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mathematics

The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?

Let the numbers x, x + 2, x + 4, x + 6 and x + 8 Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]5 = 61 or 5x + 20 = 305 => x = 57 So, required difference = (57 + 8) - 57 = 8. Answer: C The answer is: C

C

mathematics

If the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled?

We just need to find the factor thats all, w -> quadrupled -> 4w f-> doubled -> 2f z-> tripled -> 3Z Hence, Z^2 = 9Z^2 W is in numerator, and f*z in denominator. Hence, Additional factor being introduced = 4/2*9 =4/18 = 2/9 = B The answer is: B

B

mathematics

he distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?

Explanation: Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11 Answer:A The answer is: A

A

mathematics

A family has two children. find the probability that both the children are girls given that at least one of them is a girl?

Let b stand for boy and g for girl. The sample space of the experiment is S = {(g, g), (g, b), (b, g), (b, b)} Let E and F denote the following events : E : ‘both the children are girls’ F : ‘at least one of the child is a girl’ Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)} Now E n F = {(g,g)} Thus P(F) = 3/4 and P (E n F )= 1/4 Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3 B The answer is: B

B

mathematics

A train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train?

Length = Speed * time Speed = L/T S = 1500/50 S = 30 M/Sec Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 108 Kmph Answer:C The answer is: C

C

mathematics

On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 300,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?

300,000 × 2 × 2×2×2 = 300,000 × 16 = E The answer is: E

E

mathematics

Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?

3/12 + x/15 = 1 x= 11 1/4 Answer: B The answer is: B

B

mathematics

A recycling facility is staffed by 10 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/10 of all wages paid at the facility, what is the value of n?

Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 10x+xn and we are told that it equals to 10xn: 10x+xn=10xn --> reduce by x:10+n=10n -->9n= 10 n = 10/9 Answer: B The answer is: B

B

mathematics

Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.4. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?

(1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves ) =0.6*0.2+0.4*0.3+0.6*0.4 = 0.12+0.12+0.24 =0.48 D The answer is: D

D

mathematics

In how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies?

(3 men out 4) and (2 ladies out of 5) are to be chosen Required number of ways = (4C3 * 5C2) = 40 Answer is A The answer is: A

A

mathematics

What is the greatest positive integer E such that 3^E is a factor of 9^10?

What is the greatest positive integer E such that 3^E is a factor of 9^10? 9^10 = (3^2)^10 = 3^20 D. 20 The answer is: D

D

mathematics

By selling a watch for Rs.400/-, a man loses 20% what is that watch cost price?

80 % ------> 400 (80 * 5 = 400) 100 % ------>500 (100 * 5 = 500) Cost price = Rs. 500/- D) The answer is: D

D

mathematics

If 4XZ + YW = 10 and XW + YZ = 20, what is the value of the expression (2X + Y)(2Z + W)?

(2x+y)*(2z+w) = 10+2(20) =50 Answer : D The answer is: D

D

mathematics

The average of first 7 prime numbers is?

Sum of 7 prime no. = 58 Average = 58/7 = 8.29 ANSWER: C The answer is: C

C

mathematics

If x is an odd integer and y and z are even integers, which of the following CANNOT be an integer?

x = Odd y = Even z = Even Checking Options: A. y/z Even/Even may be an Integer e.g. 4/2=2 Hence Incorrect Option B. x/y Odd/Even CAN NEVER be an Integer Hence Correct Option Answer : B The answer is: B

B

mathematics

A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?

Let required number =x =22x+308=44x ⇒22x=308 ⇒x=308/22 =154/11 =14 Answer :C The answer is: C

C

mathematics

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?

Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B The answer is: B

B

mathematics

Convert the 13/36 m/s into kilometers per hour?

13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph. Answer: C The answer is: C

C

mathematics

The difference between a 8 digit number and the number formed by reversing its digit is not a multiple of

Another approach is to TEST a number. Let's say the original number is 12000002 So, the REVERSED number is 20000021 The DIFFERENCE = 20000021-12000002 = 8000019 No check the answer choices 8000019 is a multiple of 3,296297,888891,2666673 5 is NOT a multiple of 8000019 Answer ; B The answer is: B

B

mathematics

1,000^2 + 1,001^2 +1,002^2 =

Interesting problem. I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total. 1000^2 -> 00 1001^1 -> 01 . . . 1002^2 -> 5 Total -> *5 Answer C. The answer is: C

C

mathematics

Joshua and Jose work at an auto repair center with 5 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?

