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:
GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★