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# What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

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Math Revolution GMAT Instructor
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What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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28 May 2017, 23:59
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Question Stats:

85% (01:14) correct 15% (02:05) wrong based on 129 sessions

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What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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29 May 2017, 00:23
From 5^3 (125) to 5^4 (625) inclusive, we have:
125, 130, 135, ....., 625

Or: 5*25, 5*26, 5*27, ...., 5*125
We have to now count integers from 25 to 125.. = 125 - 25 + 1 = 101

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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29 May 2017, 01:45
1
MathRevolution wrote:
What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

5^3 = 125
5^4 = 625

So we have to find number of multiples of 5 between 125 and 625 inclusive.
Every 5th term from 125 will be a multiple of 5, thus the series become: 125, 130, 135 ...... 625.

It is an Arithmetic Progression (AP) with common difference of 5

Thus using nth term formula:
nth term = a + (n - 1)*d
where a = 1st term
and d = common difference

125 + (n-1)*5 = 625
(n-1)*5 = 500
n-1=100
n=101

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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29 May 2017, 01:54
MathRevolution wrote:
What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

No. of multiples of 5 from 1 to 5^4 = 625/5 = 125
No. of multiples of 5 from 1 to 124(we took 124 since , we need to consider 125 in the multiples count) = [124/5] = 24

SO total number of multiples of 5 between 5^3 and 5^4 = 125-24 = 101..

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What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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30 May 2017, 08:33
2
MathRevolution wrote:
What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

To find number of multiples in a given range, inclusive :

[(Last term - first term) / INCREMENT] + 1

1. Last term - first term:

Last term is 5^4 = 625
First term is 5^3 = 125

625 - 125 = 500

2. Divide 500 by increment 5

500 / 5 = 100, not done yet ==>

3. Add 1. 100 + 1 = 101

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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31 May 2017, 00:54
==> You get(〖5^〗^4-〖5^〗^3)/5+1=(〖5^〗^3 (5-1))/5+1=5^2(4)+1=101. The answer is C.

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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11 Jul 2017, 22:17
MathRevolution wrote:
What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

The world "inclusive" just means including the beginning and ending points of the sequence (5^3, 5^4) simply use the formula

5^4-5^3/5 + 1 = 101

If we wanted to find the number of multiples of 4 between say 4^3 and 4^4, inclusive then again

4^4-4^3/4 + 1

And we could still use this formula if the question read- how many multiples of five are between 121 and 626

5^4-5^3/5 + 1
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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16 Jul 2017, 00:24
Here you go
5^4=625
5^3=125
subtract small from large power
result==500(now divide it by 5 since we have to know multiple of 5 only)
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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19 Jul 2017, 08:20
We can also try it as series in AP

625=125+(n-1)5

500=(n-1)5

100=n-1

n=101

C
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?  [#permalink]

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25 Jul 2017, 10:53
MathRevolution wrote:
What is the number of multiples of 5 between 5^3 and 5^4,inclusive?

A. 85
B. 97
C. 101
D. 111
E. 123

From the integers 5^3 to 5^4 inclusive, 5^4 is the largest multiple of 5 and 5^3 is the smallest multiple of 5; thus, the number of multiples of 5 between them is:

(5^4 - 5^3)/5 + 1 = 5^3(5 - 1)/5 + 1 = 5^2(4) + 1 = 101

Alternate Solution:

We see that we are really being asked to determine the number of multiples of 5 between 5^3 = 125 and 5^4 = 625. This is an evenly spaced set, and so we can use the following formula: (greatest multiple of 5 – smallest multiple of 5)/5 + 1 = (625 – 125)/5 + 1 = 500/5 + 1 = 101.

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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?   [#permalink] 25 Jul 2017, 10:53
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