Two Methods 1) Probability of chosing Josh first = 1/7 Probability of chosing Jose second = 1/6 total = 1/42 Probability of chosing Jose first = 1/7 Probability of chosing Josh second = 1/6 Total = 1/42 Final = 1/42 + 1/42 = 1/21 A The answer is: A

A

mathematics

A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?

Explanation: 1/6 + 1/10 = 8/30 = 4/15 15/4 = 3.75 days Answer: A The answer is: A

A

mathematics

Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 21,the first number is :

Explanation: Let the numbers be a,b,c,d Given, a + b + c = 48, b + c + d = 45 Now, d = 21 thus, b + c + 21 = 45 ⇒ b + c = 24 Putting the value of b + c in a + b + c = 48 a + 24 = 48 ⇒ a = 24 Answer: E The answer is: E

E

mathematics

9 friends went to a super market, and everyone decided to contribute equally to the total bill of $900. If one of the friends had a coupon for 10% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?

At the non-discounted price, each friend would pay $100, as $900 divided by 9 friends is $100 per friend. But if the bill is 10% off, then each friend would pay 10% less. 10% of $100 is $10, so each friend saves $10 and pays the remaining $90 CORRECT OPTION:OPTION D The answer is: D

D

mathematics

If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?

X=120% Y=125% Z=100% X-Y/Y*100 = 5/125*100 ==>4% ANSWER B The answer is: B

B

mathematics

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 140 six-ounce servings of orange juice?

1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture. 60 ounces of mixture gives (60 / 6 ) = 10 servings. Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture. To make 140 servings of the mixture, we need 140 / 10 = 14 cans of the concentrate. The answer is B. The answer is: B

B

mathematics

Sudhir started a business with Rs.30,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be

30000*12:60000*(12-8) =360000 :240000 =3:2 ANSWER:A The answer is: A

A

mathematics

The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?

(mb + nc) / (m+ n).nswer: C The answer is: C

C

mathematics

Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?

T = 12/48 * 60 = 15 Answer: C The answer is: C

C

mathematics

An assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?

The time to produce the first 60 cogs is 60/90 = 2/3 hours. The time to produce the next 60 cogs is 60/60 = 1 hour. The average output is 120 cogs / (5/3) hours = 72 cogs per hour. The answer is E. The answer is: E

E

mathematics

If r < y < -1, which of the following is true?

Consider : r= -3 y= -2 then put for every option. U'll get ans B. The answer is: B

B

mathematics

A pump can fill a tank with water in 2 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?

Work done by the leak in 1 hour = 1/2 - 1/7 = 5/14 Leak will empty the tank in 14/5 hrs = 2hr 48min Answer is C The answer is: C

C

mathematics

On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 220 points, how many points did Bill receive?

consider john's points as x so bill's points are x +20 So sue's points are 2x +40 total of all three students is 4x +60, but this total is given as 220 x = 40 so bill's points = 40 +20 = 60 correct answer option D The answer is: D

D

mathematics

The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)?

1/2 * d * (12 + 8) = 700 d = 70 The answer is C. The answer is: C

C

mathematics

In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1.75, then the 3rd term is which of the following?

First = 1.75 Second = 2*1.75-1 = 2.5 Second = 2*2.5-1 = 4 Answer: option E The answer is: E

E

mathematics

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Answer: A The answer is: A

A

mathematics

What is the average of three tenths and five thousandths

Explanation: three tenths = 0.3 Five thousandths = 0.005 The average is (0.3 + 0.005)/2 = 0.1525 Answer: C The answer is: C

C

mathematics

A train covers a distance of 1000 km in 10hrs. Find the speed of the train?

Speed = 1000/10 = 100km/hr Answer is A The answer is: A

A

mathematics

A box is in the shape of a semicircle with a radius of 12. What is the approximate perimeter of the semicircle?

perimeter of a circle =2pi*r perimeter of a semicircle = pi*r + 2r aprox perimiter = 3.14*12 + 2*12 = 61.68 approximately 62 answer B The answer is: B

B

mathematics

The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?

Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D 1 2 3 1 =iXiX71=4; 1 3 Required probability 3/4 B The answer is: B

B

mathematics

The ratio of male to female in a class is 6:6. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?

here is my approach => males => 6x and females =6x => total =12x now 12x=> 360 therefore 6x => 180 degree . P.S => 6x is nothing but total number of students with the given preference Answer A The answer is: A

A

mathematics

A number which is divided by 13 and 26 yields same remainder?

