GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Aug 2018, 17:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# M21-29

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47920

### Show Tags

16 Sep 2014, 01:15
1
4
00:00

Difficulty:

65% (hard)

Question Stats:

53% (00:56) correct 47% (00:48) wrong based on 125 sessions

### HideShow timer Statistics

How many integers between 18 and 70, inclusive are divisible by either 7 or 9 but not both?

A. 11
B. 12
C. 13
D. 14
E. 15

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47920

### Show Tags

16 Sep 2014, 01:15
Official Solution:

How many integers between 18 and 70, inclusive are divisible by either 7 or 9 but not both?

A. 11
B. 12
C. 13
D. 14
E. 15

# of multiples of 7 in the given range is $$\frac{(last-first)}{multiple}+1=\frac{(70-21)}{7}+1=8$$;

# of multiples of 9 in the given range is $$\frac{(last-first)}{multiple}+1=\frac{(63-18)}{9}+1=6$$;

# of multiples of both 7 and 9 is 1: $$7*9=63$$. Notice that 63 is counted both in 8 and 6;

So, # of multiples of either 7 or 9 but not both in the given range is $$(8-1)+(6-1)=12$$.

_________________
Intern
Joined: 06 Jul 2015
Posts: 8

### Show Tags

11 Oct 2015, 01:53
Bunuel wrote:
Official Solution:

How many integers between 18 and 70, inclusive are divisible by either 7 or 9 but not both?

A. 11
B. 12
C. 13
D. 14
E. 15

# of multiples of 7 in the given range is $$\frac{(last-first)}{multiple}+1=\frac{(70-21)}{7}+1=8$$;

# of multiples of 9 in the given range is $$\frac{(last-first)}{multiple}+1=\frac{(63-18)}{9}+1=6$$;

# of multiples of both 7 and 9 is 1: $$7*9=63$$. Notice that 63 is counted both in 8 and 6;

So, # of multiples of either 7 or 9 but not both in the given range is $$(8-1)+(6-1)=12$$.

Hi,
Thanks for the post and knowing the fomular is very helpful.
But, just wondering why we need to add "1" after (last-first)/multiple?
# of multiples of 7 in the given range is $$\frac{(last-first)}{multiple}+1=\frac{(70-21)}{7}+1=8$$;

Thanks!
Regarda
Andy
Retired Moderator
Joined: 18 Sep 2014
Posts: 1162
Location: India

### Show Tags

12 Oct 2015, 16:19
1
Between 18 and 70 inclusive

multiples of 7 consist {21,28,35,42,49,56,63,70}

multiples of 9 {18,27,36,45,54,63}

since we need numbers that are divisible by either 7 or 9 but not both.

$$9*7=63$$ is to be removed from both the sets.

final set {18,21,27,28,35,36,42,45,49,54,56,70}

no of terms in final set = 12
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Director
Joined: 08 Jun 2015
Posts: 529
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38

### Show Tags

12 Dec 2017, 03:20
The answer is B. First find the number of multiples of 7 from 18 to 70. Then the number of multiples of 9 from 18 to 63. We need to exclude the common multiple from both. 63 has been counted two times The answer is 8+6-2 . i.e. 12. Hence B.
_________________

" The few , the fearless "

Manager
Joined: 17 Jan 2017
Posts: 61

### Show Tags

09 May 2018, 03:01
Good question. I subtracted only 1 from 14. Dumb mistake :/
M21-29 &nbs [#permalink] 09 May 2018, 03:01
Display posts from previous: Sort by

# M21-29

Moderators: chetan2u, Bunuel

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.