Veritas Prep GMAT Instructor
Joined: 01 May 2019
Posts: 50
Re: M14-13
[#permalink]
11 Jul 2019, 15:03
Quick and easy method of solving if the inequalities are giving you grief:
The question asks if \(|x| > 1\). Rewriting this question, we get "is \(|x| > 1\) OR \(|x| < -1\). Given that x is an integer, the only values that will give us a "no" for this question are -1, 0, and 1. All other integer values will give us a "yes".
Knowing this, we can try to prove each statement insufficient by getting both a "no" and a "yes".
Statement 1 tells us that \((1-2x)(1+x)\) is negative. To get a "yes", we can plug in an easy number, like 2 — this gives \((1-4)(1+2) = (-3)(3) = -9\), which is negative. This works, so we get a "yes". To get a "no", we can try -1, 0, or 1. Since 2 worked, 1 might also be a good option — this gives \((1-2)(1+1) = (-1)(2) = -2\), which is negative. This works, so we get a "no". Since we got both a "no" and a "yes", this Statement is insufficient.
Statement 2 tells us that \((1-x)(1+2x)\) is negative. Let's try the same numbers again. Plugging in 2 gives \((1-2)(1+4) = (-1)(5) = -5\), which is negative. This works, so we get a "yes". Plugging in 1 gives \((1-1)(1+2) = (0)(3) = 0\), which NOT negative. That didn't work, so we should try one of our other "no" options. Plugging in 0 gives \((1-0)(1+0) = (1)(1) = 1\), which NOT negative. That didn't work either, so we're on to our last "no" option. Plugging in -1 gives \((1-(-1))(1+(-2)) = (2)(-1) = -1\), which is negative! This works, so we get a "no". Since we got both a "no" and a "yes", this Statement is insufficient.
Putting both statements together: the two statements both work with x=2, so we can get a "yes" with both statements. The only "no" answer we could get for Statement 2 was x=-1. If x=-1 works with Statement 1 as well, we will get a "no" with both statements, but if it doesn't, there is no way to get a "no" with both statements. Plugging -1 into Statement 1 gives \((1-(-2))(1+(-1)) = (3)(0) = 0\), which is not negative. This doesn't work, so we can't get a "no" with both statements! This means that the answer can only be "yes" with both statements, and the answer is C.
When you have limited options for what will give you a "yes" or a "no" in a yes/no Data Sufficiency question, you can work directly with those options!