Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Apr 2015, 23:34

### 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 g is a the square of an integer, then what is the value

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1268
Followers: 23

Kudos [?]: 154 [0], given: 0

If g is a the square of an integer, then what is the value [#permalink]  20 Sep 2006, 14:53
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If g is a the square of an integer, then what is the value of g?

(1) Fewer than half of the factors of g are less than 12.
(2) Fewer than half of the factors of g are greater than 12.
Manager
Joined: 08 Sep 2006
Posts: 123
Followers: 1

Kudos [?]: 0 [0], given: 0

[#permalink]  21 Sep 2006, 06:28
I think it "might" be C.

Statement 1 by itself is not sufficient. The number could 169 or 289 or the square of any prime number greater than 12 and the condition would hold.

Statement 2 by itself is not sufficient. The number could be 16 or 25 and the condition would hold.

Now the question is can we solve this with both together.

By picking different numbers, both these conditions cannot be satisfied simultaneously for any other number except 144. In fact if we pick any square of an integer, it always has an equal number of factors less than its root as it has greater than its root. For example 16 has two factors less than its root 4, i.e. 1 and 2 and 2 factors greater than its root i.e. 8 and 16.

I guess the proof of this would involve the rule that the greatest prime factor of a number is always less than its root. Based on this (and maybe permutations) we should be able to derive the rule on the number of factors

Hence i would say that the number is 144 and solution is C.
Manager
Joined: 08 Sep 2006
Posts: 123
Followers: 1

Kudos [?]: 0 [0], given: 0

[#permalink]  25 Sep 2006, 03:42
Hey Kevin, can you share the OA for this one? Thanks!
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1268
Followers: 23

Kudos [?]: 154 [0], given: 0

Re: PS: The value of g [#permalink]  25 Sep 2006, 04:30
kevincan wrote:
If g is a the square of an integer, then what is the value of g?

(1) Fewer than half of the factors of g are less than 12.
(2) Fewer than half of the factors of g are greater than 12.

(1) g could be 13^2, 17^2,... NOT SUFF
(2) g could be 5^2, 7^2,... NOT SUFF

(1) and (2) 12 is a factor of g. As there is a one-to-one correspondence between factors of g that are less than sqrt(g) and those that are greater than sqrt(g), there are two possibilities:

(A) there is an even number of factors, half less than sqrt(g) and half above sqrt(g)

(B) there is an odd number of factors. In this case less than half of the factors are are less than sqrt(g) and less than half are greater than sqrt(g). The remaining factor is equal to sqrt(g).

Clearly A is not the case, so it must be that 12=sqrt(g) SUFF ANS:C
Re: PS: The value of g   [#permalink] 25 Sep 2006, 04:30
Similar topics Replies Last post
Similar
Topics:
12 What is the value of |f(x)| - |g(x)| + |f(g(x)| ? 26 30 Oct 2012, 23:57
20 The circle above circumscribes square ABCD. What is the valu 18 07 Sep 2010, 20:57
4 If g is an integer what is the value of (-1)^(g^4-1) 3 21 Dec 2008, 08:55
What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer 4 17 Jan 2008, 23:34
Display posts from previous: Sort by

# If g is a the square of an integer, then what is the value

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.