Manhattan Prep's GMAT app Question 82144

[RubenM342]

Question

Is |a| > |b|?

(1) b < −a
(2) a < 0


I initially took the time to rephrase the inequality question stem as either 1) a>b or 2) -a>b ? . When presented with two absolute values expressions and an inequality, the recommendation is to assess two scenarios: 1) both signs are the same (i.e. a>b), and 2) different signs (one positive and one negative expression) hence, -a > b as a rephrasing. This can also be re-written as a<-b if dividing the negative sign.

Upon seeing statement 1, I assumed that given it matched one alternative rephrasing of the inequality, then it was sufficient. Can you elaborate on why this is not sufficient? Does the the statement have to fulfill both conditions in order to be sufficient (ie. a>b, and a <-b)? Any additional insights would be greatly appreciated.

Alternatively, I redid this problem by testing values and saw that statement I is not sufficient, but would like to confirm the rationale behind the algebraic/theoretical approach.

Thanks,

Ruben

[Sage Pearce-Higgins]

Absolute values are confusing. This question has a double confusion: it has an inequality too. The rephrase, as you've written it, doesn't work. Not only are there multiple questions, but each question applies to a different scenario. There would actually be four scenarios: "Is a > b?" if a and b are both positive, "Is -a > b?" if a is negative and b is positive, etc. You can see that it gets pretty complicated!

Part of the skill of strategy choice is to see that, for situations such as this, turning equations into words and picking real numbers is much easier. I would encourage you to rephrase the question simply to "If I remove any negative signs from both 'a' and 'b', is a > b?".

A good takeaway is to be really careful when dealing with absolute values and inequalities and, wherever possible, avoid algebraic approaches in such situations.