If x is integer that lies between 25 and 500, for how

Question

If x is integer that lies between 25 and 500, for how many values of x is  \frac{x}{20}  the square of an integer?

A. 2
B. 3
C. 4
D. 5
E. More than 5

Mo2men · Accepted Answer

\frac{X}{20}  =  I^{2}

or X = 20 *  I^{2}

The answer choices suggests that we do not have much options, so we can plug in values

X = 20  1^{2} = 20..........out of range

X = 20  2^{2} = 80..........Ok

X = 20  3^{2} = 180..........Ok

X = 20  4^{2} = 320..........Ok

X = 20  5^{2} = 500..........out of range ( if the questions stem says 'inclusive', they it would be valid)

We have 3 Integers

Answer: B

Pradeeps0013 · Answer

If 25<x<500, for how many values of x is  \frac{x}{20}  the square of an integer?

25<x<500. Divide this inequality by 20.

Therefore  \frac{25}{20} < \frac{x}{20} <  \frac{500}{20}

1.25< \frac{x}{20} <25

Only squares in this range are 4, 9 & 16.

Therefore  Answer: B

rahul16singh28 · Answer

a^2 = \frac{x}{50} --> a = \frac{1}{2}\sqrt{\frac{x}{5}} 
 x = 5k 
As  25 < x < 500. 
 k = 9,16,64

viv007 · Answer

For a no. To be a prfct squre. X/20 must have a pair of prime factor ...20= 2*2*5

X must be between 25 to 500

Now we have to check prime factor combination which comes in range....

2*2*5*2*2/2*2*5 = 80 correct
2*2*5*3*3/2*2*5 = 180 correct
2*2*5*5*5/2*2*5 = 500 incorrect( no must between 25 to 500)

So nly 2 numbers are possible 
Ans.A

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pushpitkc · Answer

Hi  viv007

Why are you considering only prime-factor combinations only?

Consider the following case x=320, the number x/20 = 16 is a perfect square.
Hence x can have 3 values(80,180, and 320). 
Therefore, Option B(x can take 3 values) should be the answer.

Hope that clears your confusion!

viv007 · Answer

Thank you pushpitkc:

Actully 1 more combination pissible i forgot or rather missed it..

I.e.

2*2*5*2*2*2*2/2*2*5 = 320..

Thnku...

Sent from my BND-AL10 using  GMAT Club Forum mobile app

Sateni7628 · Answer

How do we know if the question says X lies between 25 & 500 inclusive or exclusive? Inclusive the answer would be C.

Bunuel · Answer

On the GMAT, it would be clear and unambiguous. The question will say it explicitly.

pierjoejoe · Answer

AMBIGUOUS --> 25 and 500 are inclusive or exclusive???

if they are exclusive than
x/20 = k^2
25<x<500
25<20k^2<500

5/(2*radq(5)) < k < 5
than approx
1<k<5
than k can be either
k = 2 x = 80 OK
k = 3 x = 180 OK 
k = 4 x = 320 OK
k = 5 x = 500 NOT INCLUDED 25<x<500

meaning that the number of integers that respect the condition above are 4

shubhim20 · Answer

Bunuel  please explain

Bunuel · Answer

You're given 25 < x < 500 and asked how many values of x make x/20 a perfect square.

Divide by 20:

25/20 < x/20 < 500/20

1.25 < x/20 < 25

So x/20 must be a perfect square between 1.25 and 25. The perfect squares in that range are:

2^2 = 4
3^2 = 9
4^2 = 16

So x/20 can be 4, 9, or 16, meaning x = 80, 180, or 320. That’s 3 values.

Answer: B.

If x is integer that lies between 25 and 500, for how

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If x is integer that lies between 25 and 500, for how

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