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

 It is currently 17 Oct 2019, 01:21 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  P and Q are both positive integers. When P is divided by Q, the remai

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58427
P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

6
19 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:51) correct 35% (02:59) wrong based on 216 sessions

HideShow timer Statistics

P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?

A. {6, 12}
B. {6, 15}
C. {9, 12}
D. {9, 15}
E. {15, 24}

Kudos for a correct solution.

_________________
Manager  Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 73
Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

1
3
p/q= d=p/q+3

d= .75 q

d= .6(q+3)

we get d = 9 and q = 12. Answer = C.
SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

Bunuel wrote:
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?

A. {6, 12}
B. {6, 15}
C. {9, 12}
D. {9, 15}
E. {15, 24}

Kudos for a correct solution.

When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that P/Q = 1020.75
Here 1020 is the quotient and Remainder/Divisor = 0.75
So, Remainder = 0.75(Divisor)
= 0.75Q

Similarly, for P/(Q+3) = 816.6
816 is the quotient and 0.6 is the Remainder/Divisor
So, Remainder = 0.6(Divisor)
= 0.6(Q+3)

Given that both the remainders are same,
0.75Q = 0.6(Q+3)
So, Q = 12

Hence remainder = 0.75(12) = 9
Hence option C.

--
Optimus Prep's GMAT On Demand course for only \$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

Bunuel wrote:
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?

A. {6, 12}
B. {6, 15}
C. {9, 12}
D. {9, 15}
E. {15, 24}

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Here, we have to use: $$decimal \ part \ of \ decimal \ quotient =\frac{remainder}{divisor}$$
to translate each act of division. The first one tells us 0.75 = D/Q, and the second one tells us that 0.60 = D/(Q + 3). These are also two simultaneous equations. Multiply both to get rid of the fractions.
D = 0.75*Q
D = 0.60*(Q + 3) = 0.60*Q + 1.80

Both are equal to D, so set them equal to each other and solve for Q.
0.75*Q = 0.60*Q + 1.80
0.15*Q = 1.80
Q = 1.80/0.15 = 180/15 = 60/5 = 12

Now that we know Q = 12, we can find D = 0.75*Q = (3/4)*12 = 9. So D = 9 and Q = 12.

_________________
Director  G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

D/Q=75/100=3/4

the only option fits is C, where 9/12=3/4

C
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

Hi All,

This is a layered question, but it has some built in Number Properties that you can take advantage of. Since the answer choices are numbers, we can use them along with the NPs to TEST THE ANSWERS.

While we're given a lot of information to work with, I want to start with two of the facts:
1) P and Q are POSITIVE INTEGERS
2) P/Q = 1020.75

From the answer choices, we know that Q is 12, 15 or 24. In the above fraction, we divide an integer by another integer and get a number that ends in .75 (and that can be rewritten as 3/4). Working 'backwards' from Q to P, we need the Q to be a number that eliminates the fraction so that P becomes an integer. Given the three options, Q would have to be either 12 or 24 - since (12)(3/4) = 9 and (24)(3/4) = 18.

It's interesting how that first example involves a 12 and a 9 - those are the numbers that occur in Answer C, so I'm going to TEST that Answer first...

IF....
D=9 and Q=12
how would that 'mesh' with everything we were told...

P/12 = ? r 9
P/15 = ? r 9
P/12 = 1020.75
P/15 = 816.6

With those last two fractions, we can create two equations that are set equal to P...
P = (1020.75)(12)
P = (816.6)(15)

So, are these two values equal to one another? To make the math steps 'smaller', I've factored out a 3...

(1020.75)(4)(3) = (4083)(3) = 12,249
(816.6)(5)(3) = (4083)(3) = 12,249

The values of P are the same. Given the complexity of the question, this is probably the correct answer, but we can double-check it against the other two pieces of information that we were given...

Will 12,249/12 have a remainder of 9 and will 12,249/15 also have a remainder of 9?

12,249/12 = 1020 r 9
12,249/15 = 816 r 9

This fits everything that we were told, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13204
Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: P and Q are both positive integers. When P is divided by Q, the remai   [#permalink] 12 Feb 2019, 19:40
Display posts from previous: Sort by

P and Q are both positive integers. When P is divided by Q, the remai

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  