GMAT Quantitative: Sample Problems IV (DS)

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GMAT 2009

GMAT Quantitative: Sample Problems IV (DS)

Author: oLahav

» GMAT Sample Problems and Solutions: Part IV

To help you crack the Quantitative Section, here are some sample problems and their solutions, step by step. These problems are based on real GMAT questions, so they may be the ones you'll get stuck on. This lesson focuses specifically on Data Sufficiency questions.

Before you begin, be sure to review the Quantitative Section lessons and the Basics of Algebra lessons.

Think you know your stuff? Practice using the Question Bank or the GMAT Tests.

» Question 1:

If a and b are positive integers what is the value of a+b?
1) a/b = 5/8
2) The greatest common divisor of a and b is 1

Answer: Let's do this the regular Data-Sufficiency way. Try to solve this using just statement 1. We know that $\frac{a}{b}=\frac{5}{8}$ ... and that's it, we don't know what a or b are- they can be 5 and 8, 10 and 16, etc. So We cancel out options A and D.

Now let's try with just 2. We know a and b are integers with a gcd of 1… so they can be 2 and 3, or 2 and 5, or 4 and 11, or… yeah, you get the point. B is wrong too.

We're left with C or E. So now we consider them together. We know that a and b have a greatest common divisor of 1, and that $\frac{a}{b}=\frac{5}{8}$ . This means that a=5 and b=8 , since if the common divisor is 1, we can't expand the ratio of a/b to be 10/16 or something like that, a has to b 5 and b has to be 8. Then from this, since we know what a and b are, we can figure out a+b, and thus the answer is C.

Question 2: What is the remainder when the positive integer n is divided by the positive integer k, where k>1?
1) n = (k+1)^3
2) k = 5

Answer: Start with just 1. If n=(k+1) ^3 , we can expand this to n=k ^3+3k ^2+3k+1 , and now it's clear that the remainder of n/k is 1. Thus the answer has to be A or D.

Now, looking at statement 2 alone, we don't know anything about n now, but we know that k is 5. Well, 6/5 has a reminder of 1, but 7/5 has a remainder of 2. In short, statement 2 isn't sufficient, so the answer is simply A.

Question 3: If there are more than 2 numbers in a certain list, is each of the numbers in the list equal to 0?
1) The PRODUCT of any 2 numbers in the list is equal to 0
2) The SUM of any 2 numbers in the list is equal to 0

Answer: This is a tricky question, and you may be tempted to just choose A, since we know that when we multiply anything by 0, we get 0. However, this isn't the question.

Let's take a look at a few cases with just statement A-
First, say we have no 0s in the list. Then clearly the condition of statement A doesn't hold.
Now, say there's one 0. Still doesn't hold- if our list is {1, 2, 0} we have a non-zero product in there. The same would happen if we throw in an extra 0.
Next case- all zeros except 1: {1, 0, 0}. Now we satisfy the condition- all products are 0, but not all the numbers in the list are 0.
Now see what happens of all are 0. Now the statement holds, but we have all zeros. This just means that statement A is insufficient- with all 0 products, we don't always have all 0 values- we can have exactly one nonzero value.

Ok, moving on to the second statement. We'll check the cases again:
All nonzero- same phenomenon as earlier, and same with the second case of 1 or more zeros.
How about 1 nonzero? Well, now clearly not all sums are 0- if we have {1, 0, 0}, we have 2 sums of 1.
You may want to try a case with numbers like {1, -1, 1, -1}. We still have a sum of 2 and -2 in there though, so it doesn't satisfy the conditions of the statement.
Finally, the only case satisfying the conditions of the statement is {0, 0, 0,...}. This means that the only set where all the sums are 0 is the 0 set.And thus, B is sufficient and the answer is B.

That's all for now!