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

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

Cheers,
Brent

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