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GMAT 2009

GMAT Quantitative: Sample Problems III (DS)

Author: oLahav

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» GMAT Sample Problems and Solutions: Part III

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 b is an integer, is $\sqrt{a ^ 2 +b ^ 2}$ an integer?
1) a ^ 2+b ^ 2 is an integer
2) a ^ 2- 3b ^ 2 = 0

Answer: This is tricky, you actually need to think here.

Start with Statement A- it clearly doesn't help- say x=a ^ 2+b ^ 2 , then we know x is an integer, but we don't know anything about $\sqrt{x}$ , so it's insufficient. Cross A and D off.

Now statement B- now we know that a ^ 2=3b ^ 2 . So we play a little substitution: $\sqrt{a ^ 2+b ^ 2}=\sqrt{3b ^ 2+b ^ 2}=\sqrt{4b ^ 2}=2b$ . Now, since b is an integer, the expression is also an integer. And so we're done, B is sufficient and so the answer is B.

Question 2: Six numbers are randomly selected and placed within a set. If the set has a range of 16, a median of 6, a mean of 7 and a mode of 7, what is the greatest of the six numbers?
1) The sum of the two smallest numbers is one-fifth of the sum of the two greatest numbers
2) The middle two numbers are 5 and 7

Answer: Let's work with what we've got before we look at the statements. We have a set with six numbers- a,b,c,d,e,f. The range is 16, so f-a=16 . The median is 6, so $\frac{c+d}{2}=6$ . The mode is 7, so we have at least 2 sevens and they clearly have to be above the median, so d and e are both 7. Now we already know that b=5 from the equation we just figured out. We also know that $\frac{a+b+c+d+e+f}{6}=7$ , since that's the mean.

Now, let's look at statement A. (a+b)=0.2(e+f) . Ok, plug it in: 0.2(7+f)+5+7+7+f=42 , and we can solve for f: $1.2f=\frac{108}{5}$ , and then f=18 . Not so bad. So it's either A or D now.

Statement B though is no help- we already know that the middle 2 numbers are 5 and 7 without the statement, so it's clearly not enough to figure anything else out.

From this, the answer is A. This was one of the tedious data sufficiency questions where you actually have to try and solve the problem to figure it out. There aren't too many of these out there, luckily.

Question 3: Each of the 25 balls in a certain box is either red, blue, or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?
1) The probability that the ball will both be white and have an even number painted on it is 0.
2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2.

Answer: This is a set question disguised as a probability question. The set formula, in case you don't remember, says this (P stands for probability): $P_{white OR even}=P_{white}+P_{even}-P_{whiteANDeven}$ .

Statement A gives us $P_{whiteANDeven}=0$ . This alone is clearly insufficient. Statement B gives us $P_{white}- P_{even}=0.2$ , which again is insufficient. Together, it's still not enough, since statement B doesn't lead to $P_{wihte}+P_{even}$ . Notice how the question contains lots of information that we've never used- the blue and red balls, and 1-10 numbers, etc. We're not given enough info to use those figures.

The answer is E, but if you weren't ready for this sort of thing you may have been totally confused with all the extra info. This example shows how important it is to focus on using just what you need for the question and figure out what the question is really asking before you dive in.

That's all for now!