How Many Multiples of 7 are there Between 21 and 343, Exclusive?

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

1. 48
2. 47
3. 46
4. 45
5. 44

“How Many Multiples of 7 are there Between 21 and 343, Exclusive?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review".  To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1

It is asked in the question that how many multiples of 7 are there between 21 and 343, exclusive.
We have to find the count of numbers that are between 21 and 343 and are multiples of 7.
Now we can see that 21 = 7 * 3
Also 343 = 7 * 49

This means that 21 is the 3rd multiple of 7 and 343 is the 49th multiple
Between the numbers 21 and 343 there will be
(49 - 3) + 1 = 47 numbers including the number 21 and 343.

It is asked in the question to find the multiples of 7 are there between 21 and 343, exclusive.
So we have to exclude 21 and 343.
Therefore we have total = 47 - 2 = 45

Therefore D is the correct option.

Approach Solution 2

It is asked in the question that how many multiples of 7 are there between 21 and 343, exclusive.
We have to find the count of numbers that are between 21 and 343 and are multiples of 7.
One thing to be noted is that,
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
Therefore the correct answer will be option D.

Approach Solution 3

It is asked in the question that how many multiples of 7 are there between 21 and 343, exclusive.
We have to find the count of numbers that are between 21 and 343 and are multiples of 7.
Now we can see that 21 = 7 * 3
Also 343 = 7 * 49
Hence, total multiples = (49-3) + 1 = 47
We need to exclude 7 & 343
= 47-2
= 45

Hence, D is the correct answer.

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