What do Mountain Dew, Tough Mudder, and Data Sufficiency have in common? Maybe they’re your plans for this weekend, but more universally they all lend themselves to the mentality, lifestyle, and even spelling of the eXXtreme!! And while we could fill this space with extreme-to-the-max tips about Mountain Dew (please don’t drink it for breakfast, high school students) and Tough Mudder (bring your wallet…their marketing is as extreme as the event itself), it’s more helpful to show you how taking it to the extreme can help you succeed on logic-based quant questions.
The name if the game with Data Sufficiency is “must be true”, as in “you have sufficient information to answer the question if the same answer must be true in all allowable cases”. So if you get a question like:
Is x^2 greater than 16?
With a statement like:
(1) x < 4
While the “obvious” values of x might be 3 (which squared is 9, so “no”) and 2 (which squared is 4, so also “no”), you’ll be rewarded for thinking of more-extreme answers allowed by the facts (what about a really, really negative number like -100: its square root will be very big and very positive, so that can give you your “yes”, making this statement not sufficient).
The GMAT likes to play to the extremes when it gives you limits on Data Sufficiency and “must be true” Problem Solving problems. When they give you the stipulation that x > 0, a wise test taker won’t start thinking only at 1 (what about a tiny fraction like 1/10?) and won’t stop thinking at 9 or 10 (what about a million?). The GMAT will reward you for pushing the limits of the possible range of values, and by that same token punish you if you stay within the typical comfort zone.
Consider this example:
If a, b, and c are consecutive odd positive integers and a < b < c, which of the following must be true?
I. at least one of the three numbers is prime
II. ab > c
III. a + b + c = 3b
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
For this question, most test-takers realize quickly that statement III must be true, as for consecutive odd integers, c will equal b + 2 and a will equal b – 2, so they’ll net out to 3b.
Statement II can be eliminated by going to the lower extreme: 1(3) is not greater than 5, but for all other versions (3*5 is greater than 7; 5*7 is greater than 9, etc.) the answer is “yes”. You have to go to the low extreme to eliminate statement II.
Statement I is the crux of this problem – about 70% of all respondents to this question in the Veritas Prep Question Bank see statement I as definitely true, when in fact it’s not. Their mistake? They don’t go to extremes. With two-digit numbers, at least one of every three odds in a row is prime. But that’s just because there aren’t enough numbers to be divisible by. There are only 14 multiples of 7 and 9 multiples of 11 within that set, meaning that you’re leaning extremely heavily on factors of 3 and 5 to find odd numbers that aren’t prime. But by the time you hit triple digits, there are plenty of potential factors, and prime numbers become much more rare. Consider 121, 123, and 125 – none are prime. If you go high enough in your search – with some logic behind it – you can fairly easily prove statement 1 not to be true. And the technique for doing so is to recognize that it’s easy to find multiples of 5 (if a number ends in 5, it’s an odd multiple of 5) and multiples of 3 (if the sum of the digits of a number is a multiple of 3, that number is divisible by 3). So you want to find multiples of 7 or 11 that don’t end in 5 and make those your starting point. 11-squared works perfectly – it’s only divisible by 11 – and then you can check two odds in either direction to see if they pass the 3s and 5s tests. 217 is another great one – you know that 210 and 7 are both divisible by 7, and then next to that you can find 215 (divisible by 5) and 213 (divisible by 3).
The problem with this problem is that people don’t look to the extremes. They’re relatively happy to check 3-4 sets of one and two digit numbers and feel that they’ve proven a trend, whereas on Must Be True questions it pays to get extreme.
By Brian Galvin