Carcass wrote:
The positive integer n is divisible by 25. If \(\sqrt{n}\) is greater than 25, which of the following could be the value of n/25 ?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
The positive integer n is divisible by 25. So we can write:
n = 25k (for some integer k)
\(\sqrt{n}\) is greater than 25Substitute to get:
\(\sqrt{25k}> 25\) Useful property: \(\sqrt{xy} = (\sqrt{x})(\sqrt{y})\)So our inequality becomes: \((\sqrt{25})(\sqrt{k})> 25\)
Simplify: \((5)(\sqrt{k})> 25\)
Divide both sides of the inequality by 5 to get: \(\sqrt{k}> 5\)
Square both sides: \(k > 25\)
Which of the following could be the value of \(\frac{n}{25}\) ?Since we already stated that
n = 25k, we can substitute to get: \(\frac{n}{25} = \frac{25k}{25} = k\)
In other words, the question is asking us to find a possible value of \(k\)
Since we already determined that \(k > 25\), the only possible value among the answer choices is k = 26
Answer: E
_________________
Brent Hanneson - founder of Greenlight Test Prep