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**Placement papers of Aspire Systems 2016**. Learn and practice the placement papers and interview questions answers of Aspire Systems and find out how much you score before you appear for your next interview and written test.

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__Aspire Systems Placement Papers - Interview Questions:__

**1. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? 1. Sixty per cent of the top academic performers were not athletes. 2. All the top academic performers were not necessarily athletes.**

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: A

Explanation:

From 1st Statement, 40% of the top academic performers were athletes. If there are x top academic performers, 10 = 0.4x.

Therefore x = 25 1st Statement is sufficient. Statement B does not give any useful information. Hence, option A.

**2. Is a44 < b11, given that a = 2 and b is an integer ? 1. b is even. 2. b is greater than 16.**

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: B

Explanation:

Solution cannot be found by using only 1st Statement since b can take any even number 2,4,6 ........ But we can arrive at solution

by using 2nd statement alone. If b > 16, say b = 17 Hence 244 < (16 + 1)11 244 < (24 + 1)11

**3. What are the unique values of b and c in the equation 4x2 + bx + c = 0 if one of the roots of the equation is (-1/2) ?**

1. The second root is 1/2. 2. The ratio of c and b is 1.

1. The second root is 1/2. 2. The ratio of c and b is 1.

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: D

Explanation:

Solution can be found using 1st Statement as we know both the roots for the equation (viz. 1/2 and -1/2). Also 2nd statement is sufficient.

Since ratio of c and b = 1, c = b. Thus the equation = 4x2 + bx + b = 0. Since x = -1/2 is one of the roots, substituting we get 1 -b/2 + b = 0 or b = -2. Thus c = -2.

**4. AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle? 1. AB is not a diameter of the circle.**

2. The distance between AB and the tangent at E is 5 cm.

2. The distance between AB and the tangent at E is 5 cm.

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: B

Explanation:

We can get the answer using the second statement only. Let the radius be r. AC = CB = 2.5 and using statement B, CE = 5, thus OC = (r - 5).

Using Pythagoras theorem, (r - 5)2 + (2.5)2 = r2 We get r = 3.125

**5. D, E, F are the mid points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimeters? A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3cm. B. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm.**

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: D

Explanation:

The question tells us that the area of triangle DEF will be 1/4th the area of triangle ABC. Thus by knowing either of the statements,

we get the area of the triangle DEF.

**6. What is the Cost Price of the article ? 1. After selling the article, a loss of 25% on Cost Price incurred. 2. The Selling Price is three-fourths of the Cost Price.**

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement

Answer: D

Explanation:

We are required to find out the exact cost price. Both the statements give the same information, i.e. the SP is 0.75 times the CP.

**7. A tractor travelled a distance of 5 m. What is the radius of the rear wheel ? 1. The front wheel rotates "N" times more than the rear wheel over this distance.**

2. The circumference of the rear wheel is "t" times that of the front wheel.

2. The circumference of the rear wheel is "t" times that of the front wheel.

A.using 1st Statement only B.using 2nd statement Only

C.using both 1st and 2nd statement D.using 1st or 2nd statement E.Cannot be answered even by using both the statement

Answer: E

Explanation:

To find the radius of the rear wheel, we need to know the numerical value of its circumference. From 1st statement, we get a relation between the

circumferences of the two wheels in terms of "N". From 2nd statement, we get similar information in terms of "t". Thus, the radius cannot be determined from the given data

**8. What is the Selling Price of the article? 1. The profit on Sales is 20%. 2. The profit on each unit is 25% and the Cost Price is Rs. 250.**

A.using 1st Statement only B.using 2nd statement only C.using both 1st and 2nd statement D.using 1st or 2nd statement E.Cannot be answered even by using both the statement

Answer: B

Explanation:

By default, the profit is always mentioned as a % of the CP. From 2nd statement, we see that the profit on the article is 25% of Rs. 250,

which is Rs. 62.50. So the SP can be determined with the help of 2nd statement alone.

**9. The number 13409 and 16760 when divided by a 4 digit integer and leave the same reminder then the value of n is**

A.1127 B.1117 C.1357 D.1547

Answer: B

Explanation:

Here 13409 and 16760 on division by n leaves the same reminder hence can be written as n * m + r and can be written n*p + r.

