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

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by Gmat_mission » Sat Mar 24, 2018 4:33 am
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

[spoiler]OA=C[/spoiler].

Is there a fast way to solve this PS question? I'd be thankful for your help. <i class="em em---1"></i>
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by [email protected] » Sat Mar 24, 2018 10:04 am
Hi Gmat_mission,

We're asked to find the number of multiples of 5 between 5^3 and 5^4, inclusive. This is an example of a 'fence post' problem. To start, we have to define those two values...

5^3 = 125
5^4 = 625

At this point, there are a couple of different ways to determine the total number of multiples of 5 in that range. Here's how you can "rewrite" the numbers and spot a pattern:

125 = (5)(25)
625 = (5)(125)

Thus, 125 can be defined as the '25th positive multiple five' and 625 as the '125th positive multiple of five.' Since we have to include BOTH of those values, the total multiples of 5 in that range is:

125 - 25 + 1 = 101

Final Answer: C

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by Scott@TargetTestPrep » Fri May 24, 2019 3:05 pm
Gmat_mission 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
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.

Answer: C

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