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How many multiples of 7 are there between 21 and 343 ?

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How many multiples of 7 are there between 21 and 343 ? [#permalink]

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

A. 48
B. 47
C. 46
D. 45
E. 44
[Reveal] Spoiler: OA

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Last edited by PareshGmat on 04 Dec 2014, 21:29, edited 1 time in total.

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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 04 Dec 2014, 11:39
1. Find out how many numbers are between 21 and 343. 343 - 21 = 322.

2. 322/7 = 46 multiples of 7 between 21 and 343

Answer C!

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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 04 Dec 2014, 16:28
PareshGmat wrote:
How many multiples of 7 are there between 21 and 343 ?

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


Missing the word "inclusive" mens that we woul dnot count 21 and 343. Therefore, it is (343-21)/7 -1 = 45

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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 04 Dec 2014, 17:50
Answer = D = 45

7 * 3 = 21

7 * 49 = 343

Total multiples = (49-3) + 1 = 47

Exclude 7 & 343 = 47-2 = 45
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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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PareshGmat wrote:
Answer = D = 45

7 * 3 = 21

7 * 49 = 343

Total multiples = (49-3) + 1 = 47

Exclude 7 & 343 = 47-2 = 45


Responding to a pm:

Yes, in the absence of explanatory words, I would take "between" to mean "excluding end points". Though, in a question where it matters whether you take the end points or not (since end points are divisible by 7), I would expect the question to clarify.
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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 06 Apr 2016, 04:34
7*3 = 21
7*49 =343
total multiples of 7 = (49 - 3) + 1 = 47
Exclude 21 & 343 (use of word exclusively) = 47 - 2 = 45
correct option - D

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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 29 Nov 2016, 20:54
21/7 = 3
343/7 = 49

so we're looking at 4 through 48 (as the multiples of 7)

48-4=44+1 = 45 (add one because it's inclusive)

D.

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Re: How many multiples of 7 are there between 21 and 343 ? [#permalink]

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New post 02 Dec 2017, 14:16
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PareshGmat wrote:
How many multiples of 7 are there 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
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Re: How many multiples of 7 are there between 21 and 343 ?   [#permalink] 02 Dec 2017, 14:16
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