GMAT Data Sufficiency: Ratio Stories:

by on March 25th, 2015

math_3How are you with story problems? Most math concepts can be presented in story form on the test and the GMAT test writers do like to get wordy with us. You’ve got a double task: you have to translate the words into math and then you still have to do the math! How can we get through these as efficiently as possible?

Try the GMATPrep® problem below and then we’ll talk about it. Give yourself about 2 minutes. Go!

* “On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?”

“(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.

“(2) The number of women on the sight-seeing tour was less than 30.”

Got your answer? (If you’re wondering where / what the answer choices are, click here to learn about Data Sufficiency before proceeding with this problem.)

All right, so W : C is 5 : 2 and they want to know…oh, that’s interesting. They’re asking for the number of men. In other words, there are three groups here, not just two.

296 - image 1 After I write that down, I glance back up at the screen to make sure I’ve got everything transcribed correctly. Okay, not much else I can do here. Moving on to statement (1).

“(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.”

Hmm. They’re giving me another ratio.

296 - image 2

Even as I’m jotting this info down, I’m skeptical. Why?

There are no real numbers here. They didn’t ask for the ratio of men to anything. They just want the actual number for M.

Statement (1) is not sufficient. Cross off choices (A) and (D). Next up, statement (2).

“(2) The number of women on the sight-seeing tour was less than 30.”

Yes! Now they’re giving me a real number! So now I can solve.

296 - image 3

Oh, wait. Careful: the question stem doesn’t contain any info about the men. This is why I organize my scrap paper in the way that I’m showing you: I’ve “segregated” the various pieces of info so that I can catch myself when I might try to use certain pieces of data at the wrong time. Right now, I have to completely ignore statement (1); it doesn’t exist. I can figure out some possibilities for the number of women but nothing about the number of men.

Okay, statement (2) doesn’t work either; cross off answer (B).

So now we get to use everything. Does that help?

Yes, it does! First, the two different ratios can be combined into one big ratio. To do that, the “like” portions of the two ratios have to be made the same:

296 - image 4

That ratio can’t be simplified further, because the 25 is not even but the 10 and 22 are.

Next, there are fewer than 30 women. The women have to represent 25 in the ratio; in other words, the number of women must be a multiple of 25. There’s only one possible multiple of 25 that is also less than 30: 25 itself! There must be exactly 25 women, 10 children, and 22 men. Done!

The correct answer is (C).

One big trap on this problem is assuming that the inequality given for statement (2) won’t be enough. The (faulty) thinking goes: the problem asks for a specific value, and a range (less than 30) isn’t going to be enough to get to one specific value.

Turns out, in this case, it is! It can be tricky on DS to know when to stop the math; you don’t want to have to solve every problem completely or you’ll take way too much time. In this case, the clues for me were:

(1) “Less than 30” isn’t all that many possible values

(2) The two “like” parts of the ratio (children and children) are different enough to start (5 and 2) that the final ratio numbers might end up being quite large…so maybe “less than 30” will be good enough after all

Okay, want to try another? Try this GMATPrep® problem from the free question set, then join me next time to discuss the solution.

“A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain?

“(1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.

“(2) If the number of oak trees were increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.”

Key Takeaways: Work methodically and don’t stop too soon!

(1) On story problems, half the battle is translating accurately. It’s easy to make careless mistakes (such as reversing two categories), and of course, sometimes the translation is just tricky. After you’ve translated the story, double-check your notes against the screen to make sure everything’s where it should be.

(2) Two ratios can be combined into one, as long as they overlap somewhere. The “like” category needs to be made the same number for both ratios; then you can combine them into one big ratio.

(3) Don’t stop too soon on DS! When they give you a range of possible values, don’t automatically assume it isn’t enough. See whether there are other constraints in the problem that might narrow down all of the possibilities to just one answer. If so, you’ve got sufficiency!

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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