There subtracting the 2 equation we get n * (m - p) = 3351 = 1117*3. But n is 4 digit number hence n is 1117.

**10. If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?**

A.25% B.16.67% C.20% D.33.3%

Answer: C

Explanation:

Let the price of petrol be Rs.100 per litre. Let the user use 1 litre of petrol. Therefore, his expense on petrol = 100 * 1 = Rs.100.

Now, the price of petrol increases by 25%. Therefore, the new price of petrol = Rs.125. As he has to maintain his expenditure on petrol constant,

he will be spending only Rs.100 on petrol. Let 'x' be the number of liters of petrol he will use at the new price.

Therefore, 125*x = 100 => x = (100/125) = 0.8 liters. He has cut down his petrol consumption by 0.2 liters = 0.2 * 100 = 20% reduction.

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**11. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year.**

The current average age of this eight member joint family is nearest to:

The current average age of this eight member joint family is nearest to:

A.23 years B.22 years C.21 years D.24 years

Answer: D

Explanation:

The sum of the ages of the members of the family ten years ago = 231 The sum of the ages of the members of the family seven years ago = 231 + (3 × 8) - 60 = 195

The sum of the ages of the members of the family four years ago = 195 + (3 × 8) - 60 = 159 The sum of the ages of the members of the family now = 159 + (4 × 8) = 191

Required average = 191/8 = 23.875 ≈ 24

**12. Two person are climbing up on two moving escalators which have 120steps. The ratio of 1st person's speed to that of 1st escalator is 2: 3. The ratio of 2nd person's speed to that of 2nd escalator is 3: 5. Find the total number of steps they both have taken together ?**

A.85 B.93 C.80 D.75

Answer: B

Explanation:

2 steps of 1st person = 3 steps of escalators Hence steps for 1st person = (2/3)*120/( 1+(2/3)) = 120 * 3/2 * 2/3 = 48.

Similarly steps for second person = 3/2 * 120 * 5/8 = 45. Total steps = 48 + 45 =93.

**13. If the product of n positive real numbers is unity, then their sum is necessarily:**

A.a multiple of n B.equal to n + 1/n C.never less than n D.a positive integer

Answer: C

Explanation:

Consider some value E.g. 2, 1/2 and 1. Thus, n = 3 and the sum of the three numbers = 3.5. Thus options 1, 2 and 4 get eliminated.

14. The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday ?

14. The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday ?

A.24 degrees B.21 degrees C.27 degrees D.30 degrees

Answer: D

Explanation:

Total temperature on Wednesday, Thursday and Friday was 25 * 3 = 750 Total temperature on Thursday, Friday and Saturday was 24 * 3 = 720 Hence,

difference between the temperature on Wednesday and Saturday = 30 If Saturday temperature = 270, then Wednesday's temperature = 27 + 3 = 300

**15. Once I had been to the post-office to buy stamps of five rupees, two rupees and one rupee. I paid the clerk Rs 20, and since he did not have change, he gave me three more stamps of one rupee. If the number of stamps of each type that I had ordered initially was more than one,**

what was the total number of stamps that I bought ?

what was the total number of stamps that I bought ?

A.10 B.9 C.12 D.8

Answer: A

Explanation:

At least two stamps of each type were ordered initially. So Rs. 2(5 + 2 + 1) = Rs. 16 have been spent. That leaves Rs. (20 - 16) = Rs. 4.

In this Rs. 4, three more stamps of one rupee were given, thus accounting for Rs. 19 in all. Since one more rupee remains, it means that one more

stamps of Rs. 2 were bought initially. So the total number of stamps is 2(0f Rs. 5) + 3 (of Rs. 2) + 4(of Re. 1).

**16. I sold two watches for Rs. 300 each, one at a loss of 10% and the other at a profit of 10%. What is the percent loss (-) or the percent profit (+) that resulted from the transaction?**

A.(+) 10 B.(-) 1 C.(+) 1 D.0

Answer: B

Explanation:

The % loss is given by (p² /100). In the given problem, p = 100, therefore % loss = 1.

