Here’s a simple Data Sufficiency problem I made up that will show you how Root(2) can help you do better on the GMAT. This is the type of question you will need to get right in order to do well on this exam:

I went to the store and bought only pens and pencils. The store sold one kind of each. I spent $10. How many pencils did I buy?

1) I bought 30 pens and pencils in all.

2) Pens cost 39 cents and pencils cost 29 cents.

**A** if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

**B** if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

**C** if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

**D** if EACH statement ALONE is sufficient to answer the question;

**E** if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Take a minute or two to answer the question before looking at the explanation below.

How sure are you that your answer is correct?

Very sure?

### Answer Explained

**A and D)** Almost no one would answer A or D to this question. It is easy to see that statement 1 is definitely insufficient by itself. Pens could cost $10 per 30 and no pencils could have been bought. Pencils could have cost $10 per thirty and 30 pencils and no pens could have been bought.

**B)** Few people would put down B for this question. If pens cost 39 cents and pencils cost 29 cents, but we don’t know how many we bought in all, it seems as though there are many combinations of pens and pencils that would cost $10 in all.

**E)** Students who still need to learn the fundamentals of mathematics might put down E as an answer. It is incorrect because we have sufficient information to answer the question. If you put down E, traditional test-prep classes or tutoring will help you understand how to set up a system of equations to solve problems. I suggest a Manhattan GMAT course. Of course, after you finish a test-prep course, you might still get a question like this wrong, as you will probably put down C as the answer choice.

**C)** Most students who have already prepared for this exam would put down C as an answer. If we know that we spent $10 and that we bought 30 pens and pencils, and we know the price of pens and pencils, we can then set up a system of equations to solve for the correct answer.

If x = # of pencils and y = # of pens, then:

x + y = 30

.29x + .39y = 10

Since y = 30 - x from the first equation, substituting in we get .29x + .39(30 - x) = 10

This becomes .29x + 11.7 - .39x = 10, or -.1x = -1.7, or .1x = 1.7, or x = 17.

With both statements, we know we bought 17 pencils. C seems like the rational answer. **But C is wrong.**

**If you put down C and thought it was right, Root(2) mentoring will definitely help you do better on the GMAT. **You will learn how to use deductive logic to increase your score. If you put down C but also knew that B might be correct, our work will be a little bit easier.

### The Correct Answer

**B)** is the correct answer because if we know that pens cost 39 cents and pencils cost 29 cents, and that we spent $10 in all, the only way to spend exactly $10 is to buy 17 pencils and 13 pens. Root(2) will help you deduce the correct answer to this question, a question which almost every sub-700 level student will get wrong.

A Root(2) student will use deductive logic to help them on every question. This student will quickly see that A and D are definitely incorrect. This student might also see that using both statements, we can figure out the number of pencils bought, so E is definitely incorrect too. But although C seems like the best answer, and B seems like it is likely wrong, B is still possibly correct until it is proven wrong. That is, C seems like a rational choice, but B is also possibly correct.

A Root(2) student will know that statement 2 is only insufficient by itself if there is more than one way to answer the original question using the information. This student will then try to show there is more than one way to answer the question using statement 2 alone.

Quickly, this student will realize that it’s hard to think of combinations of 29 cent pencils and 39 cent pens that add up to $10. Trying a little harder, the student might realize that the number of pens and pencils must be a multiple of 10 in order for there to be zero cents in the total.

That is:

.29 + .39 +.29 + .39 + .. + .. + = xx.x0 only if there is a multiple of 10 pens and pencils. If 20 pens or pencils were bought in all, the sum would definitely be less than $10-at most $7.80. If 40 pens and pencils were bought in all, the sum would definitely be more than $10-at minimum $11.60. So 30 pens and pencils must have been bought in all. Statement 2 is sufficient by itself because we can now solve for the number of pens and pencils.

A Root(2) student might have difficulty proving why B is the correct answer, but by knowing that A, D, and E are definitely wrong, and that C is rational but simplistic, the student will know that B still has a chance of being correct. It’s a surprise answer for all, but top students will answer this question correctly. Learning how to answer B instead of C to this question is what you’ll learn from Root(2). Root(2) won’t help with just this question: You’ll learn how to increase your chances of getting almost every question on the exam correct.

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