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# M22-27

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Math Expert
Joined: 02 Sep 2009
Posts: 52344

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16 Sep 2014, 00:17
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Difficulty:

35% (medium)

Question Stats:

69% (01:16) correct 31% (01:24) wrong based on 143 sessions

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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. $$f(84)$$

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Joined: 02 Sep 2009
Posts: 52344

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16 Sep 2014, 00:17
1
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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 $$f(84) = 2$$

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Joined: 24 Jun 2015
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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: 52344

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02 Jul 2015, 04:35
1
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.
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Intern
Joined: 24 Jun 2015
Posts: 46

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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: 432
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

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30 Jan 2018, 09:10
+1 for A
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Re: M22-27 &nbs [#permalink] 30 Jan 2018, 09:10
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# M22-27

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