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Re: K and L are each four-digit positive integers with thousands
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03 Jan 2015, 12:26
HI nachobioteck,
This question is far more "layered" than a typical GMAT Quant question. While you will face some "long" questions on Test Day, you won't see that many. To that end though, "your way" of handling this question is likely a big factor in how long you took to solve it.
Here are some things to keep in mind when approaching any GMAT question:
1) It was written with patterns in mind. The numbers are NOT random, the wording is NOT random - there's at least 1 pattern in it somewhere, so right from the moment you start reading, you need to be looking for that/those pattern(s).
2) You don't have to read a question twice to start taking notes on it.
For example, here's the first half of the first sentence in this prompt (after reading it ONE time, what notes could you take?):
"K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits..."
I would write down..
4-digit numbers
K = _ _ _ _
L = _ _ _ _
Now, here's the second half of the first sentence (what notes would you ADD?):
"....as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L."
I would write ADD...
4-digit numbers
K = a b c d
L = p q r s
Looking at this, it seems pretty straight-forward, but here are the BENEFITS of taking these notes now:
1) I don't have to read the first sentence EVER again.
2) I have a framework for whatever "steps" come next.
3) I can see from the first sentence that this is a THICK question, so I'm on "alert" to pay really careful attention to whatever details come next.
The other explanations in this thread properly present the math involved, so I won't rehash any of that here. The rest of the question is based on spotting prime factorization, knowing your exponent rules and doing a bit of arithmetic.
As you continue to study, remember that every question that you face on the GMAT was BUILT and that GMAT question writers don't have much of an imagination - they have a list of concepts and rules that they have to test you on. While it's a big list, it is also a LIMITED list of possibilities. Look for clues/patterns that remind you of things that you know and you'll be able to speed up even more.
GMAT assassins aren't born, they're made,
Rich