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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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Updated on: 04 Dec 2014, 21:29
5
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:20) correct 41% (01:08) wrong based on 226 sessions

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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

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Originally posted by PareshGmat on 03 Dec 2014, 23:41.
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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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

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Posts: 4
Re: How many multiples of 7 are there between 21 and 343 ?  [#permalink]

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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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04 Dec 2014, 17:50

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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04 Dec 2014, 20:35
1
PareshGmat wrote:

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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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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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)

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

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02 Dec 2017, 14:16
1
Top Contributor
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

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

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25 Apr 2018, 11:13
21 < 7x < 343
3 < x < 49

total = 48 - 4 + 1 = 45
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Re: How many multiples of 7 are there between 21 and 343 ?  [#permalink]

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25 Apr 2018, 11:28
Number of Numbers divisible by 7 up to 21 is = 21/7 = 3

Numbers divisible by 7 up to 343 is = 343/7 = 49

Hence the number of numbers divisible by 7 between 21 and 343(excluding both ) = (49 - 3) - 1 = 45, (We have removed one number from the number since 343 was included in the numbers)

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

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28 Apr 2018, 00:28
How many multiples of 7 are there between 21 and 343, exclusive

Multiples of 7 inclusive of 21 and 343 = 343-21/7 + 1 = 46+1 =7 .

since 23 and 342 are multiples and it needs to be excluded remove them from the list = 47-2 = 45
Re: How many multiples of 7 are there between 21 and 343 ?   [#permalink] 28 Apr 2018, 00:28
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