We can find it with the help of option 108=108/13 and 108/26 not gives the remainder 6 and 3 61=61/13 and 61/26 not gives the remainder 6 and 3 86=86/13 and 86/26 not gives the remainder 6 and 3 78=78/13 and 78/26 gives same remainder 0 Option D The answer is: D

D

mathematics

In a certain corporation, there are 300 male employees and 150 female employees. It is known that 30% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?

P(female) = 150/450 = 1/3 P(male with advanced degree) = 0.3*300/450 = 90/450 = 1/5 The sum of the probabilities is 8/15 The answer is D. The answer is: D

D

mathematics

If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 5 days ?

At the end of each day, the tree has 1212 it's remaining leaves. If initially the tree has x leaves. After day 1: 1/2x After day 2: 1/2x∗1/2=1/^2 x and so on .... After day 5: 1/2^5x=1/32x So leaves lost = Initial amount of leaves - Leaves remaining = x−1/32x=31/32x Answer:E The answer is: E

E

mathematics

Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.2120?

2120 = P [1 + (5*12/5)/100] P= 1892.85 ANSWER:C The answer is: C

C

mathematics

A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of C?

A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 400 C's capital = 30000*1/6 = 5000 Answer: C The answer is: C

C

mathematics

In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,9). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?

The area of the right triangle is (1/2)*4*9 = 18. Only the points (a,b) below the line y=x satisfy a - b > 0. The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8. P(a - b > 0) = 8/18 = 2/9 The answer is D. The answer is: D

D

mathematics

If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence?

if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence. 7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence. 4th - 2nd = 2 numbers away. -10 + 2= -8 Answer: C The answer is: C

C

mathematics

If x-y=10, which of the following must be true? I. Both x and y are positive II. If x is negative, y must be negative III.If x is positive, y must be positive

The best way to approach such questions is to plug in values for x and y Given: x-y=10 I. Both x and y are positive: Let x=12 and y=2 x-y=10 But, Let x=6 and y=-4 x-y=8 Therefore, NOT TRUE III. If x is positive, y must be positive Let x=12 and y=2 x-y=10 But, Let x = 6 and y=-4 x-y=10 Therefore, NOT TRUE II. If x is negative, y must be negative If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number! Therefore, TRUE Ans: 'B' The answer is: B

B

mathematics

If 9x^2-16y^2=3x+4y,then what will give the answer?

9x^2-16y^2=3x+4y (3x+4y)(3x-4y)=3x+4y 3x-4y=(3x+4y)/(3x+4y) 3x-4y=1 Answer is option C The answer is: C

C

mathematics

A library contains 90671 books in English and 405063 books in other languages. What is the total number of books available in the library?

Number of English Books = 90671 Number of in other Language Books = 405063 total number of books 90671 + 405063 = 495734 books answer :C The answer is: C

C

mathematics

In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-5, 1), (1, 1), (1, -4) and (-5, -4)?

Length of side 1= 5+1=6 Length of side 2= 4+1= 5 Area of rectangle= 6*5= 30 B is the answer The answer is: B

B

mathematics

If p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 and p(0)=48, what is p(5)

p(x)=ax^4+bx^3+cx^2+dx+e it can be written as p(x)=a*(x-1)*(x-2)*(x-3)*(x-4) ----(1) put x=0 in(1), we get p(0)=a*(-1)(-2)(-3)(-4) => 48=a*24 => a=2 so, p(x)=2*(x-1)*(x-2)*(x-3)*(x-4) => p(5)=2*(5-1)*(5-2)*(5-3)*(5-4)=2*4*3*2*1=48 p(5) = 48 ANSWER:A The answer is: A

A

mathematics

Each of the 26 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 11 students sign up for the poetry club, 17 students for the history club, and 15 students for the writing club. If 5 students sign up for exactly two clubs, how many students sign up for all three clubs?

The total number in the three clubs is 11+17+15=43. All 26 students signed up for at least one club. 5 of those students signed up for exactly one more club. 43 - 31 = 12 so 6 students must have signed up for exactly three clubs. The answer is E. The answer is: E

E

mathematics

If the value of a piece of property decreases by 10% while the new tax rate on the property represent 110% of the original tax rate, what is the effect on the taxes?

