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

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

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27 Feb 2015, 06:00
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55% (hard)

Question Stats:

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

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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.

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Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

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27 Feb 2015, 07:41
1
3
p/q= d=p/q+3

d= .75 q

d= .6(q+3)

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

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28 Feb 2015, 03:03
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.

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

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02 Mar 2015, 05:57
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.

Answer = C.
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Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

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20 Sep 2015, 03:41
D/Q=75/100=3/4

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

C
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Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

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23 Jan 2018, 14:09
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.

Final Answer:

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Rich
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Re: P and Q are both positive integers. When P is divided by Q, the remai  [#permalink]

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12 Feb 2019, 19:40
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Re: P and Q are both positive integers. When P is divided by Q, the remai   [#permalink] 12 Feb 2019, 19:40
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# P and Q are both positive integers. When P is divided by Q, the remai

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