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mathematics

If a man can cover 18 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?

18 m/s = 18 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 18 * 18/5 * 15/4 km = 243 km. Answer: A The answer is: A

A

mathematics

On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.7, what is the probability that Malachi will return home at the end of the day on the following Monday?

Re-phrasing the question: What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain Probability of rain = 0.7 Therefore, probability of no rain = 0.3 0.3*0.3*0.7 = 0.063 Hence A The answer is: A

A

mathematics

The difference between a two-digit number and the number after interchanging the position of the two digits is 63. What is the difference between the two digits of the number?

Let the two-digit no. be l0x + y. Then, (10x + y) – (10y + x) = 63 or, 9(x – y) = 63 or, x – y = 7 Answer B The answer is: B

B

mathematics

Tim bought a new machine to help him picking apples from apple trees. If this new machine can pick 20 apples every 30 minutes and Tim wants to pick 500 apples today. How many hours he is going to take?

The machine picks 20 apples every 30 minutes = 40 apples/hour. 500 apples is going to take 500/40 apples/hour = 12.5 hours. Correct Option: 12.5. Answer: B The answer is: B

B

mathematics

In Orange County, one fourth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?

The number must be a multiple of both 4 and 7 so the answer is 252. The answer is E. The answer is: E

E

mathematics

The average weight of 3 packets A, B and C is 84 kg. Another packet D added into the group and the average now becomes 80 kg. If another packet E, whose weight is 3 kg more than that of D, replaces A then the average weight of B, C, D and E becomes 79 kg. The weight of A is:

Explanation : A+B+C = (84x3) = 252kg, A+B+C+D=(80x4) = 320kg. D = (320 - 252) = 68 , E = (68+3) =7l. B+C+D+E = (79x4)=316. (A+B+C+D) -(B+C+D+E)=(320 - 316)kg = 4kg. A - E = 4 = A = (4+E)=75kg Answer : C The answer is: C

C

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 10 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?

The percentage of tagged deer in the second sample = 10/50*100=20%. So, 150 tagged deers comprise 10% of total # of deers --> total # of deers = 150*20 = 3,500. Answer: C The answer is: C

C

mathematics

The length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is?

Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (180 + x)/30 = 25/2 => 2(180 + x) = 750 => x = 195 m. Answer: C The answer is: C

C

mathematics

log root(8)/log 8 is equal to

=> log(8)^1/2/log 8 = 1/2 log 8/log 8 = 1/2 ANSWER A The answer is: A

A

mathematics

The speed of a car is 70 km in the first hour and 90 km in the second hour. What is the average speed of the car?

S = (70 + 90)/2 = 80 kmph Answer:B The answer is: B

B

mathematics

If the range T of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?

The range T of a set is the difference between the largest and smallest elements of a set. Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15. The the difference between the greatest possible value of x and least possible value of x is 15-2=13. Answer: D. The answer is: D

D

mathematics

A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?

Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph. Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7 Solving the equation, the speed of man in still water is 12.5 kmph. Answer:D The answer is: D

D

mathematics

81 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?

(81 * 8)/30 = (x * 6)/50 => x =180 180 – 81 = 99 Answer:A The answer is: A

A

mathematics

A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?

we have 3 places (---)to fill & we can use only digits 2, 4, 5 First place can be filled in 3 ways 2nd place can be filled in 3 ways because we can repeat the digits 3rd place can be filled in 3 ways because we can repeat the digits Total no of codes = 3 x 3 x 3= 27 but one combination (555) will not be even so total no of even codes = 27 - 1 = 26 Answer D The answer is: D

D

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: D The answer is: D

D

mathematics

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only). Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5) = (525 + 210 + 21) = 756. ANSWER B 756 The answer is: B

B

mathematics

John has 5 flavors of chocolate in him shop. How many options are there for Jones to pick a one-flavor, two-flavor, three-flavor, four-flavor or five-flavor order?