Consider the value of property = 100, Original tax rate 10%, hence tax value = 100*10% = 10. Decreased value of property = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9 10-9.9 = decrease by 1%. Answer D. The answer is: D

D

mathematics

A box contains 25 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is

Solution P( None is defective) = 21C2 / 25C2 = 7/10 P( at least one is defective) = (1- 7/10) =3/10. Answer A The answer is: A

A

mathematics

This topic is locked. If you want to discuss this question please re-post it in the respective forum. Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 16 days. In how many days Peter complete the work separately.

Together they complete the job in 20 days means they complete 12/20 of the job after 12 days. Peter completes the remaining (8/20) of the job in 16 days which means that the whole job(1) can be completed in X days. <=> 8/20->16 <=> X=16/(8/20)=40 Thus the answer is E. The answer is: E

E

mathematics

The difference between the place value and the face value of 8 in the numeral 856973 is

(Place value of 8) - (Face value of 8) = (800000 - 8) = 799992 Answer: Option E The answer is: E

E

mathematics

The difference between the ages of two persons is 30 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the younger person is?

Let their ages be x years and (x+30) years Then, (x+30) - 15 = 2(x-15) x +15 = 2x-30 x = 45 Answer is C The answer is: C

C

mathematics

In an examination 65% failed in Math and 35% failed in French. If 22% failed in both. What % of students passed in both.

Passed in Math = 100 - 65 = 35% Passed in French = 100 - 35 = 65% Students who passed Math or French = 100 -22 = 78% Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 35+65-78 =22% ANSWER:A The answer is: A

A

mathematics

The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x)) is equal to :

Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7. ANSWER:C The answer is: C

C

mathematics

If y ≠ 3 and 2 x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers.

Let 2 x/Y = K , Where k is a prime number > 2 ( 3, 5, 7, 11 ...etc) so 2x = Ky --> ( 3y or 5y or 7y or 11y etc...) Which implies always X > Y So answer is (A) The answer is: A

A

mathematics

A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly M new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?

At the end of the first week, there are 5 new members; At the end of the second week, there are 5M new members (since each 5 new members from the previous week brings M new members); At the end of the third week, there are 5M^2 new members (since each 5M new members from the previous week brings M new members); ... At the end of the twelfth week, there are 5M^11 new members (since each 5M^10 new members from the previous week brings M new members). We are given that 5M^11=y. Out of the answers only D yields integer value for M: 5M^11=3^11 * 5^12 --> M=3*5=15. Answer: D. The answer is: D

D

mathematics

The sum of first four prime numbers is?

Required sum = (2 + 3 + 5 + 7) = 17. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. A The answer is: A

A

mathematics

The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly six elements each?

nC2 = 36 => n*(n-1)/2 = 36 by middle term factor and n cannot be negative => n = 9 nC3 = 9C6 = 9!/6!*(9-6)!= 9*8*7*6!/6!*3*2 =84 So, Answer is C. The answer is: C

C

mathematics

In a vessel, there are 10 litres of alcohol. An operation is defined as taking out five litres of what is present in the vessel and adding 10 litres of pure water to it. What is the ratio of alcohol to water after two operations?

Final concentration = Initial concentration (1−replacement quantityfinal volume)(1−replacement quantityfinal volume) Final concentration = =1×(1−1015)=13=1×(1−1015)=13 Final concentration = 13×(1−1020)=1613×(1−1020)=16 So ratio of alcohol : water = 1 : 5 Answer:B The answer is: B

B

mathematics

The average weight of a group of boys is 30 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?

Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 36 kg joins the group, total weight of boys = 30x + 36 So 30x + 36 = 31(x + 1) = > x = 5. Answer:A The answer is: A

A

mathematics

How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together?

Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter. Then, the letters to be arranged are DGNTR (AUE). Then 6 letters to be arranged in 6p6 = 6! = 720 ways. The vowels in the group (AUE) may be arranged in 3! = 6 ways. Required number of words = (720x6) = 4320. Ans: B The answer is: B

B

mathematics

If x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ?

Use answer options to solve this problem - Put x = 2 So, 5x+2y=4 Or, 5(2)+2y=4 Or, 10+2y=4 Or, 2y=4-10;2y=-6 Or, y=-3(y is negative integer) Answer will be (C) The answer is: C

C

mathematics

If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1110 will be:

Z share = Z, Y = 1.2Z X = 1.25×1.2Z, X+Y+Z =111 (1.25× 1.2+1.2+1)Z=1110 3.7Z=1110, Z=300 Answer: . A The answer is: A

A

mathematics

Two goods trains each 720 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?

Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 750 + 750 = 1500 m. Required time = 1500 * 6/125 = 72 sec. Answer:E The answer is: E

E

mathematics

If the price of a book is first decreased by 50% and then increased by 60%, then the net change in the price will be?

