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

Question

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

Bunuel · Accepted Answer

\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.

PareshGmat · Answer

n should be divisible by 25 &  \sqrt{n} > 25

So, n^2 > 625

Looking at all the options, only 26 fits in

Answer = E

Ayselka · Answer

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.

WpackAlumDukeBound · Answer

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!

ScottTargetTestPrep · Answer

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.

Shiv2016 · Answer

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?

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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

anikpait17 · Answer

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?

btsaami · Answer

There is nothing wrong with the approach.
I am assuming that you thought the answer will be close to 30.

However, the first thing which should strike when you get N>25 is that the only number satisfying this criteria is 26. That's the only answer.

Second thing to note here is that the options are close to each other therefore, i will not use such kind of assumptions in such type of questions and solve in such a way that the value should either match or be as close as possible to the one of the options.

totaltestprepNick · Answer

E https://www.youtube.com/watch?v=qKaSPBu3oKQ Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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