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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  [#permalink]

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New post 31 Jan 2018, 05:40
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Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT

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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 31 Jan 2018, 05:41
Reserving this post for the official solution. :)
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 31 Jan 2018, 05:59
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EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


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

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
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If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 06 Feb 2018, 05:04
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


\(a^2 = \frac{x}{50} --> a = \frac{1}{2}\sqrt{\frac{x}{5}}\)
\(x = 5k\)
As \(25 < x < 500.\)
\(k = 9,16,64\)
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 07 Feb 2018, 05:16
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


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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If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 07 Feb 2018, 05:34
viv007 wrote:
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


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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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!
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 07 Feb 2018, 06:31
pushpitkc wrote:
viv007 wrote:
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


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

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


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!

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...

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If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 07 Feb 2018, 12:06
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT



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
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 12 Feb 2018, 12:57
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


How do we know if the question says X lies between 25 & 500 inclusive or exclusive? Inclusive the answer would be C.
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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New post 12 Feb 2018, 21:38
saski07 wrote:
EgmatQuantExpert wrote:
Q.)
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


Regards,
Saquib
Quant Expert
e-GMAT


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


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