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The positive integer n is divisible by 25. If [m][square_root]n[/squar
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28 Mar 2022, 07:58
28 Mar 2022, 07:58
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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
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
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Re: The positive integer n is divisible by 25. If [m][square_root]n[/squar
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28 Mar 2022, 09:01
28 Mar 2022, 09:01
1
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
(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 25
Substitute 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
Re: The positive integer n is divisible by 25. If [m][square_root]n[/squar
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28 Mar 2022, 19:03
28 Mar 2022, 19:03
The positive integer n is divisible by 25, which means 25 is a factor of n. Hence, n = 25k, where k is a positive integer.
If √n > 25, then √25k > 25
Squaring both sides
25k > 25^2
Hence, k > 25
n/25 = 25k/25 = k
And it is known that k is greater than 25, only option is 26
E is correct
If √n > 25, then √25k > 25
Squaring both sides
25k > 25^2
Hence, k > 25
n/25 = 25k/25 = k
And it is known that k is greater than 25, only option is 26
E is correct
