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# What is the number of multiples of 4 between 2^5 and 2^6, inclusive?

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What is the number of multiples of 4 between 2^5 and 2^6, inclusive?  [#permalink]

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Updated on: 20 Sep 2017, 09:30
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[GMAT math practice question]

What is the number of multiples of 4 between 2^5 and 2^6, inclusive?

A. 8
B. 9
C. 10
D. 11
E. 12

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 20 Sep 2017, 00:58. Last edited by Bunuel on 20 Sep 2017, 09:30, edited 2 times in total. Renamed the topic and edited the question. Math Expert Joined: 02 Sep 2009 Posts: 49251 Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive? [#permalink] ### Show Tags 20 Sep 2017, 01:17 1 MathRevolution wrote: [GMAT math practice question] What is the number of multiples of 4 between 2^5 and 2^6, inclusive? A. 8 B. 9 C. 10 D. 11 E. 12 Similar questions: https://gmatclub.com/forum/what-is-the- ... 41446.html https://gmatclub.com/forum/what-is-the- ... 33779.html _________________ Intern Status: Do. Or not do. There is no try. Joined: 22 Apr 2015 Posts: 2 Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive? [#permalink] ### Show Tags 20 Sep 2017, 03:26 1 MathRevolution wrote: [GMAT math practice question] What is the number of multiples of 4 between 2^5 and 2^6, inclusive? A. 8 B. 9 C. 10 D. 11 E. 12 In my sense it could be B (9) but OA shows its A (8). My calculation follows 2^5 (32) to 2^6 (64) inclusive, we have multiples of 4: 32, 36, 40, 44, 48, 52, 56, 60 and 64 (counting 9). Senior SC Moderator Joined: 22 May 2016 Posts: 1973 Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive? [#permalink] ### Show Tags 20 Sep 2017, 08:13 1 MathRevolution wrote: [GMAT math practice question] What is the number of multiples of 4 between 2^5 and 2^6, inclusive? A. 8 B. 9 C. 10 D. 11 E. 12 Bunuel or MathRevolution , is the OA correct? I get the same answer as mhsagor67. OA says Answer A. I think it is Answer B. One approach: The number of multiples between 2^5 and 2^6, inclusive, I think should be Number of terms in arithmetic sequence of multiples is $$\frac{(Last-First)}{(Increment)} + 1$$ Last Term is $$2^6 = 64$$ First Term is $$2^5 = 32$$ $$\frac{(64-32)}{4} = 8 + 1 = 9$$ multiples of 4 Another approach: List multiples. 2$$^5$$ = 32, 2$$^6$$ = 64 32, 36, 40, 44, 48, 52, 56, 60, 64. There are 9 multiples of 4. If the answer is 8 (and I can't understand why with inclusive counting we should calculate this way), it seems to come from 2$$^6$$ - 2$$^5$$ = 2$$^5$$(2 - 1) = 2$$^5$$ = 34 32/4 = 8 (??) I think the Answer is B _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Expert Joined: 02 Sep 2009 Posts: 49251 Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive? [#permalink] ### Show Tags 20 Sep 2017, 09:32 1 genxer123 wrote: MathRevolution wrote: [GMAT math practice question] What is the number of multiples of 4 between 2^5 and 2^6, inclusive? A. 8 B. 9 C. 10 D. 11 E. 12 Bunuel or MathRevolution , is the OA correct? I get the same answer as mhsagor67. OA says Answer A. I think it is Answer B. One approach: The number of multiples between 2^5 and 2^6, inclusive, I think should be Number of terms in arithmetic sequence of multiples is $$\frac{(Last-First)}{(Increment)} + 1$$ Last Term is $$2^6 = 64$$ First Term is $$2^5 = 32$$ $$\frac{(64-32)}{4} = 8 + 1 = 9$$ multiples of 4 Another approach: List multiples. 2$$^5$$ = 32, 2$$^6$$ = 64 32, 36, 40, 44, 48, 52, 56, 60, 64. There are 9 multiples of 4. If the answer is 8 (and I can't understand why with inclusive counting we should calculate this way), it seems to come from 2$$^6$$ - 2$$^5$$ = 2$$^5$$(2 - 1) = 2$$^5$$ = 34 32/4 = 8 (??) I think the Answer is B Yes, the OA should be B Edited. Thank you. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6206 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the number of multiples of 4 between 2^5 and 2^6, inclusive? [#permalink] ### Show Tags Updated on: 29 Sep 2017, 22:06 => $$\frac{(2^6 - 2^5)}{4} + 1$$ = $$\frac{32}{4}$$ + 1 = 8 + 1 = 9 Ans: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Originally posted by MathRevolution on 24 Sep 2017, 19:23.
Last edited by MathRevolution on 29 Sep 2017, 22:06, edited 1 time in total.
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Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive?  [#permalink]

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25 Sep 2017, 18:02
1
MathRevolution wrote:
[GMAT math practice question]

What is the number of multiples of 4 between 2^5 and 2^6, inclusive?

A. 8
B. 9
C. 10
D. 11
E. 12

2^5 = 32 and 2^6 = 64. So, we need to determine how many multiples of 4 there are from 32 to 64 inclusive:

(64 - 32)/4 + 1 = 32/4 + 1 = 9

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Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive?  [#permalink]

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26 Sep 2017, 19:55
If the question has the word Inclusive, looking for factors between two numbers, will we always add 1. So making the answer 8+1. And if Exclusive does that mean we do not +1 so answer would be 8?
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Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive?  [#permalink]

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29 Sep 2017, 22:08
brtboy wrote:
If the question has the word Inclusive, looking for factors between two numbers, will we always add 1. So making the answer 8+1. And if Exclusive does that mean we do not +1 so answer would be 8?

The formula is (Last - First)/Difference + 1.
$$\frac{( 2^6 - 2^5 )}{4} + 1 = \frac{(64 -32)}{4} + 1 = \frac{32}{4} + 1 = 8 + 1 = 9$$
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Re: What is the number of multiples of 4 between 2^5 and 2^6, inclusive? &nbs [#permalink] 29 Sep 2017, 22:08
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