Let the original price be $100 New final price = 160% of (50% of $100) = 160/100 * 50/100 *100 = $80 Decrease is 20% Answer is A The answer is: A

A

mathematics

The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 44. What is a possible value for the mean of the distribution?

The standard deviation ({SD}) = 2; 3 standard deviations below the mean is greater than 44: {Mean} - 3*{SD} > 44; {Mean} - 6 > 44; {Mean} > 50. Answer: E. The answer is: E

E

mathematics

At present, the ratio between the ages of Arun and Deepak is 4:3. After 2 years, Arun's age will be 26 years. What is the age of Deepak at present?

Let the present ages of Arun and Deepak be 4x and 3x years respectively. Then, 4x + 2 = 26 => x = 8 Deepak's age = 3x = 18 years. Answer: D The answer is: D

D

mathematics

In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 18 percent of revenues. The profits in 2009 were what percent of the profits in 2008?

x = profits r= revenue x/r = 0,1 x= 10 r=100 2009: r=80 x/80 = 0,18 = 18/100 x= 80*18/100 x= 14.4 14.4/10 = 1,44 = 144%, Answer D The answer is: D

D

mathematics

A shopkeeper buys two articles for Rs.1000 each and then sells them, making 30% profit on the first article and 30% loss on second article. Find the net profit or loss percent?

Profit on first article = 30% of 1000 = 300. This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss. Answer: D The answer is: D

D

mathematics

The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: A. The answer is: A

A

mathematics

In an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?

Solution: In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following: Integer 1: x Integer 2: x + 1 Integer 3: x + 2 Integer 4: x + 3 Integer 5: x + 4 Integer 6: x + 5 Integer 7: x + 6 Integer 8: x + 7 We are given that the sum of the first 4 integers is 570. This means that: x + x+1 + x+2 + x+3 = 570 4x + 6 = 570 4x = 564 x = 141 The sum of the last 4 integers can be expressed and simplified as: x+4 + x+5 + x+6+ x+7 = 4x + 22 Substituting 141 for x yields: (4)(141) + 22 = 586 Answer: C The answer is: C

C

mathematics

A certain high school has 500 students. Of these students, 50 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?

We're given a series of facts to work with: 1) A certain high school has 500 students. 2) Of these students: X are taking music, Y are taking art, and Z are taking BOTH music and art. We're asked how many students are taking NEITHER music nor art? Let's TEST X = 50 Y = 20 Z = 10 So, we have 50 students taking music, 20 taking art and 10 taking BOTH music and art. 40 student taking JUST music 10 student taking JUST art 10 student taking BOTH music and art Total = 60 students We're asked for the total number of students who are taking NEITHER Course. That is 500 - 60 = 440. B The answer is: B

B

mathematics

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer:B The answer is: B

B

mathematics

If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?

Explanation: X = 125% Y = 130% Z = 100% X-Y/Y * 100 = 5/130 * 100 = 500/130 % = 3 11/13% smaller than Y Answer: Option C The answer is: C

C

mathematics

In the xy-plane, line e passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line e?

If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line e should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A. The answer is: A

A

mathematics

Walking at 6/7th of his usual speed, a man is 25 mins too late. His usual time is

As the distance is same s*t=6/7s*(t+25) solving this we get t=150 sec 150/60=2.5 hrs ANSWER:C The answer is: C

C

mathematics

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?

Explanation: Let the number of candidates appeared from each state be x. In state A, 6% candidates got selected from the total appeared candidates In state B, 7% candidates got selected from the total appeared candidates But in State B, 80 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State B = 80 => total appeared candidates in State B = 80 x 100 = 8000 => total appeared candidates in State A = total appeared candidates in State B = 8000 Answer: B) 8000 The answer is: B

B

mathematics

When she chooses a password, Eloise always uses exactly ten different characters: five letters (A, B, C, D, and E) and five numbers (2, 3, 4, 5, and 6). Additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. How many different passwords conform to these rules?

The first character of the password can be any letter or number, so Eloise has ten options. Her second choice must be from the set (letter or number) not yet used, so she has five options. Choice 3 is from the same set as Choice 1, and she has four options left. Choice 4 is the second item from the same set as Choice 2, so she has four options. Choices 5 and 6 are from different sets, each with three options; Choices 7 and 8 are from different sets, each with two options; Choices 9 and 10 are from different sets, each with only one option remaining. You can see this information in the following chart: 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 10 5 4 4 3 3 2 2 1 1 To find the total number of possible passwords, multiply these numbers together: 10 × 5 × 4 × 4 × 3 × 3 × 2 × 2 × 1 × 1 = 28,800 correct anser C)between 10,000 and 100,000 The answer is: C

C

mathematics

If m is a positive integer and m^2 is divisible by 33, then the largest positive integer that must divide m is?

