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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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[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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 Sep 2017, 09:30, edited 2 times in total.
Renamed the topic and edited the question.

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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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New post 20 Sep 2017, 01:17
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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
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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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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).

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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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New post 20 Sep 2017, 08:13
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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

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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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New post 20 Sep 2017, 09:32
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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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

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New post 24 Sep 2017, 19:23
=>

\(\frac{(2^6 - 2^5)}{4} + 1\) = \(\frac{32}{4}\) + 1 = 8 + 1 = 9

Ans: B
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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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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

Answer: B
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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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New post 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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New post 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?   [#permalink] 29 Sep 2017, 22:08
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