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13)Question

The sum of the first 100 numbers, 1 to 100 is divisible by

(1) 2, 4 and 8
(2) 2 and 4
(3) 2 only
(4) None of these

Correct Choice is (3) and Correct Answer is 2 only

Explanatory Answer

The sum of the first 100 natural numbers is given by (n(n + 1))/2 = (100(101))/2 = 50(101).

101 is an odd number and 50 is divisible by 2. Hence, 50*101 will be divisible by 2.
 
14)Question
How many different factors are there for the number 48, excluding 1 and 48?

(1) 12
(2) 4
(3) 8
(4) None of these

Correct Choice is (3) and the correct answer is 8

Explanatory Answers

To find the number of factors of a given number, express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (24 * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 - 2 = 8 factors.
 
15)Question:

1025 - 7 is divisible by
1.2
2.3
3.9
4.Both (2) and (3)
Correct Answer - 3. Correct choice is (2)

Explanatory Answers

1025 - 7 = (1025 - 1) - 6

The number 1025 - 1 = 99.....9 (25 digits) is divisible by 3 and 4.

Therefore, (1025 - 1) - 6 = (24 nines and unit digit is 3) 99.......93.

This number is only divisible by 3 (from the given choices).
 
16)Question

Find the G.C.D of 12x2y3z2, 18x3y2z4, and 24xy4z3

(1) 6xy2z2
(2) 6x3y4z3
(3) 24xy2z2
(4) 18x2y2z3

Correct Choice is (1) and Correct Answer is 6xy2z2

Explanatory Answer

G.C.D of 12, 18 and 24 is 6.

The common factors are x, y, z and their highest powers common to all are 1, 2 and 2 respectively.

Therefore, G.C.D = 6xy2z2
 
17)Question
What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; Where M and N are single digit integers?

(1) 7, 8
(2) 8, 6
(3) 6, 4
(4) 5, 4

Correct Choice is (3) and correct answer is 6, 4

Explanatory Answers

If the last three digits of a number is divisible by 8, then the number is divisible by 8 (test of divisibility by 8).

Here, last three digits 58N is divisible by 8 if N = 4. (Since 584 is divisible by 8.)

For divisibility by 11. If the digits at odd and even places of a given number are equal or differ by a number divisible by 11, then the given number is divisible by 11.

Therefore, (M+9+4+4+8)-(3+0+8+5+N)=(M+5) should be divisible by 11 => when M = 6.
 
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