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From 1: 2a – b < 7 AND |2a – b| < 7 WHERE 2a -b > -7 2a – b < 7 BUT |2a – b| > 7 WHERE 2a -b < -7 INSUFFICIENT

to confirm this you can find values of a & b that satisfy the condition 2a – b < 7 but provide different answers for |2a – b| < 7 ? A: a = 3, b = 0 2a - b = 6 - 0 = 6 6 < 7 and |6| < 7 B: a = -10, b = 1 2a - b = -20 - 1 = -21 -21 < 7 but |-21| > 7

From 2 you can refactor the original question: Is |2(b + 3) - b| < 7? => is |b + 6| < 7? This is true for -13 < b < 1 but false for value outside of this range. Again INSUFFICIENT.

Together, we can further combine in a similar manner as above to see that b + 6 < 7 so we find that b < 1, but we still don't know if b > -13.

So together is INSUFFICIENT.

Again, to see that this is the case, you can substitute numbers that satisfy both 1 & 2, but give different answers to the main question:

A: a = 3, b = 0 2a – b < 7 : 2a - b = 6 - 0 = 6 < 7 a = b + 3 : 3 = 0 + 3 |2a – b| < 7 ? : |6| < 7 TRUE

B: a = -20, b = -17 2a – b < 7 : 2a - b = -40 - (-17) = -23 < 7 a = b + 3 : -20 = -17 + 3 |2a – b| < 7 ? : |-23| < 7 FALSE

See there lies your fallacy.. Both can be possible so it is NOT possible ( SUFFICIENT) to answer conclusively. Had there been some other condition outlining that 2a-b is always greater than 0 , then it would have been SUFFICIENT. Right now as it is stands , it is ambiguous.

Absolute value can be understood as distance from zero on the number line. The quantity 2 a – b has an absolute value less than 7 if (and only if) that quantity is less than 7 units away from 0 on a number line.

(1) INSUFFICIENT: This statement tells us that 2 a – b is less than 7, but this does not tell us whether it is less than 7 units away from 0. For instance, 2 a – b could be equal to –20.

(2) INSUFFICIENT: We can manipulate the equation a = b + 3 so that it tells us the value of 2 a – b:

a = b + 3 2 a = 2 b + 6 2 a – b = b + 6

Since there is no restriction on the value of b, b + 6 can be anywhere on the number line. This implies that 2 a – b can be anywhere on the number line, making both “yes” and “no” answers possible.

(1) & (2) INSUFFICIENT: Statement (2) does not restrict the value of 2 a – b at all, so combining it with statement (1) yields the same result as for statement (1) alone. In a sense, the catch in this problem is that there is no catch: we should be suitably suspicious when a problem seems easier than it ought to be, but we should then trust our analysis and choose confidently.

The correct answer is E.

gmatclubot

Re: Is |2a – b| < 7?
[#permalink]
23 Mar 2017, 17:09

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