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Manager  Joined: 02 Dec 2012
Posts: 173
The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Question Stats: 77% (01:22) correct 23% (01:26) wrong based on 1197 sessions

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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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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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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

$$\sqrt{n}>25$$ --> $$n>25^2$$.

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.

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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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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

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Posts: 3
Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Bunuel 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.

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.
Manager  Joined: 04 Jan 2013
Posts: 68
Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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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

since $$[square_root]n[square_root]$$ is greater than 25 then our n is also greater than 25..i will try using the try and error method..lets say the value of n/25 =22,then n=550..$$[sqaure_root]550[sqaure_root]$$ is less than and i guess it wont it wont work..going through all options integer 26 proved worth for an answer by satisfying the following points;it was a result of a division between positive integer n and 25 i.e integer n (650)is a multiple of 25 whose sqaure root is greater than 25..hence option E serves as the answer.

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Intern  Joined: 22 Dec 2012
Posts: 16
GMAT 1: 720 Q49 V39 Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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the questions says n = 5*5*k (as its divisible by 25)
and then asks to find out possible value of K.

now it also says (n^0.5) > 25
which means 5* (k^0.5) > 25
squaring both sides we get K > 25.

Only possible ans is 26!

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.[/quote]
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GMAT 1: 640 Q42 V35 Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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4
Ayselka wrote:
Bunuel 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.

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]

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Bunuel 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.

Hello,

I am confused on how to comprehend this question. I understand we are not looking for the value of n and that we are looking for the value of n/25, however, how are you dividing both sides of the inequality: n>25^2 by 25?
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Math Expert V
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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DelSingh wrote:
Bunuel 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.

Hello,

I am confused on how to comprehend this question. I understand we are not looking for the value of n and that we are looking for the value of n/25, however, how are you dividing both sides of the inequality: n>25^2 by 25?

What do you mean by "how"? Just divide both sides of $$n>25^2$$ by 25.
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Apologies... I meant "why" not "how". However, I do know now what they are asking. I guess the way OG presents the question didn't seem very linear to me so I was confused.
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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1
Another explanation may be:

n/25 is an integer and the Square root of n is greater than 25, so:

n > 25 * 25

The first number that is more than 25*25 and divisible by 25 is 25*25 + 25 -> 25*25 + 25/25 = 25 + 25/25 = 26
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The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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N is divisible by 25 means that N is a muplitple of 25. So, could be 25*1=25, 25*2=50 etc etc.

Only this sentence helps you reject A,B,C, as they already are less than 25.

The second sentence says:
SQRTN>25, so
N> SQRT25 --> N> 625

N/25= 625/25= 25. So, N needs to be greater than 25. Only possible option is ANS E

And also let me add this small piece of advice: when you see greater than flag it somehow (circle it, underline it, write down
greater than, "GT" or whatever).
Than because in this case for example, managing to come to a solution could direct you to answer option D, as this was your result. However, the question wanted sth more than your result (greater than). It is a pitty to give the wrong answer like this...
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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1
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

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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Hi!

A question on this please.

The Tag says this is a OG question. I am using OG-2016 and could not find this question. Does this mean that this is part of an older OG? Also, does this mean that the later OG's may not contain some of the questions contained in Older OG's? Just curious, so that I don't miss out on any OG questions while practicing.
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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susheelh wrote:
Hi!

A question on this please.

The Tag says this is a OG question. I am using OG-2016 and could not find this question. Does this mean that this is part of an older OG? Also, does this mean that the later OG's may not contain some of the questions contained in Older OG's? Just curious, so that I don't miss out on any OG questions while practicing.

Yes, it's Problem Solving Question #176 from Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory: https://gmatclub.com/forum/the-official ... 43450.html
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Thank you so much Bunuel! Glad that we have you in the forum guiding us Bunuel wrote:
susheelh wrote:
Hi!

A question on this please.

The Tag says this is a OG question. I am using OG-2016 and could not find this question. Does this mean that this is part of an older OG? Also, does this mean that the later OG's may not contain some of the questions contained in Older OG's? Just curious, so that I don't miss out on any OG questions while practicing.

Yes, it's Problem Solving Question #176 from Official Guide for GMAT® Review, 13th Edition Quantitative Question Directory: https://gmatclub.com/forum/the-official ... 43450.html

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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Bunuel 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.

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]

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n is divisible by 25 that means n has at least 5^2 as its prime factors.

Also it's given that sq. root of n>25
Squaring both the sides, we get:

n>625
So n/25 has to be greater than 25 (because 625/25= 25 but n is > than 625).

E it is
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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Shiv2016 wrote:
Bunuel 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.

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:

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

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

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

Hope this helps.
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Re: The positive integer n is divisible by 25. If n^1/2 is  [#permalink]

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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

Since $$\sqrt{n}$$ > 25

-> n > 25^2
-> n> 25*25

Also n is a multiple of 25.

26*25, 27*25, 28*25,....................

So n = 26
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