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# What is the number of multiples of 25 between 5^4 and 5^5, inclusive?

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Math Revolution GMAT Instructor
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What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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10 Feb 2017, 02:05
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What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125
[Reveal] Spoiler: OA

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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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10 Feb 2017, 03:42
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MathRevolution wrote:
What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

Hi
To find answer, convert 5^4 and 5^5 in multiples of 25...
$$5^4=25*25.......5^5=25*125$$

So multiples of 25=(125-25)+1=101....

Otherwise answer =$$\frac{5^5-5^4}{25}+1=\frac{25(5^3-5^2)}{25}+1=5^2(5-1)+1=25*4+1=101$$
C
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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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10 Feb 2017, 08:50
MathRevolution wrote:
What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

Multiples of $$25 = 5^2$$

Numbers between $$5^4$$ and$$5^5$$ = Numbers between 625 to 3125

There are 2500 numbers...

So, Total number of multiples of 25 between 625 to 3125 inclusive = $$\frac{2500}{25} + 1$$ => 100 + 1

Hence, Correct answer must be (C) 101

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Math Revolution GMAT Instructor
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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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12 Feb 2017, 17:27
==> The number of multiples become (last-first/n)+1, then you get $$\frac{5^5-5^4}{25}+1=\frac{(5-1)5^4}{25}+1=4(5^2)+1=101$$.

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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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15 Feb 2017, 09:50
MathRevolution wrote:
What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

We need to determine the number of multiples of 25 between 5^4 = 625 and 5^5 = 3,125.

We can use the following formula:

(largest multiple of 25 in the set - smallest multiple of 25 in the set)/25 + 1

(3125 - 625)/25 + 1 = 2500/25 + 1 = 100 + 1 = 101.

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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive?   [#permalink] 15 Feb 2017, 09:50
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