**17. A man travels three-fifths of distance AB at a speed of 3a, and the remaining at a speed of 2b. If he goes from B to A and back at a speed of 5c in the same time, then:**

A.1/a + 1/b = 1/c B.a + b = c C.1/a + 1/b = 2/c D.None of these

Answer: A

Explanation:

A..........C...........B AB = x => AC = 3x/5 and CB = 2x/5. Distance = Speed * Time Time taken to travel the distance between A and C = 3x/5 = 3a * T1 = T1 = x/5a

Time taken to travel the distance between C and B = 2x/5 = 2b * T2 = T2 = x/5b. Time taken to travel between A and B back and fourth = x = 5c * T = T = x/5c Given that,

T = T1 + T2 x/5a + x/5b + x /5c 1/a + 1/b + 1/c.

**18. Instead of a meter scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash payment, what is his overall percent profit ?**

A.20% B.25% C.40% D.15%

Answer: A

Explanation:

Let the price of 100m of cloth be Rs 100, but he gets 120cm of cloth for Rs 100. Hence, his actual cost for 1cm = 100/120 = Rs. 5/6.

Now, instead of selling 100cm, by cheating he sells 80cm of cloth for the cost price of 100cm of cloth. to calculate his profit, the cost price of 80cm of

cloth = 5/6 x 80 = Rs.66.66. Selling price of 80cm of cloth (actually 100cm for the buyers) at a discount of 20% = 100 x 0.8 = Rs.80.

Profit% = 80 - 66.66 x 100 = 20.01% or 20% approximately. 66.66

**19. In 4 years, the SI on a certain sum of money is 7/25 of the principal. What is the annual rate of interest ?**

A.4% B.4.5% C.7% D.9%

Answer: C

Explanation:

Simple interest = (P x 4 x r) / 100 (7P/25) = (P x 4 x r) / 100 => 7/25 = (4r) / 100 => r = 7%

**20. In a mile race Akshay can be given a start of 128 meters by Bhairav. If Bhairav can given Chinmay a start of 4 meters in a 100 meters dash,**

then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser ?

then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser ?

A.Akshay, 1/12 miles B.Chinmay, 1/32 miles C.Akshay, 1/24 miles D.Chinmay, 1/16 miles

Answer: D

Explanation:

When Bhairav (B) covers 1600 m, Akshay (A) covers (1600 - 128) m. So, when B covers (1600/16) = 100 m, A covers (128/16) m = 8 m less.

When B covers 100 m, C covers (100 - 4) = 96 m. Thus the ratio in which A and C cover distances is 92: 96. In 96 m, C gains (96 - 92) = 4 m over A.

So in 1.5 miles (i.e. 2400 m), c gains 100 m = (1/16) miles over A.

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**21. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed ?**

A.499 B.500 C.375 D.376

Answer: D

Explanation:

The minimum number that can be formed is 1000 and the maximum number that can be formed is 4000. As 4000 is the only number in which the first digit is 4,

first let us calculate the numbers less than 4000 and then we will add 1 to it. Therefore First digit can be 1, 2 or 3. Remaining 3 digits can be any of the 5 digits.

Therefore Total numbers that can be formed, which are less than 4000 = 3 × 5 × 5 × 5 = 375. Total numbers that satisfy the given condition = 375 + 1 = 376.

**22. Thirty days are in September, April, June and November. Some months are of thirty one days. A month is chosen at random. Then its probability of having exactly three days less than maximum of 31 is .......**

A.15/16 B.1 C.3/48 D.none of these

Answer: D

Explanation:

February is the only month having 28 or 29 days. Probability of choosing February = 1/12.

**23. What is the number of distinct terms in the expansion of (a + b + c)20 ?**

A.231 B.253 C.242 D.210

Answer: A

Explanation:

(a + b + c)1 = a + b + c [i.e. 3 terms = (1 + 2) terms] (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac

[i.e. 6 terms = (1 + 2 + 3) terms] (a + b + c)3 = a3 + b3 + c3 + 6abc + 3ab2 + 3ac2 + 3a2b + 3bc2 + 3a2c + 3b2c

[i.e. 10 terms = (1 + 2 + 3 + 4) terms] Similarly, (a + b + c)n will have (1 + 2 + 3 + ... + (n + 1)) terms Therefore (a + b + c)20 will have (1 + 2 + 3 + ... + 21) = 231 terms.

