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The positive integer n is divisible by 25. If n^1/2 is

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Walkabout
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The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   20 Dec 2012, 06:52
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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
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E
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Bunuel
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The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   20 Dec 2012, 06:55
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Walkabout 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


    \(\sqrt{n}>25\);

    \(n>25^2\).


Divide both parts by 25:

    \(\frac{n}{25}>\frac{25^2}{25}\);

    \(\frac{n}{25}>25\).


The only answer choice that is greater than 25 is 26.

Answer: E.
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   02 Jul 2014, 02:34
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n should be divisible by 25 & \(\sqrt{n} > 25\)

\(So, n^2 > 625\)

Looking at all the options, only 26 fits in

Answer = E
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   14 Jan 2013, 11:09
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Bunuel wrote:
Walkabout 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


\(\sqrt{n}>25\) --> \(n>25^2\).

Divide both parts by 25: \(\frac{n}{25}>\frac{25^2}{25}\) --> \(\frac{n}{25}>25\). The only answer choice that is greater than 25 is 26.

Answer: E.


Hello,

Maybe I don't understand something here, but how can 26/25 be more than 25?
26/25 is 1.04.
Can you please explain.
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   27 Mar 2013, 21:38
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Ayselka wrote:
Bunuel wrote:
Walkabout 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


\(\sqrt{n}>25\) --> \(n>25^2\).

Divide both parts by 25: \(\frac{n}{25}>\frac{25^2}{25}\) --> \(\frac{n}{25}>25\). The only answer choice that is greater than 25 is 26.

Answer: E.


Hello,

Maybe I don't understand something here, but how can 26/25 be more than 25?
26/25 is 1.04.
Can you please explain.


Ayselka,

I know it looks confusing but the question was what is a possible value for \(\frac{n}{25}\) not "what is a possible value for n." Thus, \(\frac{n}{25}=26\), n=650 in this scenario. I hope that helps, and good luck!
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   28 Jun 2016, 05:44
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Walkabout 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


We can solve this problem by translating the given information into math equations. We are first given that the positive integer n is divisible by 25. Translating this we have:

n/25 = integer

We are next given that the square root of n is greater than 25. So we can say:

√n > 25

Next we eliminate the square root by squaring both sides.

n > 25^2

n > 625

Since n must be a multiple of 25 and now we know it must be greater than 625, n/25 must be greater than 625/25, or 25. The only number greater than 25 in the answer choices is 26, so the answer must be E

Answer is E.
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   22 Jun 2017, 03:37
Bunuel wrote:
Walkabout 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


\(\sqrt{n}>25\) --> \(n>25^2\).

Divide both parts by 25: \(\frac{n}{25}>\frac{25^2}{25}\) --> \(\frac{n}{25}>25\). The only answer choice that is greater than 25 is 26.

Answer: E.


Hello Bunuel

In an inequality like in the above, when should we cancel variables or values on both sides or take their square roots and when should we bring them on one side of the inequality to solve?
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   22 Jun 2017, 04:25
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Shiv2016 wrote:
Bunuel wrote:
Walkabout 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


\(\sqrt{n}>25\) --> \(n>25^2\).

Divide both parts by 25: \(\frac{n}{25}>\frac{25^2}{25}\) --> \(\frac{n}{25}>25\). The only answer choice that is greater than 25 is 26.

Answer: E.


Hello Bunuel

In an inequality like in the above, when should we cancel variables or values on both sides or take their square roots and when should we bring them on one side of the inequality to solve?


I think the following topic covers all the cases: Inequality tips

Other useful articles on inequalities:

Inequalities Made Easy!

Solving Quadratic Inequalities - Graphic Approach
Wavy Line Method Application - Complex Algebraic Inequalities

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

https://gmatclub.com/forum/inequalities-trick-91482.html
https://gmatclub.com/forum/data-suff-ine ... 09078.html
https://gmatclub.com/forum/range-for-var ... 09468.html
https://gmatclub.com/forum/everything-is ... 08884.html
https://gmatclub.com/forum/graphic-appro ... 68037.html

Hope this helps.
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The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   Updated on: 20 Mar 2022, 11:43
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Walkabout 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 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

Originally posted by BrentGMATPrepNow on 20 Mar 2022, 11:38.
Last edited by BrentGMATPrepNow on 20 Mar 2022, 11:43, edited 1 time in total.
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink] New post   27 Feb 2024, 08:00
I was thinking of picking up numbers approach. Lets say Root N > 25. If N value = 625 it will break the given condition. So I thought the next best value would be 900 which is divisible by 25 and Root of 900 = 30 > 25. I see that the solutions have been constructed algebrically by squaring on both the sides. But if I think logically, whats wrong with my approach?
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Re: The positive integer n is divisible by 25. If n^1/2 is [#permalink]
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