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# Aptitude Questions and Answers with Explanation for placement, MBA

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 1 Find the number of factors of 1728? A. 18 B. 28 C. 30 D. 20
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Explanation

1728= 26 * 33

Hence the Number of factors = (6+1) x (3+1) = 7 x 4 = 28.

We know that if a number represented in standard form (am *bn)  ,  then the number of factors Is given by  (m+1)(n+1).

Example: 40 =2x2x2x5 = 23 x 51 .

Hence the number of factors is (3+1) x (1+1)= 4 x 2 = 8

Now Let’s Verify this ,

The Factors are: 1,2,4,5,8,10,20,40 which are 8 in numbers including 1 and the number 40 itself.

 2 Find the number of divisors of 1080 excluding the divisors which are perfect squares. A. 28 B. 30 C. 29 D. 31
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Explanation

1080=23 x 33 x 51

So, Number of divisors/factors = 4 x 4 x 2 = 32
Out of all the factors  1, 4(22), 9(33) and 36 (9 x 4) are perfect Squares.

So the answer is 32-4 = 28.

 3 Find the sum and number of divisors of 544 excluding 1 and 544. A. 1089, 9 B. 589, 10 C. 579, 11 D. 1134, 12
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Explanation

544 = 2 5  + 171

The  number of factors are (5 + 1)x(1+1)= 12.

The factors also include 1 and 544. So , the answer is : 12 - 2 = 10

To Find Sum:

544= 25  + 171=(20+21+22+23+24+25) x (170 + 171)=(1 + 2+ 4+ 8+16+32)x(1 + 17) =63 x 18 = 1134

Excluding 1 and 544 = 545 we get, 1134- 545=589.

 4 Find the sum of divisors of 544 which are perfect squares. A. 32 B. 64 C. 42 D. 21
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Explanation

544= 25 + 171 =(20+21+22+23+24+25) x (170 + 171).

Here 20=1 =11 A perfect Square,

22 and 24=16=44 are perfect Squares, Hence,

1 + 4 + 16= 21

 5 Sum of 36 odd numbers is? A. Even B. Odd C. Cannot Say D. None of the Above
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Explanation Sum of odd numbers is always even for even number of odd numbers and odd for odd number of odd numbers.

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