  # Application of content

Have a look at this data sufficiency question:

If b is a factor of 16, is 10b a multiple of 16?

(1) b is the square of a non-prime integer

(2) b>4

A  Statement 1 is sufficient to answer the question statement 2 is not

B  Statement 2 is sufficient to answer the question, statement 1 is not

C  Neither statement alone is sufficient to answer the question, but together they are sufficient

D  Either statement alone is sufficient to answer the question

E  Neither statement alone is sufficient to answer the question, nor together are they sufficient

Everybody who gets this question correct knows what a factor is and what a multiple is.

Most people who get this question incorrect also know what a factor is and what a multiple is.

So why do they get this question wrong?

Because, at its heart, even the quantitative section of the GMAT is not a Mathematics test. It is a test of critical reasoning that is written in the language of Mathematics.

So if you don't speak Mathematics, you will not be able to succeed on the test, but what is much more important is how you apply your knowledge to answer questions and navigate your way around the logical tricks and traps that the GMAT uses and the way in which it tries to lure you into wrong answers.

The gap between knowing your stuff and being able to answer questions is massive.

That's why we use our most valuable and expensive resource - our 99th percentile scoring tutors - where they are truly needed: showing you how to actually answer questions.

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There are two reasons why you learn your content online: one is that it is a better way to learn content because it can start from your level and repeat as many times as you need. The other is that it reserves teacher time for showing you how to actually master what the test is really about.

The answer is B, by the way. 1 is not sufficient, 2 is.

Here's why:

First, simplify the question. There's a finite range of possible scenarios. The factors of 16 are 1, 2, 4, 8, and 16. So there are only 5 possible values for b.

10*1 is not a multiple of 16, neither are 10*2 or 10*4, but 10*8 and 10*16 both are. So if b is 1, 2, or 4 the answer will be no, whereas if b is 8 or 16 the answer will be yes.

Defining the options for b and, out of the options, which ones answer the question with no and which ones answer the question with yes, is the most important part of solving this problem, and the step that most students miss as they rush straight to the statements.

(1) Statement 1 tells us that b is either 1 or 16. 1 is 1 squared, 16 is 4 squared, so they are both the square of a non-prime integer (1 is not a prime number). b cannot be 4 because 4 is the square of 2, which is a prime. b cannot be 2 or 8 because they are not the square of an inteeger. SO b is either 1 or 16. We already said that if b=1 the answer is no, whereas if b=16 the answer is yes, so this is not sufficient because it gives us conflicting answers.

(2) Statement 2 tells us that b is either 8 or 16. If b=8, the answer is yes, if b=16 the answer is also yes. So yes, 10b is a multiple of 16. SUFFICIENT.

This question, like most on the GMAT, is all about your approach - generating the options, simplifying the question, figuring out what a yes answer and a no answer look like - not about how well you know your Mathematics.

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