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

 It is currently 24 Apr 2019, 05:06

### 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

# If p and q are both positive integers such that p/9 + q/10 is also an

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Jan 2017
Posts: 128
If p and q are both positive integers such that p/9 + q/10 is also an  [#permalink]

### Show Tags

26 Jul 2017, 03:38
2
4
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:01) correct 11% (02:38) wrong based on 88 sessions

### HideShow timer Statistics

If p and q are both positive integers such that $$\frac{p}{9}$$+ $$\frac{q}{10}$$ is also an integer, then which one of the following numbers could p equal?

(A) 3
(B) 4
(C) 9
(D) 11
(E) 19

Source: GMAT NOVA MATH BIBLE
A KUDO = A Thank you.

_________________
A KUDO = A Thank-you. If this post helped you, please send a KUDO across.

YOU CAN LEARN ANYTHING!
MY GMAT BLOG ---> https://gmatclub.com/forum/a-fitness-mat-some-music-few-books-and-the-gmat-245808.html
Senior Manager
Joined: 28 Jun 2015
Posts: 290
Concentration: Finance
GPA: 3.5
If p and q are both positive integers such that p/9 + q/10 is also an  [#permalink]

### Show Tags

26 Jul 2017, 04:48
1
Inten21 wrote:
If p and q are both positive integers such that $$\frac{p}{9}$$+ $$\frac{q}{10}$$ is also an integer, then which one of the following numbers could p equal?

(A) 3
(B) 4
(C) 9
(D) 11
(E) 19

Source: GMAT NOVA MATH BIBLE
A KUDO = A Thank you.

Let $$k$$ be an integer such that $$\frac{p}{9} + \frac{q}{10} = k$$.

Since all three numbers $$p$$, $$q$$, and $$k$$ are integers, among the given options, the only case could be:
integer $$(\frac{p}{9})$$ + integer $$(\frac{q}{10})$$ = integer $$(k)$$

The only value that fits the condition is (C). So, Ans - C.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
##### General Discussion
Manager
Joined: 18 Jan 2017
Posts: 128
Re: If p and q are both positive integers such that p/9 + q/10 is also an  [#permalink]

### Show Tags

26 Jul 2017, 09:51
TimeTraveller wrote:
Inten21 wrote:
If p and q are both positive integers such that $$\frac{p}{9}$$+ $$\frac{q}{10}$$ is also an integer, then which one of the following numbers could p equal?

(A) 3
(B) 4
(C) 9
(D) 11
(E) 19

Source: GMAT NOVA MATH BIBLE
A KUDO = A Thank you.

Let $$k$$ be an integer such that $$\frac{p}{9} + \frac{q}{10} = k$$.

Since all three numbers $$p$$, $$q$$, and $$k$$ are integers, among the given options, the only case could be:
integer $$(\frac{p}{9})$$ + integer $$(\frac{q}{10})$$ = integer $$(k)$$

The only value that fits the condition is (C). So, Ans - C.

That's absolutely correct. Great work.
_________________
A KUDO = A Thank-you. If this post helped you, please send a KUDO across.

YOU CAN LEARN ANYTHING!
MY GMAT BLOG ---> https://gmatclub.com/forum/a-fitness-mat-some-music-few-books-and-the-gmat-245808.html
Senior SC Moderator
Joined: 22 May 2016
Posts: 2651
If p and q are both positive integers such that p/9 + q/10 is also an  [#permalink]

### Show Tags

26 Jul 2017, 10:14
Inten21 wrote:
If p and q are both positive integers such that $$\frac{p}{9}$$+ $$\frac{q}{10}$$ is also an integer, then which one of the following numbers could p equal?

(A) 3
(B) 4
(C) 9
(D) 11
(E) 19

Source: GMAT NOVA MATH BIBLE
A KUDO = A Thank you.

Interesting question. I like NOVA, too.

I tested one answer to get a theoretical sense of the question quickly.

Test Answer A. p = 3, yields $$\frac{1}{3}$$ + $$\frac{q}{10}$$

q is an integer. There is nothing q can be to make the sum an integer. That is, $$\frac{q}{10}$$ cannot be made to equal $$\frac{2}{3}$$, e.g., such that sum = 1.

One more quick step to cement the pattern. Plug q = 10 in. Result is $$\frac{1}{3}$$ + 1 = $$\frac{4}{3}$$ = improper fraction (sum must be integer)

So this result must be avoided: fraction + integer (and vice versa) because result = improper fraction

Because the prompt and answer choices restrict us to controlling the first expression, we must guarantee that it is not a fraction.

The only way to do that is if p is a multiple of 9. (If p = 9 or multiple of 9, q = 10 or multiple of 10.)

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
If p and q are both positive integers such that p/9 + q/10 is also an   [#permalink] 26 Jul 2017, 10:14
Display posts from previous: Sort by

# If p and q are both positive integers such that p/9 + q/10 is also an

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.