5C1 + 5C2+ 5C3+5C4+5C5 = 31. Answer: B The answer is: B

B

mathematics

The positive number a is q percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true? I. c > a II. c = a III. c < a

a = (1 + q%)b b = (1-p%)a a = (1 + q%)*(1-p%)a So (1 + q%)(1 - p%) = 1 = No change One easy solution to this would be q = 0 and p = 0. In that case, a = b = c. So statement II can hold. Assuming p and q are not 0, (1 + q%)(1 - p%) = 1 = No change So if you increase something by q% (it becomes bigger) and then decrease it by p% (now you will need to decrease it by a lesser %), there is no change. Such as, you increase 100 by 25% and it becomes 125. Then you decrease 125 by only 20% and it comes back to 100. (This should remind you of cost price, sale price, profit and margin). So q would be a higher percentage than p. Now if you increase something by p% (the lower %) and then decrease by q% (the higher %), the value you will obtain will certainly be lower than original. Say you increase a (100) by p% (20%) to get 120 and then decrease it by q% (25%), you will get c (90). Hence c < a is possible too. Answer (E) The answer is: E

E

mathematics

There are 4 runners on a track team who run an average of 4.5 seconds per 40 yards. If another runner joins their team who runs 4.3 seconds per 40 yards, what will the new average 40 yard time be?

(sum of the 4 times)/4 = 4.5 sum of the 4 times = 18 new sum = 18+4.3 = 22.3 new average = 22.3/5 = 4.46 ans: A The answer is: A

A

mathematics

P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?

Let work done by P in 1 day = p work done by Q in 1 day =q Work done by R in 1 day = r p + q = 1/8 ---(1) q + r= 1/12 ---(2) p+ q+ r = 1/6 ---(3) (3) – (2) => p = 1/6 - 1/12 = 1/12 (3) – (1) => r = 1/6 – 1/8 = 1/24 p + r = 1/12 + 1/24 = 3/24 = 1/8 => P and R will finish the work in 8 days Option B The answer is: B

B

mathematics

What profit percent is made by selling an article at a certain price, if by selling at 4/5rd of that price, there would be a loss of 20%?

SP2 = 4/5 SP1 CP = 100 SP2 = 80 4/5 SP1 = 80 SP1 = 100 100 --- 100 => 0% Answer: A The answer is: A

A

mathematics

Find the simple interest on Rs.350 for 10 months at 5 paisa per month?

I = (350*10*5)/100 = 175 Answer: B The answer is: B

B

mathematics

A certain company employs 9 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?

Number of ways to select 3 senior officers from 9 of them = 9C3 = 84 ways Next we can determine the number of ways to select 1 junior officer. number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways Thus the number of ways to select 3 senior officers and 1 junior officer is 84 x 4 = 336 ways. Answer: D The answer is: D

D

mathematics

A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?

12:16 = 3:4 ANSWER:E The answer is: E

E

mathematics

There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

I think the above logic is correct except one thing: # of arrangements is 5!3!=205!3!=20. But a car can be arranged facing TWO directions (within one particular parking space), so we should multiply 20 by 2, 20∗2=4020∗2=40 Answer: C. The answer is: C

C

mathematics

nine baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

it is like a circular arrangement. total ways for n people to arrange in a circle is = factorial (n-1) in this case n= 9 hence ans = 8 factorial = 40320 hence A The answer is: A

A

mathematics

Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?

Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10. Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16. So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10. Solving this equation for d+ed+e gives d+e=−66d+e=−66. Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33. Hence, the answer is A: -33 The answer is: A

A

mathematics

Steve is laying floor tiles in 2 rooms of his house. Each room requires 30 tiles, all the same size. How many of the following combinations could Steve buy if: A Small box (1 box@$8.00 w/tax) contains 10 tiles, and a Large box (1 box@$20.00 w/tax) contains 25 tiles. Steve only has $50 on him when he gets to the store.

The Correct Answer must total at least 60 tiles (2 rooms of 30) AND cost $50 or less A=Total of 60 tiles (6*10) and costs $48 (6*$8.00) *Correct Answer* B=Total of 75 tiles (3*25) (while sufficient amount of tiles, cost would be $60 which is $10 over budget) C=Total of 55 tiles (3*10 +25) (while sufficient cash is on hand of $49 [3*8+25] he is 5 tiles short. D=A is correct however C is not E=A is correct however B and C are not The Correct Answer is A The answer is: A

A

mathematics

The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?

