What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?

Question:
The sum of all two digit numbers divisible by 5 is:

[A].

1035

[B].

1245

[C].

1230

[D].

945

Answer: Option D

Explanation:

Required numbers are 10, 15, 20, 25, …, 95

This is an A.P. in which a = 10, d = 5 and l = 95.

tn = 95       a + (n – 1)d = 95

10 + (n – 1) x 5 = 95

(n – 1) x 5 = 85

(n – 1) = 17

n = 18

Requuired Sum =	n	(a + l)	=	18	x (10 + 95)   = (9 x 105)   = 945.
	2			2

Question: Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
[A].

(47 – 43)

[B].

(47 + 43)

[C].

(4743 + 4343)

[D].

None of these

Answer: Option B

Explanation:

When n is odd, (xn + an) is always divisible by (x + a).

Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).