[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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How many multiples of 4 lie between 4^4 and 4^5, inclusive?
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Max@Math Revolution
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The positive multiples of 4 constitute an EVENLY SPACED SET.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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Brent@GMATPrepNow
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Mitch used the same approach I would have used, so here's a different solution.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 = (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
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Jeff@TargetTestPrep
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4^4 = 256Max@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
4^5 = 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
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=>
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
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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