The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 42/3 = 14 kmph..Answer: C The answer is: C

C

mathematics

What is the value of the following expression? (1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (16^2 – 1))

it can be written into 1/3+1/15+ 1/35.....1/256 i.e 1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/17) all terms from 1/5 .. to second last term get cancelled left with 1/3+1/6-1/34=1/2-1/34=16/34=8/17 E The answer is: E

E

mathematics

Sum of ages of two friends is 30 while difference is 2 then their ages are

16,14 ANSWER:B The answer is: B

B

mathematics

John bought 2 shares and sold them for $24 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had

Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss Total Selling Price = 24*2 = $48 Total Cost Price = 48/(0.96) = $50 Loss = 50-48 = $2 Answer: Option C The answer is: C

C

mathematics

A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability Z that the game will end after the fourth throw?

Another approach: Two likely scenarios would be : HHTH or THTH for each of the scenarios probability would be 1/16 So Probablilty Z is 1/16 + 1/16 = 1/8.C The answer is: C

C

mathematics

A person incurs 5% loss by selling a watch for $1140 . At what price should the watch be sold to earn 5% profit?

Let the new S.P be $ x then, (100-loss%):(1st S.P)=(100+gain%):(2nd S.P) (100-5)/1140=(100+5)/x x=(105*1140)/95=$1260 ANSWER C 1260 The answer is: C

C

mathematics

You collect coins. Suppose you start out with 18. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?

Solution Start with 18 coins. Sharon takes 3 coins from you: 18 - 3 = 15 coins. Steven takes 4 coins from you: 15 - 4 = 11 coins. So you have 11 at the end. Correct answer : E The answer is: E

E

mathematics

How many two-element subsets of <1, 2,3,4,5,6,7> are there that do not contain the pair of elements 2 and 4?

7C2 - 1 = 20 Answer is E The answer is: E

E

mathematics

If m and n are positive integers and m^2 + n^2 = 89, what is the value of m^3 + n^3?

You need to integers which squared are equal 89. Which could it be ? Let's start with the first integer: 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 Stop. The integers can't be greater than 8 or we will score above 89. The second integer need to be picked up the same way. 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 The only pair that matches is 8^2 + 5^2 = 89. So 8^3 + 5^3 = 637. Answer E.) The answer is: E

E

mathematics

If two of the four expressions x + y , x + 7y , x - y , and 7x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?

Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6 now we have to find the expressions that are in form of x^2 - (by)^2 one is (x+y)(x-y) = x^2 - (1y)^2 If you see any other combination we are always going to have one term of xy since 7x and 7y are there, so there can be only one type of combination like this. therefore, probablity is 1/6 Answer : D The answer is: D

D

mathematics

A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 65 years, that of the parents is 45 years and that of the grandchildren is 8 years. What is the average age of family?

Required average = (65 x 2 + 45 x 2 + 8 x 3 )/(2 + 2 + 3) = (130 + 90 + 24)/7 =244/7 = 34 6/7years. Answer is A The answer is: A

A

mathematics

A meal cost $ 37.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:

10%(37.5) = 3.75 15%(37.5) = 5.625 total amount could have been 37.5+3.75 and 37.5+5.625 => could have been between 41.25 and 43.125 => approximately between 41 and 43 Answer is A. The answer is: A

A

mathematics

A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?

Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50 Let the marked price be Rs. x. Then, 95/100 x = 123.50 x = 12350/95 = Rs. 130 Now, S.P. = Rs. 130, C.P. = Rs. 100 Profit % = 30%. Answer: C The answer is: C

C

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 27, the how old is B? A. 7 B. 8 C. 9 D. 10 Explanation:

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 x = 5. Hence, B's age = 2x = 10 years. Answer: Option D The answer is: D

D

mathematics

Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?

Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9 => 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18 => x = 18. Answer: A The answer is: A

A

mathematics

On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options. One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord). Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle. There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle. If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D The answer is: D

D

mathematics

A certain collage has total of 200 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

Answer C 200 = 150 + 20 + x => x = 25 = 3/4 * 200 in 4 subjects + 20 min for 5th subject + x = 200 The answer is: C

C

mathematics

The food in a camp lasts for 25 men for 55 days. If five more men join, how many days will the food last?

one man can consume the same food in 25*55 = 1375 days. 5 more men join, the total number of men = 30 The number of days the food will last = 1375/30 = 46 days. Answer:C The answer is: C

C

mathematics

Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams D could be selected from the eight candidates?

