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

 It is currently 19 Sep 2018, 12:13

### 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 y is an integer such that 2 < y < 100 and if y is also the square

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49251
If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

14 Jan 2015, 02:35
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:26) correct 32% (01:27) wrong based on 174 sessions

### HideShow timer Statistics

If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?

(1) y has exactly two distinct prime factors

(2) y is even.

Kudos for a correct solution.

_________________
Manager
Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

14 Jan 2015, 11:15
1
1
First, let's rewrite the question stem. We know that y is a perfect square. Therefore $$2\leq\sqrt{y}\leq 9$$, because $$2 < y < 100$$.

Now, we can have a look at the 2 statements:

(1): We are told that y has exactly two prime factors. Since squaring an integer does not create any new prime factors and y can't be a prime itself, we know that $$\sqrt{y} = p_1* p_2$$, where $$p_1$$ and $$p_2$$ are the two prime factors. Checking the integers between 2 and 9 inclusive, we see that the only number for which that is the case is 6. It has the prime factors 2 and 3. Therefore $$\sqrt{y}=6$$ and $$y=36$$.

This statement is sufficient.

(2): We are told that y is even. However, there are several perfect squares between 2 and 100: 4, 16, 36, 64. Therefore, this statement is not sufficient.

_________________

$$\sqrt{-1}$$ $$2^3$$ $$\Sigma$$ $$\pi$$ ... and it was delicious!

Please consider giving +1 Kudos if deserved!

Senior RC Moderator
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1182
Location: India
WE: General Management (Aerospace and Defense)
Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

14 Jan 2015, 11:17
1
1
Bunuel wrote:
If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?

(1) y has exactly two distinct prime factors

(2) y is even.

Kudos for a correct solution.

Question says, that y is between 2 and 100. And Y is square of an integer. In that case we have following squares below 100.

Y should be either of 4,9,16,25,36,49,64,81.

Statement-1 : It says Y has 2 DISTINCT Prime Factors. So eliminate all the odd numbers as they have only one prime factors(3 apart from prime factorization of 49 which has 7) in it.

We are left with even numbers(4,16,36,64)-- In this eliminate 4, 16 and 64. These got 2 has their only prime factor. But when we do prime factorization,

$$36= 2^2 * 3^2$$. We get 2 distinct prime factors- 2 and 3.

So sufficient.

Statement-2 : Doesn't say anything other than y is even number. Not sufficient as we have 48 even numbers between 2 and 100,

So Statement-1 is sufficient. Answer is A.

Also, we can verify that our answer (y=36) is correct as statement-2 says y is even. And in GMAT DS, the statements never contradicts each other.

Hope i made my choice justifiable :D
_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 421
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

07 Feb 2015, 11:30
Yes I did the same:

2<y<100
y = square of integer
y = 4,9,16,25,36,49,64,81.

[1] y has 2 distinct prime factors
Only the prime factorization of 36 has 2 different primes: 36 = 2*3*2*3. S

[2] y = even. NS

So, ANS A
Manager
Status: Never Say Never
Joined: 27 May 2014
Posts: 55
Location: India
Concentration: International Business, Technology
GMAT 1: 640 Q46 V32
GMAT 2: 670 Q49 V33
GPA: 3.89
WE: Information Technology (Computer Software)
Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

19 May 2015, 10:24
A

Listed all squares below 100
4 9 ... 81
then did prime factorization keeping in mind 2 ,3, 5,7

arrived at 36

hence a is sufficient as its the only one.

using b) 4,16 ... are also included , hence not sufficient.
_________________

never say never !
-Give a kudos if my answer helped you.

Non-Human User
Joined: 09 Sep 2013
Posts: 8094
Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

### Show Tags

28 Jun 2018, 18:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If y is an integer such that 2 < y < 100 and if y is also the square &nbs [#permalink] 28 Jun 2018, 18:05
Display posts from previous: Sort by

# If y is an integer such that 2 < y < 100 and if y is also the square

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# 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®.