. P = 1. ANSWER A The answer is: A

A

mathematics

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

Let original length = x metres and original breadth = y metres. Original area = (xy) m2. 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 m2 = 36 xy m2. 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%. 25 xy B The answer is: B

B

mathematics

A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 Answer:E The answer is: E

E

mathematics

Find the value of X, Y by solving the below equations X + Y = 12 X - Y = 4

X + Y = 12 ---(I) X - Y = 4 -----(II) by adding (I) and (II) ------------ 2X = 16 ==> X = 16/2 = 8 By Replacing the value of X in (I) we get 8 + Y = 12 ==> Y = 12-8=4. So, X = 8, Y = 4 Answer B) 8, 4 The answer is: B

B

mathematics

To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.

Solution: Let xx be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−100 25x=75+30x−90−100 190−75=30x−25 115=5x x=23 So the company worked 23 days and they made 23⋅25+100=675 pieces. Answer C The answer is: C

C

mathematics

If (A+B) = 4, (B+C) = 8 and (C+D) = 3, what is the value of (A+D)?

Given A+B = 4 B+C = 8 C+D = 3 Then (A+B)-(B+C)+(C+D)=4-8+3=-1 Option E... The answer is: E

E