If an executive team is considered different if any of the same people hold different offices,.... so you will not have answer as 6720.. president could be by any of 8 person.. treasurer could be any out of remaining 7 person.. remaining three order does not matter, so we have to choose 3 out of 6=6c3=20.. total ways D= 8*7*20=1120.. ans D... The answer is: D

D

mathematics

In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?

x*110/100 * 90/100 = 7920 X*0.99=7920 X=7920/0.99 => 8000 Answer:B The answer is: B

B

mathematics

List K consists of 10 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?

Answer = A = 5 If least = -3, then largest = 6 Range = 6- 1 = 5 The answer is: A

A

mathematics

Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 70 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach?

Every hour, Nil gets ahead of Ethan 70 - 20 = 50 miles. When Nil arrived at the beach, Ethan is only 20 × 0.5 = 10 miles behind. That tells us they only drove 1 hour when Nil arrived at the beach. The distance between their home and the beach is Nil’s speed × Nil’s time = 70 × 1 = 70 miles. correct answer B The answer is: B

B

mathematics

A and B can do a work in 18 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?

One day work of A and B = 1/18 One day work of B and C = 1/30 One day work of C and A = 1/36 2(A + B + C) = 1/18 + 1/30 + 1/36 2(A + B + C) = 21/180 (A + B + C) = 13/360 Number of days required = 360/13 days. ANSWER:A The answer is: A

A

mathematics

If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?

The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2 Answer: A The answer is: A

A

mathematics

A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?

Original Price = x Sold to collector at 1.2x re-buy price = 1.2x * 0.5 = 0.6x therefore, x - 0.6x = 100; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 ANSWER:A The answer is: A

A

mathematics

A walks at 10 kmph and 4 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?

Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours. x/10 - x/20 = 4 x = 80 km Answer is C The answer is: C

C

mathematics

Patrick has three daughters named Avery, Bridget, & Catherine. He decides he wants to make a 3-letter password using the a combination of the each of their first initials (e.g. ABC, CBA, etc.). How many different permutations can he come up with?

Permutation calc is: n P r = n! / (n-r)! 3 P 3 = 3!/(3-3)! = 3x2x1/0!=6/1=6 Correct answer is C (6) ANSWER:C The answer is: C

C

mathematics

As a treat for her two crying children, a mother runs to the freezer in which she has five cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?

Probability of not getting the same flavor -> Favourable -> Cherry - orange [ 5C1 * 3C1 [or simply 5*3 ] or Cherry - lemon [ 5*4] or orange - lemon [3*4] Prob = (5*3 + 5*4 + 3*4 ) / 9C2 = 47/47520 = 1/999 Answer -> D The answer is: D

D

mathematics

To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables t are there in the warehouse?

Total number of ways to choose 2 chairs from 5 t= 5C2=10 Total number of combination=150 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C2=15..... 15*10=150 Answer is 6... A The answer is: A

A

mathematics

How many positive integers will divide evenly into 440?

520 = 10*13*4 = 8*5*13 = 2^3*5*13 We need to positive integers will divide evenly into 520 or simply the factors of 520 If a number is of the form 2^a*3^b*5^c, Total factors = (a+1)(b+1)(c+1) Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18 Option D The answer is: D

D

mathematics

A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?

Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:B The answer is: B

B

mathematics

The average mark of a class of twenty two students is 65. If four students whose marks are 25, 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.

Exp. Total mark of 22 students = 65*22 = 1430, Total mark after the removal of 4 students = 1430 –(25+32+28+34 ) = 1430 – 119 = 1311 Approximate average mark = 1311/(22-4) = 1311/ 18 = 73 Answer: B The answer is: B

B

mathematics

A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?

Let the average score of 19 innings be x. Then, 18x+98/19=x+4 The average score after 20th innings = x + 4 = 22 + 4 = 26 Answer D The answer is: D

D

mathematics

A man walking at a rate of 15km/hr crosses a bridge in 20 minutes. The length of the bridge is?

Speed = 15*5/18 = 15/18 m/sec Distance covered in 20minutes = 15/18 *20 *60 = 1000m Answer is D The answer is: D

D

mathematics

Two trains, each 150 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?

Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (150 + 150)/8 = 3x => x = 25/2. So, speed of the faster train = 50/2 = 25 * 18/5 = 90 km/hr. Answer:A The answer is: A

A

mathematics

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 97% water by weight. What is the new weight of the cucumbers, in pounds?

Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 97% water and 3% of non-water, so now 1 pound of non-water composes 3% of cucucmbers, which means that the new weight of cucumbers is 1/0.03=34 pounds. Answer: B. The answer is: B

B

mathematics

Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?

Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs. Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs = 2 5/6 = 2 hrs 50 min Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min. So, Anna reached city A at 10.25 a.m. Answer: E The answer is: E

E

mathematics

What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4?

Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 4 = 10x +y = x^2 y^2 -11 Thus 2xy +4 = x^2 + y^2 - 11 x^2 + y^2 -2xy = 16 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 26 or 98 Thus the answer is C The answer is: C

C

mathematics

The ratio of two cow A,B milk is 5:3.3kg milk of cow A get distributed and 1kg milk of cow B get distributed.now,8kg milk of cow B left.Now what is the ratio of cow A and B left milk?

left milk of cow B=3x-1=8,3x=9,x=3. left milk of cow A=15-3=12 12/8=3:2. answer A The answer is: A

A

mathematics

Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of hydrogen are there in 117 grams of water?

(2/18)*117 = 13 grams The answer is D. The answer is: D

D

mathematics

On dividing a certain number by 234, we get 43 as remainder. If the same number is divided by 13, what will be the remainder?

Description : Solution : suppose that on dividing the given number by 234, we get quotient=x and remainder= 43 then, number= 234*x+43----> (1). => (13*18x)+(13*3)+4 => 13*(18x+3)+4. So, the number when divided by 13 gives remainder=4. Answer :(C) The answer is: C

C

mathematics

A sum of Rs.4500 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.

Let A be the amount received at the end of the three years. A = 4500[1 + 10/100][1 + 20/100][1 + 25/100] A = (4500 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7425 So the interest = 7425 - 4500 = Rs.2925 ANSWER:A The answer is: A

A

mathematics

If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer?

If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer? f = (x)^2 where x is a positive integer To calculate - (x+1)^2 = x^2 + 2x + 1 root(f) = x Ans - f + 2 root(f) + 1 This should beD The answer is: D

D

mathematics

What is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours?

Distance= Time x Speed Distance = 150 x 8 = 1200 Answer: E The answer is: E

E

mathematics

What is the square root of 400, divided by 2?

Square root is a number times itself Square root of 400=20, 20/2=10 (E)1 The answer is: E

E

mathematics

Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?

A = 8000(21/20)3 = 9261 Answer: B The answer is: B

B

mathematics

One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to

Tap 1 : 283 secs Tap 2 : 287 secs Considering the average of these 2 taps : 285 secs. So 1 tap can fill the tank in 285 secs, so 2 taps can fill the tank in 285/2 = 142.5 secs. Closest answer is A. The answer is: A

A

mathematics

The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 3 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?

Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4. so ans can either be 8 0r 12. With 8 as answer - no of girls = 8 With 12 as answer - no of girls = 12 Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5. So we are looking for number of girls in B to be divisible by 5. With 8 as answer -> Girls = 8-2 = 6. (Not possible) With 12 as answer -> Girls = 12-2 = 5. So, answer = 8. ( A) The answer is: A

A

mathematics

A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 45 more than the correct answer. Find the number.

Let the number be x. (5/4) * x = (4/5)*x + 45 25x = 16x + 900 9x = 900 x = 100 The answer is C. The answer is: C

C

mathematics

In a group of 70 people,60 like swimming,50 like wrestling. How many like both swimming and wrestling?

Make a Venn diagram, and enter your data. Let the number of people who like both swimming and wrestling be x 60-x+x+50-x = 70 x = 40 so number who like both swimming and wrestling = 40 Answer C The answer is: C

C

mathematics

The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?

13 CP = 11 SP 11 --- 2 CP 100 --- ? =>18 2/11% Answer: B The answer is: B

B

mathematics

A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform m calculations?

