Numbers

Question:
(51 + 52 + 53 + … + 100) = ?

[A].

2525

[B].

2975

[C].

3225

[D].

3775

Answer: Option D

Explanation:

Sn = (1 + 2 + 3 + … + 50 + 51 + 52 + … + 100) – (1 + 2 + 3 + … + 50)

=	100	x (1 + 100) –	50	x (1 + 50)
	2		2

    = (50 x 101) – (25 x 51)

    = (5050 – 1275)

    = 3775.

Question:
The sum of even numbers between 1 and 31 is:

[A].

6

[B].

28

[C].

240

[D].

512

Answer: Option C

Explanation:

Let Sn = (2 + 4 + 6 + … + 30). This is an A.P. in which a = 2, d = 2 and l = 30

Let the number of terms be n. Then,

a + (n – 1)d = 30

     2 + (n – 1) x 2 = 30

    n = 15.

Sn =	n	(a + l)	=	15	x (2 + 30) = (15 x 16) = 240.
	2			2

Question:
How many 3 digit numbers are divisible by 6 in all ?

[A].

149

[B].

150

[C].

151

[D].

166

Answer: Option B

Explanation:

Required numbers are 102, 108, 114, … , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n – 1)d = 996

   102 + (n – 1) x 6 = 996

   6 x (n – 1) = 894

   (n – 1) = 149

   n = 150.

Question:
Which one of the following numbers is exactly divisible by 11?

[A].

235641

[B].

245642

[C].

315624

[D].

415624

Answer: Option D

Explanation:

(4 + 5 + 2) – (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) – (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

Question:
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred’s and ten’s places are respectively:

[A].

7 and 4

[B].

7 and 5

[C].

8 and 5

[D].

None of these

Answer: Option C

Explanation:

Let the given number be 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) – (y + 6 + 4) = (x – y -3) must be either 0 or 11.

x – y – 3 = 0   y = x – 3

(17 + x + y) = (17 + x + x – 3) = (2x + 14)

x= 2 or x = 8.

x = 8 and y = 5.

Question: Which of the following number is divisible by 24 ?
[A].

35718

[B].

63810

[C].

537804

[D].

3125736

Answer: Option D

Explanation:

24 = 3 x8, where 3 and 8 co-prime.

Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

Consider option (D),

Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.

Also, 736 is divisible by 8.

3125736 is divisible by (3 x 8), i.e., 24.

Question:
If the number 5 * 2 is divisible by 6, then * = ?

[A].

2

[B].

3

[C].

6

[D].

7

Answer: Option A

Explanation:

6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.

Then, (5 + x + 2) must be divisible by 3. So, x = 2.

Question:
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:

[A].

2

[B].

5

[C].

6

[D].

8

Answer: Option E

Explanation:

Clearly, 4864 is divisible by 4.

So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.

P = 1.

Question:
What is the unit digit in the product (365 x 659 x 771)?

[A].

1

[B].

2

[C].

4

[D].

6

Answer: Option C

Explanation:

Unit digit in 34 = 1 Unit digit in (34)16 = 1

Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3

Unit digit in 659 = 6

Unit digit in 74 Unit digit in (74)17 is 1.

Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3

Required digit = Unit digit in (3 x 6 x 3) = 4.

Question: If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?
[A].

2 or 6

[B].

4

[C].

4 or 8

[D].

8

Answer: Option A

Explanation:

80 = 2 x 5 x 8

Since 653xy is divisible by 2 and 5 both, so y = 0.

Now, 653x is divisible by 8, so 13x should be divisible by 8.

This happens when x = 6.

x + y = (6 + 0) = 6.