Know the GMAT Code: Translation Traps
The problem were going to talk about today is a work of art. (Yes, Im a geek. Did you not know that already? :) )
But Im serious: its a thing of beauty. It looks super easy. Its notthere 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 Code series and then well talk about the awesome lessons here. Note: this ones from the GMATPrep free exams.
*Of the 60 animals on a certain farm, [pmath]2/3[/pmath]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 havent done Data Sufficiency before or are new enough to DS that youre wondering where the answer choices are, start here and come back to this article later.)
Lets do this!
1-second Glance. DS. Story. Will need to translate.
Read. The story seems pretty straightforward. I feel like this is a question theyd give me in 5th grade I better be careful!
Lets jot this stuff down and see whats going on.
Reflect Okay, so only two-thirds of the animals are pigs or cows. What about the rest? I dont knowI guess I just know that there are other animals that arent pigs or cows. Ill table that for now, but Ive 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 Im 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 its 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 youre testing true. I know it seems a little silly to make a separate column for that on this problem, but if Ive learned one thing over the years, its this: careless mistakes are the bane of any standardized test-takers existence. Have a process. Follow the processevery 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 [pmath]c = 2p[/pmath]. But thats not what it says. Rather, there are more than twice as many. Is that just an inequality?
Try it out. If the equation is [pmath]c[/pmath]> [pmath]2p[/pmath], do real-life, logical numbers work? If you have 4 pigs, youd 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): [pmath]c[/pmath] > [pmath]2p[/pmath]. If youre 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 youre only allowed to test numbers that make the statement that youre testing true. But theres actually one more thing you have to do. If the question stem gives you any true (or whats called given) information, you have to make that true, too.
In my first case for statement (1), [pmath]p[/pmath]and [pmath]c[/pmath]dont 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 isnt sufficient, either. Cross off (A).
Time to try the two statements together.
Hmm. First, according to statement (2), [pmath]p[/pmath]has to be at least 13. So, according to statement (1), c has to be at least [pmath]13(2) + 1 = 27[/pmath].
Oh, and those two numbers do add up to the right total: [pmath]13 + 27 = 40[/pmath]. Great! So this is one possible set of values for [pmath]p[/pmath]and [pmath]c[/pmath]. Is there another?
If p is 14, then c has to be at least [pmath]14(2) + 1 = 29[/pmath]. So there is a second value wait! [pmath]14 + 29 = 43[/pmath]. Thats the wrong total. And as I keep increasing [pmath]p[/pmath], Im going to keep increasing the total, so theres no other pair of numbers that will properly add up to 40.
This is it: [pmath]c[/pmath]has to be 27. The two statements together are sufficient.
The correct answer is (C).
That wasnt 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, youre going to think that more than one pair of numbers is possible and get (E) as your answer.
Even if youre fully up to speed on the 40, you have to remember to bring that fact back in as a check at the end. Otherwise, youre going to think: could be 13 and anything over 27, so there are multiple possible values for [pmath]c[/pmath]... and youre going to get (E) again.
Its 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, youre starting to get mentally fatigued, you might be worried about timing and thinking, Yes, this is an easy one! I can save time! Thats where careless mistakes pounce.
If you think statement (1) just says twice as many, not more than twice as many, youll 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 youd have to have 13 pigs and 26 cows? That doesnt add up right. Theres 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 Code:
(1) Easier-looking does not necessarily mean easier. A lot of times, easier-looking problems have some easy-to-fall-for traps. Work carefullydont get ahead of yourself. Write everything down. Map out the problem.
(2) Turn any knowledge you gain into Know the Code flash cards:
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.