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How many multiples of 7 are between 21 and 343, exclusive?

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by Brent@GMATPrepNow » Sat Dec 02, 2017 2:14 pm
swerve wrote:How many multiples of 7 are between 21 and 343, exclusive?

A. 48
B. 47
C. 46
D. 45
E. 44
ASIDE: there are various formulas that students can memorize for this kind of question. Here's a solution that uses a nice easy rule (which can be applied in many ways):
The number of integers from x to y inclusive equals y - x + 1

exclusive: so, we're not going to count 21 and 343
The multiples of 7 to be counted are:
28
35
42
.
.
.
336

We can REWRITE the values as follows:
28 = (7)(4)
35 = (7)(5)
42 = (7)(6)
.
.
.
336 = (7)(48)

So, we need only find the number of integers from 4 to 48 inclusive
Applying the above rule, the number of integers = 48 - 4 + 1 = 45
Answer: D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Matt@VeritasPrep » Mon Dec 04, 2017 6:19 pm
21 = 7*3
343 = 7*49

So we want every multiple of 7 from 7*1 to 7*48, but we can't have 7*1, 7*2, or 7*3. That means we have 48 - 3 = 45 multiples.
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by Scott@TargetTestPrep » Thu Oct 03, 2019 11:07 am
swerve wrote:How many multiples of 7 are between 21 and 343, exclusive?

A. 48
B. 47
C. 46
D. 45
E. 44

The OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
We can calculate the number of multiples of 7, from 28 to 336 inclusive:

(336 - 28)/7 + 1 = 45

Answer: D

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