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

Question

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.

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

OptimusPrepJanielle · Accepted Answer

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: https://www.optimus-prep.com/gmat-on-demand-course

Bunuel · Answer

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.

ynaikavde · Answer

p/q= d=p/q+3

d= .75 q

d= .6(q+3)

we get d = 9 and q = 12. Answer = C.

Temurkhon · Answer

D/Q=75/100=3/4

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

C

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made, 
Rich

Fdambro294 · Answer

P/Q = (1,020) + D/Q

P / (Q + 3) = (816) + D/ (Q + 3)

P = 1,020Q + D

And

P = 816 (Q + 3) + D

Set the 2 equations equal to each other:

1,020Q = 816Q + 2,448

Solving for Q

Q = 12

Rule: the Decimal Part of the Solution when you divide (P/Q) represents the Remainder left over

The integer form of the remainder can be found by:

D = (Divisor) * (Decimal Portion of Solution)

D = (Q) * (.75) = 12 * (3/4) = 9

Or

D = (Q + 3) * (.6) = 15 * (3/5) = 9

D = 9
Q = 12

(C)

Posted from my mobile device

GMATWhizTeam · Answer

Using the division algorithm, 
Dividend = Divisor * Quotient + Remainder, we will be able to set up equations and solve for the values of the unknowns, D and Q.

P and Q are positive integers.

When P is divided by Q, the remainder is a positive integer D. Here, the dividend is P, the divisor Q and the remainder D; since the quotient is not given, we can assume it to be a variable, say K
Therefore, P = Q * K + D

The result of dividing P by Q = 1020.75.

In any division, the decimal part of the result represents the remainder, when the decimal part is multiplied with the divisor.    
Therefore, 0.75 * Q = D

When P is divided by (Q + 3), the remainder is the same positive integer D. Here, the dividend is P, the divisor (Q + 3) and the remainder D; since the quotient is not given, we can assume it to be a variable, say M
Therefore, P = (Q + 3) * M + D

The result of dividing P by (Q + 3) = 816.6.
Therefore, 0.6 * (Q + 3) = D.

From the two equations for D, we can say 0.75 * Q = 0.6 * (Q + 3)

Simplifying, ¾ * Q =  \frac{3}{5}  (Q + 3)

Cancelling off 3 and simplifying further, 5Q = 4Q + 12.
Solving for Q, we get Q = 12.

Therefore, the second number in the set {D,Q} should be 12. Based on this, answer options B, D and E can be eliminated.

Since D = ¾ * Q, substituting Q = 12, we get D = 9.

The correct answer option is C.

bumpbot · Answer

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