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# Quantitative Comparison – Common Traps

Wouldn’t it be great if you could just look at a GRE math problem and say, “Hey, that’s so easy”? Well, the reality is the GRE math is never that easy. If a question looks too obvious, then step back for a moment and really think the problem through. If you don’t, you are likely to fall for any number of traps which ETS lays.

A leather pouch contains 10 light bulbs, two of which are defective.

 Column A Column B The probability of drawing two defective light bulbs (without replacement) The probability of drawing two defective light bulbs (without replacement) and then a non-defective bulb

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

On first glance, you may be tempted to think that the probability of Column B is lower. After all, you have to grab one more bulb in column B, which would therefore lower the probability. Right?

Well, if you stop at this point, you’ve fallen for the trap. So let’s think through the problem a little more carefully. If you have already removed the two defective bulbs (both Column A and B), then the probability of removing a non-defective on the third grab (Column B) is 100%. Therefore, the probability of both columns will be the same.

To show this, I am going to use the actual numbers—but remember, when possible, try to avoid solving quantitative comparison problems.

The probability of removing a defective bulb on my first grab is 1/5. On my second grab it is 1/9. Now, what is the probability of drawing a non-defective? Well, if we’ve already grabbed the only two defective bulbs, then the remaining bulbs will all be non-defective. Thus, the probability of grabbing one is 100%.

If we were to solve, it would look like this: Column A: (1/5)(1/9) and Column B : (1/5)(1/9)(1). These two results are equal. Therefore, the answer is C.

Again, your first quick hunch on quantitative comparison is often wrong. Make sure you test your assumptions, with numbers, if necessary, or that you read the question more carefully. For if a quantitative comparison problem seems too easy, it’s probably a trap.

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### 4 Responses to Quantitative Comparison – Common Traps

1. Vinod September 1, 2015 at 10:27 am #

Chris,
Correct me if I am wrong, but I find this question ambiguous. We don’t know whether the defective bulbs after picking were replaced or not replaced. It is given that the defective bulbs are picked without replacement but no information regarding replacement policy after picking two defective bulbs is given.

2. tade September 3, 2013 at 5:52 am #

hi Sir
Thanks a lot.

• Chris Lele September 3, 2013 at 1:15 pm #

You are welcome!

3. Srujan March 8, 2012 at 1:28 am #

Hi Chris,

This always sound ambiguous to me. say in the question above “The probability of drawing two defective light bulbs if two bulbs are removed”.

Initially i was skeptic how to consider this, should i consider this as “with replacement” or “without replacement”? I presumed to consider it “without replacement” unless specified. correct me if i am wrong.

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