M^2 is divisible by 33 so M^2 must be multiple of 48. If the value of M is Multiples of 11 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is D but if M = 33 then answer should be 16. Is the question right? Or am i missing some thing? D The answer is: D

D

mathematics

Two trains are moving in opposite directions with speed of 70 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds

Explanation: Relative speed = 70+90 = 160 km/hr (Since both trains are moving in opposite directions) Total distance = 1.1+.9 = 2km Time = 2/160 hr = 1/80 hr = 3600/80 seconds = = 45 seconds Answer: Option B The answer is: B

B

mathematics

How many prime numbers exist between 1 and 20?

E) The answer is: E

E

mathematics

Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 4 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away. Interest earned after the first time interval: $10,000*2%=$200; Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306; Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420; Total: 200+306+(~420)=~$920.24 Answer: D. The answer is: D

D

mathematics

In a survey of 350 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?

---------UI----------------NUI-------Total PT----(12.5/100)*104 = 13----------- --54 NPT---104-13-------------- x--------296 Total--104----------------------------350 we have to find not part time and not uninsured . in other words not part time and insured = x/350 = (296-104+13)/350 = 41/70 Answer is E. The answer is: E

E

mathematics

The value of (2.502+0.064)^2 - (2.502-0.064)^2/2.502*0.064

(2.502+0.064)2 - (2.502-0.064)2/2.502*0.064 = (a+b)2 - (a-b)/ab = 4ab/ab = 4 ANSWER:C The answer is: C

C

mathematics

On flipping 2 coins together what is the outcomes for at least two heads?

Sample space, S = {HH, TH, TH, TT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HH} A The answer is: A

A

mathematics

The difference between simple and compound interest on Rs. 1600 for one year at 10% per annum reckoned half-yearly is?

S.I. = (1600 * 10 * 1)/100 = Rs. 160 C.I. = [1600 * (1 + 5/100)2 - 1600] = Rs. 164 Difference = (164 - 160) = Rs.4. Answer:D The answer is: D

D

mathematics

Two cars cover the same distance at the speed of 50 and 45 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?

50(x + 1) = 45 x X = 10 60 * 10 = 600 km Answer:D The answer is: D

D

mathematics

Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 20000, then find his savings?

Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively. Income, 5x = 20000 => x = 4000 Savings = Income - expenditure = 5x - 4x = x So, savings = Rs.4000 Answer: B The answer is: B

B

mathematics

Dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?

Say Dhoni's earning last month was $100. Dhoni spent 40 percent of his earning last month on rent --> $40 on rent; 20 percent less than what he spent on rent to purchase a new dishwasher --> $40*0.8=$32 on the dishwasher. Left over amount 100 - (40 + 32) = $28 Answer: B The answer is: B

B

mathematics

The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?

(P*5*15)/100 - (P*3.5*15)/100 = 144 75P/100 – 52.5P/100 = 144 22.5P = 144 * 100 => P = Rs.640.Answer: B The answer is: B

B

mathematics

Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:

Explanation: Let first number be x. So,2nd no. = 4x & 3rd no.=8x. So,x+4x+8x=78 × 3 = 234. 13x = 234 x = 234/13 Hence,smallest Number x=18. Answer: A The answer is: A

A

mathematics

If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 6, respectively, what is the probability that b/a will not be an integer?

a is from the following set {1,2,3,4} b is from the following set {6,8,10} The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways. The possibilities where b/a is not an integer is for the following outcomes: {b,a} = {6,4},{8,3},{10,3},{10,4} = 4 ways Thus the probability is 4/12 = 1/3 The answer is C. The answer is: C

C

mathematics

A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?

Explanation: A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work. => In one day A came complete 1/9th of the task(x/9) => In one day B can complete 1/12th of the job.(x/12) First day x/9th work will be done next day x/12th and so on: Together A and B can do x/9 + x/12 work. =>(x/9) + (x/12) = 7/36th work done In 10 days 35/36th of the work will be done. On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work. So, 1/36th work will be done in 1/4 days. =>10.25 days ANSWER: D The answer is: D

D