How many multiples of 4 lie between 4^4 and 4^5, inclusive?

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu May 03, 2018 1:03 am

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[GMAT math practice question]

How many multiples of 4 lie between 4^4 and 4^5, inclusive?

A. 128
B. 129
C. 192
D. 193
E. 256

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu May 03, 2018 2:52 am

Max@Math Revolution wrote:[GMAT math practice question]

How many multiples of 4 lie between 4^4 and 4^5, inclusive?

A. 128
B. 129
C. 192
D. 193
E. 256

The positive multiples of 4 constitute an EVENLY SPACED SET.

For any evenly spaced set:
Number of values = (biggest - smallest)/increment + 1.
The INCREMENT is the distance between one term and the next.

The positive multiple of 4 have an increment of 4.
Thus:
Number of multiples of 4 between 4� and 4� = (biggest - smallest)/increment + 1 = (4� - 4�)/4 + 1 = 4� - 4³ + 1 = 4³(4 - 1) + 1 = 64(3) + 1 = 193.

The correct answer is D.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu May 03, 2018 4:52 am

Max@Math Revolution wrote:[GMAT math practice question]

How many multiples of 4 lie between 4^4 and 4^5, inclusive?

A. 128
B. 129
C. 192
D. 193
E. 256

Mitch used the same approach I would have used, so here's a different solution.

4^4 = (4³)(4) = (64)(4)
4^5 = (4�)(4) = (256)(4)

So, we want the multiples of 4 from (64)(4) to (256)(4) inclusive.
The multiples of 4 are: (64)(4), (65)(4), (66)(4), (67)(4), (68)(4), . . . (256)(4)

A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 64 to 256 inclusive = 256 - 64 + 1 = 193

Answer: D

Cheers,
Brent

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri May 04, 2018 9:30 am

Max@Math Revolution wrote:[GMAT math practice question]

How many multiples of 4 lie between 4^4 and 4^5, inclusive?

A. 128
B. 129
C. 192
D. 193
E. 256

4^4 = 256

4^5 = 1,024

We use the formula for the number of multiples: (greatest multiple of 4 - least multiple of 4)/4 + 1. The number of multiples of 4 from 256 to 1,024, inclusive, is:

(1,024 - 256)/4 + 1 = 193

Answer: D

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon May 07, 2018 1:08 am

=>
Since we are including the end points, the number of multiples of 4 is

( 4^5 – 4^4 ) / 4 + 1 = 4^4(4-1)/4 + 1 = 4^3*3 + 1 = 64 * 3 + 1 = 193.

Therefore, D is the answer.

Answer : D

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