It is currently 23 Feb 2018, 00:51

### 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

# M22-27

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43891

### Show Tags

16 Sep 2014, 00:17
Expert's post
7
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:05) correct 26% (01:24) wrong based on 91 sessions

### HideShow timer Statistics

If $$f(x)$$ is defined as the largest integer $$N$$ such that $$x$$ is divisible by $$2^N$$, which of the following numbers is the greatest?

A. $$f(24)$$
B. $$f(42)$$
C. $$f(62)$$
D. $$f(76)$$
E. $$f(84)$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43891

### Show Tags

16 Sep 2014, 00:17
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
Official Solution:

If $$f(x)$$ is defined as the largest integer $$N$$ such that $$x$$ is divisible by $$2^N$$, which of the following numbers is the greatest?

A. $$f(24)$$
B. $$f(42)$$
C. $$f(62)$$
D. $$f(76)$$
E. $$f(84)$$

Often the hardest part is rewording a question to understand what it's really asking.

So, we have an integer $$x$$. It has some power of 2 in its prime factorization ($$2^n$$) and $$f(x)$$ is the value of that $$n$$. Basically $$f(x)$$ is the power of 2 in prime factorization of $$x$$.

For example, if $$x$$ is say 40, then $$f(x)=3$$. Why? Because the largest integer $$n$$ such that 40 is divisible by $$2^n$$ is 3: $$\frac{40}{2^3}=5$$, or $$40=2^3*5$$ - the power of 2 in prime factorization of 40 is 3.

Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.

A. $$f(24)$$: factorize 24: $$24 = 2^3*3$$, thus $$f(24) = 3$$

B. $$f(42)$$: factorize 42: $$42 = 2*21$$, thus $$f(42) = 1$$

C. $$f(62)$$: factorize 62: $$62 = 2*31$$, thus $$f(62) = 1$$

D. $$f(76)$$: factorize 76: $$76 = 2^2*19$$, thus $$f(76) = 2$$

E. $$f(84)$$: factorize 84: $$84 = 2^2*21$$, thus $$f(84) = 2$$

_________________
Intern
Joined: 24 Jun 2015
Posts: 46

### Show Tags

02 Jul 2015, 04:32
Hi,

I find this answer hard to do the algebraic translation, does some body has a shortcut or an easier way to de the algebraic translate of question stem?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700
Math Expert
Joined: 02 Sep 2009
Posts: 43891

### Show Tags

02 Jul 2015, 04:35
1
KUDOS
Expert's post
luisnavarro wrote:
Hi,

I find this answer hard to do the algebraic translation, does some body has a shortcut or an easier way to de the algebraic translate of question stem?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700

Often the hardest part is rewording the question to understand what it's really asking.

So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.

For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --> the power of 2 in prime factorization of 40 is 3.

Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.

A. f(24) --> 24 = 2^3*3
B. f(42) --> 42 = 2*21
C. f(62) --> 62 = 2*31
D. f(76) --> 76 = 2^2*19
E. f(84) --> 84 = 2^2*21

Hope it's clear.
_________________
Intern
Joined: 24 Jun 2015
Posts: 46

### Show Tags

02 Jul 2015, 05:10
Bunuel wrote:
luisnavarro wrote:
Hi,

I find this answer hard to do the algebraic translation, does some body has a shortcut or an easier way to de the algebraic translate of question stem?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700

Often the hardest part is rewording the question to understand what it's really asking.

So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.

For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --> the power of 2 in prime factorization of 40 is 3.

Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.

A. f(24) --> 24 = 2^3*3
B. f(42) --> 42 = 2*21
C. f(62) --> 62 = 2*31
D. f(76) --> 76 = 2^2*19
E. f(84) --> 84 = 2^2*21

Hope it's clear.

Thanks, now it is very clear to me¡¡¡

Regards

Luis Navarro
Looking for 700
Senior Manager
Joined: 08 Jun 2015
Posts: 369
Location: India
GMAT 1: 640 Q48 V29

### Show Tags

30 Jan 2018, 09:10
+1 for A
_________________

" The few , the fearless "

Re: M22-27   [#permalink] 30 Jan 2018, 09:10
Display posts from previous: Sort by

# M22-27

Moderators: chetan2u, Bunuel

 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®.