As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES. We're told that a computer can perform C calculations in S seconds. Let's TEST.... C = 2 S = 3 2 calculations every 3 seconds = 40 calculations every 1 minute We're asked how many MINUTES it will take to perform K calculations. Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST... m = 80 So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80 Answer A: 60mS/C = 60(80)(3)/2 = 7200 This is NOT a match Answer B: mS/C = (80)(3)/2 = 120 This is NOT a match Answer C: mS/60C = (80)(3)/(60)(2) = 2 This IS a match Answer D: 60C/mS = 60(2)/(80)(3) = 1/2 This is NOT a match Answer E: m/60CS = 80/(60)(2)(3) = a fraction. This is NOT a match C The answer is: C

C

mathematics

David buys an old scooter for Rs. 2400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 3600, his gain percent is :

Explanation : Solution: C.P. =Rs. (2400+600) =Rs. 3000; S.P. = Rs. 3600. Gain% = (600*100/3000) = 20%. Answer : A The answer is: A

A

mathematics

What is the remainder when 25472 is divided by 2?

If the digit in unit place is even, the number will be divisible by 2. 2 is an even number,so the number is divisible by 2 ANSWER:0 The answer is: E

E

mathematics

As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>3

II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3; I. y<3x --> is not always true. Answer: C The answer is: C

C

mathematics

T divided by S equals 405.24 what is a possible remainder?

With the decimal being 24/100, the simplest form is 6/25. If the divisor is a multiple of 25, the remainder must be a multiple of 6. The only number that is so is 54. Answer A. The answer is: A

A

mathematics

A train passes a station platform in 36 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?

Speed = (72 * 5/18) m/sec = 20 m/sec. Length of the train = (20 x 10)m = 200 m. Let the length of the platform be x meters. Then, (x + 200)/36 = 20 ==> x + 200 = 720 ==> x = 520 m. Answer: C The answer is: C

C

mathematics

A circular well with a diameter of 2 metres , is dug to a depth of 8 metres. What is the volume of the earth dug out?

Solution Volume = πr2h ‹=› (22 /7 ×1×1×8)m3 ‹=›25.1 m3. Answer B The answer is: B

B

mathematics

If 2x = 3y = 10, then 9xy = ?

2x = 10;x=5 3y = 10;y=10/3 Multiply: 9xy=9*5*10/3=150 Answer: C. The answer is: C

C

mathematics

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991. ANSWER:A The answer is: A

A

mathematics

How many two-digit integers exist such that all their digits are odd?

so last digit can be filled in 5 ways- 1,3,5,7,9 there are 5 possibilities. The answer is 5∗5=25 The correct answer is B The answer is: B

B

mathematics

A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?

8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles? 675 ÷ 150 = 4.5 = 4 and 1/2 For each of these groups 8 minutes are needed. For 4 groups and 1/2 8 × 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time) correct answer C The answer is: C

C

mathematics

In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women?

6C3 = 6!/(3! . 3!) = (6 × 5 × 4)/(3 × 2) = 5 × 4 = 20 B) The answer is: B

B

mathematics

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg

By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3 Answer: B The answer is: B

B

mathematics

The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?

Answer : A. Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years. The answer is: A

A

mathematics

A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?

Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec. Length of the train = 20 * 6 = 120 m. Answer: C The answer is: C

C

mathematics

Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2 : 3, then find the number of pens that D gets ?

Let the number of pens that A, B, C and D get be a, b, c and d respectively. a : b = 2 : 1 a = c + 25 b : c = 2 : 3 a : b : c : d = 4 : 2 : 3 : 3 a,d get 4p, 3p pens => 4p - 3p = 25 (given) p = 25 => D gets 3p = 3 * 25 = 75 pens. Answer:C The answer is: C

C

mathematics

A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane?

Eq of line = Y = MX +C M= 4 X=50 Y=50*4 + C, Substitute Y by 300 as given in question. 300=200+C , C =100 correct option is C The answer is: C

C

mathematics

Which of the following is a prime number?

Clearly, 2 is a prime number. Ans : A The answer is: A

A

mathematics

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

39 = 19 + 18 + 12 - 4 - 2x 2x = 19 + 18 + 12 - 4 - 39 = 45 - 39 = 6 x = 3 ANSWER:B The answer is: B

B

mathematics

A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?

Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices. N = 4*4*4*4 = 16*16 = 256 Answer = (C) The answer is: C

C

mathematics

In how much time will a train of length 130 m, moving at 36 kmph cross an electric pole?

Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 130/10 = 13 sec. Answer:D The answer is: D

D