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PareshGmat
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Posts: 1,531
Updated on: 04 Dec 2014, 21:29
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.
Last edited by PareshGmat on 04 Dec 2014, 21:29, edited 1 time in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:14) correct
41%
(01:10)
wrong
based on 380
sessions
History
Date
Time
Result
Not Attempted Yet
How many multiples of 7 are there between 21 and 343, exclusive ?
A. 48
B. 47
C. 46
D. 45
E. 44
A. 48
B. 47
C. 46
D. 45
E. 44
Posts: 6,727
PareshGmat
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
General Discussion
Posts: 90
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!
2. 322/7 = 46 multiples of 7 between 21 and 343
Answer C!
PareshGmat
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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Answer = D = 45
7 * 3 = 21
7 * 49 = 343
Total multiples = (49-3) + 1 = 47
Exclude 7 & 343 = 47-2 = 45
7 * 3 = 21
7 * 49 = 343
Total multiples = (49-3) + 1 = 47
Exclude 7 & 343 = 47-2 = 45
PareshGmat
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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Posts: 385
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
7*49 =343
total multiples of 7 = (49 - 3) + 1 = 47
Exclude 21 & 343 (use of word exclusively) = 47 - 2 = 45
correct option - D
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.
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.
21 < 7x < 343
3 < x < 49
total = 48 - 4 + 1 = 45
3 < x < 49
total = 48 - 4 + 1 = 45
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
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
renjana
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Concentration: Marketing, Leadership
Schools: CMU MSPM "21 (A)
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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
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
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Expert reply
Posts: 22,740
PareshGmat
We can calculate the number of multiples of 7, from 28 to 336 inclusive:
(336 - 28)/7 + 1 = 45
Answer: D
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PareshGmat
21 = 7*3 ie 3 multiples of 7
343 = 7*49 ie 49 multiples of 7
Between 7 & 343,
49 - 3 - the number 343
= 49-3-1
=45
D is Correct
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Products:
it is (343-21)/7 -1 = 45
Option D
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Option D
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