Bunuel wrote:
If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Note that this doesn’t look like a remainder problem. It has some algebra to it – we’re solving for n, and what we know about n is based on an inequality presented in fairly abstract form. Your flashcards won’t label this as a remainder problem, but your problem-solving skills should. Before we solve for n, let’s talk about n. What is n in a conceptual sense?
We know that if we subtract n from 13,333, then the resulting number is divisible by 11. Logically, then, we can make the leap that
n needs to be taken off of 13,333 in order for it to be divisible by 11. Accordingly, n is the left-over portion of 13,333 when it is divided by 11 – it’s that last remaining portion that makes 13,333 not divisible by 11. So n, conceptually, is the remainder – it’s what’s left over when we try to make this division work.
That logic we just used reverse-engineers the concept of a remainder. We had to create it conceptually, but now that we know that n is just the remainder, this is now a division problem. If we take 13,333 and divide by 11, we end up taking off:
13,333
-11,000
→ 2,333
-2,200
→ 133
-110
→23
-22
→ 1
The remainder is 1, and the correct answer is A (Note: because the problem only asked for the remainder – n – we didn’t need to bother with the quotient, so this problem can be done a little quicker with less hassle).
Keep in mind here that the GMAT isn’t really testing your ability to calculate the remainder in a division problem; that ability is assumed. The GMAT does want to know whether you can take an asset – your ability to perform division problems – and find a way to use it to solve a unique-looking problem. The division is just a vehicle for the GMAT to test your ability to reverse-engineer a concept, to solve a problem using a familiar tool in an unfamiliar way.
To do so, yes, you must have that fundamental math ability, but that’s just the price of admission to showcase your reasoning skills on a problem like this. Your flashcards can’t teach you to do this; reading back through your notes can’t teach you to do this; you need to think analytically: what is the problem? How can I rephrase the question to make it better fit my knowledge base? Were the numbers different and easier to manage, how would I go about solving this, and therefore how can I apply it to this more complex situation? These are the thought processes that business schools want!
If you’re like the student described at the beginning of this article – if you’ve worked hard to build and polish your knowledge base with regard to GMAT content but have hit a plateau with your score – these are the things you need to master. When you study math skills, don’t merely learn them top-down, but ask yourself how the question could be flipped around to test it from another angle. Ask yourself if there are unique cases that might challenge your typical approach to a problem like this (what if there were no remainder? Could n be both 11 and 0?). Challenge yourself to think, and not just to remember.
While many tests you’ve taken could be beaten by what you remembered and what you knew, the GMAT cannot. It’s very nature as a reasoning test is to force you to think in unique ways from odd angles, and if you’ve hit that plateau of frustration with your scores, that’s when you need to challenge yourself not only to follow and remember instructions, but to be able to create them yourself. _________________