GMAT Data Sufficiency: Ratio Stories
Recently, we took a look at a story problem dealing with ratios, and I finished up by giving you a second problem to test your skills. How did you do?
If you havent already, try the GMATPrep problem below and then well talk about it. Give yourself about 2 minutes. Go!
* 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.
Ready? (If youre wondering where / what the answer choices are, click here to learn about Data Sufficiency before proceeding with this problem.)
The question stem doesnt give a lot of info. There are 56 oak trees and we need to find the number of pine trees.
Statement (1) is shorter, so lets start there.
(1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.
Okay, a ratio. Is that useful?
Aside: Wondering why I wrote my os like that? If I didn't add the slash, I might mix them up with zeros. I also put slashes through zs (they look like my 2s) and ss (they look like my 5s).
Okay, so if you have a ratio and you also have the real number for any one portion of that ratio, then you can figure out everything in that ratio.
In this case, if there are 56 oak trees in a ratio of 8 oaks to 5 pines, then the unknown multiplier is 56/8 = 7. There are (8)(7) = 56 oaks and (5)(7) = 35 pines.
This is data sufficiency, so you dont actually need to calculate that; you just need to be able to tell that you can calculate it. Statement (1) is sufficient. Cross off choices (B), (C), and (E).
Next up, the slightly more annoying (by length) statement (2):
(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.
Hmm. More complicated. Lets see: there are 56 oak trees, so if they are increased by 4, then there would be 60 oak trees. We can still use p to represent the pines; that number doesnt change.
Oh, check that out. Im glad I wrote that out so that I could see what was going on. Turns out, we have the same info that statement (1) gave us: a real number for the oak trees and a ratio. That allows you to calculate the new number of pines, which is the same as the old number.
Okay, statement (2) also works, so the correct answer is (D).
By the way, just to practice your computation skills, how many pines are there in the second scenario? (You dont actually have to solve this on data sufficiency, of course.)
If there are 60 oaks, then the unknown multiplier is 60/12 = 5. Therefore, there are (7)(5) = 35 pine trees.
Key Takeaways: Write everything out!
(1) It can be tempting to eyeball some information and go with a gut feel, but this can sometimes get you into trouble. Ive seen people look at statement (2) and think that its not sufficient without actually writing out the work. Theyll sometimes think that you can calculate the new number but not the old one, forgetting that the number of pine trees doesn't change.
(2) Know the unknown multiplier rule: if you have the ratio and one real number for anything in that ratio, then you can calculate the real numbers for all parts of that ratio.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.