It is currently 21 Feb 2018, 06:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

31 Jan 2018, 04:40
00:00

Difficulty:

75% (hard)

Question Stats:

51% (01:23) correct 49% (01:58) wrong based on 97 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

31 Jan 2018, 04:41
Reserving this post for the official solution.
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

VP
Joined: 26 Mar 2013
Posts: 1430
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

31 Jan 2018, 04:59
3
KUDOS
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

Senior Manager
Joined: 31 Jul 2017
Posts: 295
Location: Malaysia
WE: Consulting (Energy and Utilities)
If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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 $$25 < x < 500.$$
$$k = 9,16,64$$
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Joined: 26 Sep 2017
Posts: 47
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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

Sent from my BND-AL10 using GMAT Club Forum mobile app
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2058
Location: India
GPA: 3.12
If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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.

_________________

Stay hungry, Stay foolish

Intern
Joined: 26 Sep 2017
Posts: 47
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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
Intern
Joined: 09 Jan 2014
Posts: 6
Location: India
Schools: ISB '20, IIMA , IIMB, IIMC , XLRI
GMAT 1: 690 Q48 V37
GPA: 4
WE: General Management (Manufacturing)
If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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: 44
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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: 43851
Re: If x is integer that lies between 25 and 500, for how [#permalink]

### Show Tags

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.
_________________
Re: If x is integer that lies between 25 and 500, for how   [#permalink] 12 Feb 2018, 20:38
Display posts from previous: Sort by