GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Aug 2018, 19:54

### 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

# If x and y are positive integers, what is the value of x ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 48037
If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 01:42
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:24) correct 56% (01:22) wrong based on 81 sessions

### HideShow timer Statistics

If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5

_________________
DS Forum Moderator
Joined: 27 Oct 2017
Posts: 675
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 04:55
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.
_________________
SVP
Joined: 08 Jul 2010
Posts: 2139
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 05:55
Bunuel wrote:
If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5

Question : WHat is the value of x?

STatement 1: x, y, and xy are distinct perfect squares less than 100

Case 1: x = 4, y = 9, xy = 36
Case 2: x = 9, y = 4, xy = 36
Multiple values of x hence,
NOT SUFFICIENT

STatement 2: x<5
No information about y and xy and hence x may be 1 or 2 or 3 or 4 etc
NOT SUFFICIENT

Combining the two statements
x, y, and xy are distinct perfect squares and x <5

less than 5 theer are only two perfect squares 1 and 4
but x can NOT be 1 because x*y will be equal to y which is unacceptable because given that x, y and xy are distinct
hence
x = 4
SUFFICIENT

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

SVP
Joined: 08 Jul 2010
Posts: 2139
Location: India
GMAT: INSIGHT
WE: Education (Education)
If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 05:56
gmatbusters wrote:
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.

None of x and y can be equal to 1 because if anyone of them is 1 then x, y and xy will not remain DISTINCT
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 02 Feb 2017
Posts: 3
GMAT 1: 720 Q49 V32
GPA: 3.36
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 06:51
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?
DS Forum Moderator
Joined: 27 Oct 2017
Posts: 675
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 07:24
yes, you are right... but x can only be 4. hence Answer is C

chirkut1488 wrote:
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?

_________________
DS Forum Moderator
Joined: 27 Oct 2017
Posts: 675
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 07:49
thanks for pointing out my mistake...

GMATinsight wrote:
gmatbusters wrote:
Statement 1: we can have (x, y) as (1, 4) or (4, 9)... so not sufficient
Statement 2: x can be 1, 2, 3 or 4.
Combining statement 1 &2
We can have (x,y) as (1,4) or (4,1)
hence the value of x can be 1 or 4; the unique value of x cannot be determined.

None of x and y can be equal to 1 because if anyone of them is 1 then x, y and xy will not remain DISTINCT

_________________
Manager
Joined: 24 Nov 2016
Posts: 152
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

17 Dec 2017, 12:03
Bunuel wrote:
If x and y are positive integers, what is the value of x ?

(1) x, y, and xy are distinct perfect squares less than 100.
(2) x < 5

Positive integers are numbers greater than 0 {1,2,3,4,5...}

(1) x, y, and xy are distinct perfect squares less than 100.

x = 4 (2*2), y = 9 (3*3) and xy = 9*4 = 36 (6*6); or,
x = 9 (3*3), y = 49 (7*7) and xy = 9*49 = 196 (14*14).

They are all distinct perfect squares and there is more than one value for x, so insufficient.

(2) x < 5.

So x can be {1,2,3 or 4}, insufficient.

(3) Combining both informations we can only have one value for x < 5 that is a perfect square: $$x=4$$, sufficient.

Senior Manager
Joined: 12 Feb 2015
Posts: 379
Re: If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

15 Jun 2018, 09:41
chirkut1488 wrote:
can x=4 y =16 and xy = 64 be a case as well along with the one mentioned above ?

Since X<5 then x has to be 4 hence the answer is C
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1203
Location: India
GPA: 3.82
If x and y are positive integers, what is the value of x ?  [#permalink]

### Show Tags

06 Jul 2018, 23:21
TippingPoint93 wrote:
If x and y are positive integers, what is the value of x?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5

Statement 1: as $$x$$, $$y$$ & $$xy$$ are distinct perfect squares so $$x$$ or $$y$$ cannot be equal to $$1$$ because in that case $$xy$$ will be equal to either $$x$$ or $$y$$.

Some of the possible $$x$$ & $$y$$ combinations are $$(4,9)$$ & $$(9,4)$$. There are multiple values of $$x$$. hence Insufficient

Statement 2: $$x$$ could be $$1$$ or $$4$$. Insufficient

Combining 1 & 2: Only possible value for $$x=4$$. Sufficient

Option C
If x and y are positive integers, what is the value of x ? &nbs [#permalink] 06 Jul 2018, 23:21
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.