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The problem we’re going to talk about today is a work of art. (Yes, I’m a geek. Did you not know that already? )
But I’m serious: it’s a thing of beauty. It looks super easy. It’s not—there are traps all over the place. The GMAT test writers have a genius for tying us into knots!
Try out this next problem in our Know the GMAT Code series and then we’ll talk about the awesome lessons here. Note: this one’s from the GMATPrep® free exams.
“*Of the 60 animals on a certain farm, ²/³ are either pigs or cows. How many of the animals are cows?
“(1) The farm has more than twice as many cows as it has pigs.
“(2) The farm has more than 12 pigs.”
(If you haven’t done Data Sufficiency before or are new enough to DS that you’re wondering where the answer choices are, start here and come back to this article later.)
Let’s do this!
1-second Glance. DS. Story. Will need to translate.
Read. The story seems pretty straightforward. I feel like this is a question they’d give me in 5th grade…I better be careful!
Let’s jot this stuff down and see what’s going on.
Reflect…Okay, so only two-thirds of the animals are pigs or cows. What about the rest? I don’t know—I guess I just know that there are other animals that aren’t pigs or cows. I’ll table that for now, but I’ve got it in the back of my mind in case it comes up later with the statements.
Oh, and I can calculate one thing: two-thirds of 60 is 40, so there are 40 total animals that are either pigs or cows.
Statement (1) is a little confusing. I think I’m going to start with statement (2).
“(2) The farm has more than 12 pigs.”
Time to test some cases. If there are 13 pigs…
At whatever point you can tell that it’s possible to get more than one value for the number of cows, you can stop. Cross off the top row (BD) and move on to the other statement.
Note: That middle column, v?, stands for “is this a valid case to test?” You are only allowed to try numbers that make the statement that you’re testing true. I know it seems a little silly to make a separate column for that on this problem, but if I’ve learned one thing over the years, it’s this: careless mistakes are the bane of any standardized test-taker’s existence. Have a process. Follow the process—every time. Trust the process.
Okay, so answers (B) and (D) are out; time to test statement (1).
“(1) The farm has more than twice as many cows as it has pigs.”
Er. How does that get translated? If there are exactly twice as many cows as pigs, then the equation would be c = 2p. But that’s not what it says. Rather, there are more than twice as many. Is that just an inequality?
Try it out. If the equation is c > 2p, do real-life, logical numbers work? If you have 4 pigs, you’d have to have 9 or more cows. 9 > 2(4) is true. If you have 4 pigs, you couldn’t have just 8 cows. 8 > 2(4) is false.
Okay, this is the right equation (or, technically, inequality): c > 2p. If you’re ever not sure, take your best guess on the translation and then test it with some real numbers to see whether it makes sense.
So, is this statement enough? Test it out!
I said earlier that you’re only allowed to test numbers that make the statement that you’re testing true. But there’s actually one more thing you have to do. If the question stem gives you any true (or what’s called “given”) information, you have to make that true, too.
In my first case for statement (1), p and c don’t add up to 40. So let me try that again.
Okay, same deal as statement (2). There are at least two possible values for the number of cows, so this statement isn’t sufficient, either. Cross off (A).
Time to try the two statements together.
Hmm. First, according to statement (2), p has to be at least 13. So, according to statement (1), c has to be at least 13(2) + 1 = 27.
Oh, and those two numbers do add up to the right total: 13 + 27 = 40. Great! So this is one possible set of values for p and c. Is there another?
If p is 14, then c has to be at least 14(2) + 1 = 29. So there is a second value…wait! 14 + 29 = 43. That’s the wrong total. And as I keep increasing p, I’m going to keep increasing the total, so there’s no other pair of numbers that will properly add up to 40.
This is it: c has to be 27. The two statements together are sufficient.
The correct answer is (C).
That wasn’t crazy math or anything. Why did I say this question is harder than it looks?
It has to do with the traps. First of all, they tell us there are 60 animals but then go on to say that ²/³ are either pigs or cows…in other words, the real total number is only 40, not 60. If you work with the number 60, you’re going to think that more than one pair of numbers is possible and get (E) as your answer.
Even if you’re fully up to speed on the 40, you have to remember to bring that fact back in as a “check” at the end. Otherwise, you’re going to think: could be 13 and anything over 27, so there are multiple possible values for c…and you’re going to get (E) again.
It’s also super easy to roll right over the “more than” in statement (1). The test has been going on for a couple of hours now, you’re starting to get mentally fatigued, you might be worried about timing and thinking, “Yes, this is an easy one! I can save time!” That’s where careless mistakes pounce.
If you think statement (1) just says twice as many, not more than twice as many, you’ll think the answer is (A). The only thing that might help you catch that mistake is if you try to do the math: if you have 40 cows and pigs, then you’d have to have…13 pigs and 26 cows? That doesn’t add up right. There’s no way to get to 40 using whole numbers of pigs and cows. But you may not even try to do that math because, after all, this is Data Sufficiency! And if you think the total is 60, then the math does add up: 20 pigs and 40 cows, still leaving you with incorrect (A).
Key Takeaways for Knowing the GMAT Code
(1) Easier-looking does not necessarily mean easier. A lot of times, easier-looking problems have some easy-to-fall-for traps. Work carefully—don’t get ahead of yourself. Write everything down. Map out the problem.
(2) Turn any knowledge you gain into Know the GMAT Code flash cards:
*GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
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Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey’s upcoming GMAT courses here.