How many multiples of 7 are there between 21 and 343 ? : Problem Solving (PS)

PareshGmat

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

Updated on: 04 Dec 2014, 22:29

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A

B

C

D

E

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45% (medium)

Question Stats:

58% (01:14) correct

42% (01:09) wrong

based on 225 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 04 Dec 2014, 00:41.
Last edited by PareshGmat on 04 Dec 2014, 22:29, edited 1 time in total.

DangerPenguin

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

04 Dec 2014, 12:39

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!

cstew

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

04 Dec 2014, 17:28

1

Kudos

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

PareshGmat

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

04 Dec 2014, 18:50

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Answer = D = 45

7 * 3 = 21

7 * 49 = 343

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

Exclude 7 & 343 = 47-2 = 45

L

KarishmaB

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

04 Dec 2014, 21:35

1

Kudos

Expert Reply

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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rhine29388

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

06 Apr 2016, 05:34

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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law258

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

29 Nov 2016, 21:54

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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BrentGMATPrepNow

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Location: Canada

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

02 Dec 2017, 15:16

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Expert Reply

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
Answer: D

Cheers,
Brent

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hellosanthosh2k2

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

25 Apr 2018, 12:13

21 < 7x < 343
3 < x < 49

total = 48 - 4 + 1 = 45

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zishu912

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

25 Apr 2018, 12:28

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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renjana

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

28 Apr 2018, 01:28

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