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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2456
If x is integer that lies between 25 and 500, for how  [#permalink]

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31 Jan 2018, 04:40
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Question Stats:

51% (01:57) correct 49% (02:08) wrong based on 150 sessions

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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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31 Jan 2018, 04:59
4
1
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

##### General Discussion
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2456
Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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31 Jan 2018, 04:41
Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
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If x is integer that lies between 25 and 500, for how  [#permalink]

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06 Feb 2018, 04:04
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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Joined: 26 Sep 2017
Posts: 97
Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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07 Feb 2018, 04:16
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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07 Feb 2018, 04:34
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

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.

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Joined: 26 Sep 2017
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Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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07 Feb 2018, 05:31
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.

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
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GMAT 2: 730 Q50 V39
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WE: General Management (Manufacturing)
If x is integer that lies between 25 and 500, for how  [#permalink]

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07 Feb 2018, 11:06
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.

Intern
Joined: 18 Jan 2018
Posts: 48
Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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12 Feb 2018, 11:57
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.
Math Expert
Joined: 02 Sep 2009
Posts: 52295
Re: If x is integer that lies between 25 and 500, for how  [#permalink]

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12 Feb 2018, 20:38
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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Re: If x is integer that lies between 25 and 500, for how &nbs [#permalink] 12 Feb 2018, 20:38
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