GMAT Tip of the Week: Biggie's Juicy Secret About GMAT Inequality

As Hip Hop Month rolls on in the GMAT Tip of the Week space, we’re reminded that small nuances in the ways that GMAT questions are structured can have big consequences for test-takers. So who would be a more fitting man to teach that lesson – what’s small can have big consequences – than Biggie Smalls?

Biggie’s most timeless classic, Juicy, may tell the rags-to-riches story you’re hoping to live out once you grab that top tier MBA: “and my whole crew is lounging, celebrating every day no more public housing.” But first you need to get into b-school, and that’s where this lyric can prove helpful:

“Damn right I like the life I live, ’cause I went from negative to positive … and if you don’t know, now you know.”

What secret is Big Poppa passing along? It’s a critical message in two parts:

…went from negative to positive” is a word of caution. When you’re dealing with inequalities on the GMAT, you need to remember that when a number goes from negative to positive – when you multiply or divide by a negative number to change the sign from positive to negative or from negative to positive – you must also change the direction of the inequality:

If 10 > 5, then -10 is LESS THAN -5
If x > 10, then -x < -10

The lesson: Be careful when going from negative to positive – if you’re working with inequalities and need to multiply or divide by a negative, you MUST change the direction of the inequality.

Perhaps more useful is the next line, however:

And if you don’t know, now you know.” If you don’t know whether a variable is positive or negative, here’s what you need to know: The GMAT is baiting you into assuming that it’s positive. If you’re asked to multiply or divide by a variable in an inequality question, it’s almost always a trap, as the testmaker knows that negative numbers are our blind spots – we tend to overlook them until they’re made absolutely explicit. So as Biggie said, if you don’t know (whether a variable is positive or negative)…now you know that there’s a high likelihood that that distinction will be important. Consider this Data Sufficiency example:

Is a > 3b?

(1) a/b > 3
(2) b > 3

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D) EACH statement ALONE is sufficient to answer the question asked
E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

The trap on this question is to select A, thinking that you can simply multiply both sides of that inequality by b:

a/b > 3 –> a > 3b

But you don’t know whether b is negative or positive. The above technique works if, say, a = 4 and b = 1 –> 4/1 is greater than 3, and 4 (a) is greater than 1 (b). So you get “yes”. But the situation also encompasses a = -4 and b = -1, as -4/-1 is 4, which is greater than 3. But in this case -4 (a) is LESS than -1 (b). So you get “no”. The trap is to get you to blindly multiply both sides by b…but as Biggie cautions: If you don’t know, now you know (to be careful). Statement 2 isn’t much value on its own, but as it guarantees that b is positive, when you take both statements together, now you know that you can multiply both sides by b. So the correct answer is C, but the takeaway is most important here:

When dealing with inequalities, if you don’t know (the + or – sign of a variable) now you know that the question probably hinges on that point. Heed Biggie’s sage advice and you’ll be on your way to one of the world’s most notorious b-schools.

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