### Archives For quant

I’ve got another one for you from our 5 lb. Book of GRE® Practice Problems, and this one’s serious. I took it from the Advanced Quant chapter. Try it out and then we’ll chat!

“Triplets Adam, Bruce, and Charlie enter a triathlon. There are nine competitors in the triathlon. If every competitor has an equal chance of winning, and three medals will be awarded, what is the probability that at least two of the triplets will win a medal?

(A) 3/14

(B) 19/84

(C) 11/42

(D) 15/28

(E) 3/4

Yuck. I’m not a fan of probability in general and this one is particularly annoying. Why? Because they ask for the probability that at least two will win. Most of the time, when a probability question uses at least or at most language, we can use the cool 1 – x shortcut because there’s only one not-included case.

For example, if I tell you I’m going to flip a coin three times, I might ask you to calculate the probability that I’ll get at least one heads. There’s only one case where I wouldn’t: zero heads. So you can just calculate the probability of zero heads and subtract from 1.

But we can’t do that here, because it’s possible for just 1 twin to win a medal and it’s also possible for zero twins to win a medal. Sigh.

Okay, how are we going to tackle this? Probability is a measure of the number of “desired outcomes” divided by the total number of possibilities. Let’s figure out the total number of possibilities first.

Take a look at the question again. Is this one of those questions where the order matters? If you don’t win, you don’t win. If you do win, does the question make a distinction between coming in first, second, or third?

We’ve got another problem for you from our new book, the 5 lb Book of GRE® Practice Problems. The book contains more than 1,100 pages of practice problems (and solutions), so you can drill on anything and everything that might be giving you trouble.

This “regular” problem solving question asks us to pick one correct answer (other variations might ask us to select more than one answer or to type in our own answer). Give yourself approximately 2 minutes to finish (or make a guess).

I’ve spoken with multiple students lately who received a disappointing (lower than they were expecting) score on the quant section and who all said that the quant felt relatively easy or straightforward. How is that possible?

First of all, thinking that a test like the GRE is easy is actually a warning sign: unless you are poised to get a perfect score, chances are you’re missing something. Some of the questions are really very challenging and they should feel hard even to someone like me (who did get a perfect score on this test! ).

Second, the test writers are phenomenal at writing questions that don’t seem all that complicated… but are in fact your worst nightmare. My worst nightmare is not an impossible question – I know I can’t do it, so I just pick an answer and move on. My worst nightmare is a question that I think I can do, and I spend a decent chunk of time doing it, and then I get it wrong anyway – even though I’m sure I got it right!

The problem I’ve chosen is actually a GMAT problem; I chose it because it perfectly illustrates the point that I’m trying to make, and it is actually in the same form as GRE problems. Try this GMATPrep problem and you might see what I mean. Set your timer for 2 minutes…. and… GO!

* ” Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?

“(A) 25%

“(B) 22.2%

“(C) 20%

“(D) 12.5%

“(E) 11.1%”

Have you ever gotten a GRE question wrong because you thought you were supposed to take a square root and get two different numbers but the answer key said only the positive root counted? Alternatively, have you ever gotten one wrong because you took the square root and wrote down just the positive root but the answer key said that, this time, both the positive and the negative root counted? What’s going on here?

It's also hip to be able to solve a square root question on a standardized test.

There are a couple of rules we need to keep straight in terms of how standardized tests (including the GRE) deal with square roots. The Official Guide does detail these rules, but enough students have found the explanation confusing – and have complained to us about it – that we decided to write an article to clear everything up.

#### Doesn’t the OG say that we’re only supposed to take the positive root?

Sometimes this is true – but not always. This is where the confusion arises. Here’s a quote from the OG 2nd edition, page 212:

“All positive numbers have two square roots, one positive and one negative.”

Hmm. Okay, so that makes it seem like we always should take two roots, not just the positive one. Later in the same paragraph, though, the book says:

“The symbol √n is used to denote the nonnegative square root of the nonnegative number n.”

Translation: when there’s a square root symbol given with an actual number underneath it – not a variable – then we should take only the positive root. This is confusing because, although they’re not talking about variables, they use the letter n in the example. In this instance, even though they use the letter n, they define n as a “nonnegative number” – that is, they have already removed the possibility that n could be negative, so n is not really a variable.

If I ask you for the value of √9, then the answer is 3, but not -3. That leads us to our first rule.