**24. If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a reminder of**

A.0 B.1 C.69 D.35

Answer: A

Explanation:

x = 163 + 173 + 183 + 193 = (163 + 193) + (173 + 183) (16 + 19)(162 + 16 × 19 + 192) + (17 + 18) (172 + 17 × 18 + 182) = 35 ×

(an odd number) + 35 × (another odd number) = 35 × (an even number) = 35 × (2k) ... (k is a positive integer) ∴ x = 70k ∴ x is divisible by 70.

Remainder when x is divided by 70 = 0.

**25. A chemical plant has four tanks (A, B, C and D), each containing 1000 liters of a chemical. The chemical is being pumped from one tank to another as follows:**

From A to B at 20 liters/minute From C to A at 90 liters/minute. From A to D at 10 liters/minute From C to D at 50 liters/minute. From B to C at 100 liters/minute From D to B at 110 liters/minute. Which tank gets emptied first and how long does it take (in minutes) to get empty after pumping starts ?

From A to B at 20 liters/minute From C to A at 90 liters/minute. From A to D at 10 liters/minute From C to D at 50 liters/minute. From B to C at 100 liters/minute From D to B at 110 liters/minute. Which tank gets emptied first and how long does it take (in minutes) to get empty after pumping starts ?

A.A, 16.66 B.C, 20 C.D, 20 D.D, 25

Answer: C

Explanation:

The change in the amount of chemical in each tank after every minute is as follows: A: -20 -10 + 90 = 60 B: -100 + 110 + 20 = 30 C: -50 -90 + 100 = -40 D: -110 + 10 + 50 = -50

Since tank D loses the maximum amount of chemical in a minute, it will be emptied first. Let n minutes be the time taken by tank D to get empty.

1000 - 50n = 0 n = 20minutes.

**26. Find the next term in the series ? 36 31 29 24 22 17 15**

A.13 11 B.10 5 C.13 8 D.10 8

Answer: D

Explanation:

This is an alternating subtraction series, which subtracts 5, then 2, then 5, and so on.

**27. A manufacturer has 200 liters of acid solution which has 15% acid content. How many liters of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25% ?**

A.More than 100 liters but less than 300 liters

B.More than 120 liters but less than 400 liters

C.More than 100 liters but less than 400 liters

D.More than 120 liters but less than 300 liters

Answer: C

Explanation:

Amount of acid content in the solution = 15% of 200 = 30 liters Let the amount of solution to be added be x When acid content is 20%,

we get 150 + 1.5x = 200 + x 50 = 0.5x x = 100 liters When acid content is 25%, we get 120 + 1.2x = 200 + x 80 = 0.2x x = 400 liters

So the solution to be added should be more than 100 liters but less than 400 liters.

**28. The average of nine numbers is M and the average of three of these is p. If the average of remaining numbers is N, then**

A.M = N + P B.2M = N + P C.3M = 2N + P D.3M = 2P + N

Answer: C

Explanation:

Let A1, A2, A3... A9 be the numbers and their average = M So A1 + A2 + ........ +A9 = 9M A1 + A2 + A3 = 3P (since average of A1, A2 & A3 = P) A4 + A5 + ......... A9 = 6N

(since average of A4 to A9 = n) adding above three equations and divide by 3 => 3M = 2N + P

**29. Let S be a set of positive integers such that every element n of S satisfies the conditions:- a) 1000 < n < 1200 b) every digit in n is odd.**

Then how many elements of S are divisible by 3 ?

Then how many elements of S are divisible by 3 ?

A.9 B.10 C.11 D.12

Answer: A

Explanation:

n will be of the form 11ab, where a and b are odd numbers. We are looking for all n's divisible by 3. ∴ 1 + 1 + a + b = 3 or 9 or 12 or 15 or 18

∴ a + b = 1 or 4 or 7 or 10 or 13 or 16 ∴ a + b = 1 or 7 or 13 is not possible as the sum of two odd numbers cannot be odd.

∴ (a, b) = (1, 3), (3, 1), (1, 9), (3, 7), (5, 5), (7, 3), (9, 1), (7, 9), (9, 7) ∴ 9 elements of S are divisible by 3.

**30. The Intersection of two cubes cannot be:-**

A.cube B.triangle C.a rectangle D.none of these

Answer: A

Explanation:

Cubes are 3 dimensional so their interaction will be two dimensional. Hence, it cannot be a cube.