Q6 of 31 Page 1

How many two digit numbers are divisible by 7?

Two digits numbers divisible by 7 are:


14, 21, 28, …, 98


Above sequence is clearly an AP, with


First term, a = 7


Common difference, d = 21 – 14 = 7


Let the number of terms be n, then


Last term, an = 98


We know,


nth term of an AP, an = a + (n – 1)d


⇒ 98 = 14 + (n – 1)7


⇒ 84 = (n – 1)7


⇒ n – 1 = 12


⇒ n = 13


Hence, 13 two digit numbers are divisible by 7


More from this chapter

All 31 →
4

Find the value of a, for which point P (a, 2) is the midpoint of the line segment joining the points Q (–5, 4) and R(–1, 0).

 5

If 2 is a root of the equation x2 + kx + 12 = 0 and the equation x2 + kx + q = 0 has equal roots, find the value of q.

 7

Find a relation between x & y such that the point P(x,y) is equidistant from the points A(–5,3) and B(7,2).

 8

Find the perimeter of the shaded region if ABCD is a square of side 21 cm and

APB & CPD are semicircles. (Use π=22/7).