For the following two (02) items: Let p = ∑_ j=1 ^ n _ 10 2^j and q = ∑_ j=1 ^ n _ 10 5^j . If p + q = 66 , then which one of the following is correct?

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 9 < n < 12

Given p = ∑_ j=1 ^ n _ 10 2^j and q = ∑_ j=1 ^ n _ 10 5^j Adding p and q : p + q = ∑_ j=1 ^ n ( _ 10 2^j + _ 10 5^j) p + q = ∑_ j=1 ^ n _ 10 (2^j · 5^j) p + q = ∑_ j=1 ^ n _ 10 (10^j) p + q = ∑_ j=1 ^ n j _ 10 10 Since _ 10 10 = 1 , we get: p + q = ∑_ j=1 ^ n j = (n(n+1))/(2) Given p + q = 66 : (n(n+1))/(2) = 66 n(n+1) = 132 n^2 + n - 132 = 0 (n - 11)(n + 12) = 0 Since n must be a positive integer, n = 11 . The value n = 11 satisfies the condition 9 Answer: 9 < n < 12

For the following two (02) items: Let p = ∑_ j=1 ^ n _ 10 2^j and q...

Options

Correct answer

Step-by-step solution

More from Basics of Mathematics