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Is a > |b|? (1) 2^(a - b) > 16 (2) |a b| < b 20 Sep 2019, 01:30
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EgmatQuantExpert
Official Explanation

Correct Answer: C

We are asked to find if a > |b|

Note that in order for the answer to be YES:

i) a should be positive, AND
ii) a should be greater than the magnitude of b.

If we find that a is negative or that a is positive but its magnitude is lesser than that of b, then our answer will be NO.

Analysing Statement 1
\(2^{a-b} > 16\)
\(2^{a-b} > 2^4\)

This means, a – b > 4
That is, a > b

However, note that we cannot say for sure if a is positive or not. For example, a = -2, b = -6 also satisfy the inequality a – b > 4.

So, Statement 1 alone is not sufficient to answer the question.

Analysing Statement 2

|a - b | < b

For all possible values of a and b, |a-b| will be non-negative (that is, greater than or equal to zero)
So, if b > |a-b| (as given in Statement 2),
This means b is positive.

But in order to answer the question asked, we need to find if a is positive AND its magnitude is greater than that of b.

Since we are not able to answer this, St. 2 is clearly not sufficient.

Combining the two statements

From Statement 1, a > b
From Statement 2, b is positive.
Since b is positive, |b| = b . . . (1)

Substituting Equation 1 in the inequality from Statement 1:
a > |b|

Thus, the two statements together are sufficient to answer the question.
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Hi EgmatQuantExpert,

The example you provided above violates the first statement. If a = -2 and b = -6, as you wrote, then a - b is not greater than 4 becuase 4>4 is incorrect.
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Is a > |b|? (1) 2^(a - b) > 16 (2) |a b| < b Updated on: 17 May 2021, 09:45
Originally posted by BrentGMATPrepNow on 17 Apr 2020, 06:41.
Last edited by BrentGMATPrepNow on 17 May 2021, 09:45, edited 1 time in total.
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EgmatQuantExpert
Is \(a > |b|?\)

(1) \(2^{a-b} > 16\)
(2) \(|a – b| < b\)
Show more

Target question: Is \(a > |b|?\)

Statement 1: \(2^{a-b} > 16\)
Rewrite as: \(2^{a-b} > 2^4\)
This means: a - b > 4
There are several values of a and b that satisfy the inequality a - b > 4. Here are two:
Case a: a = 6 and b = 1. Since 6 > |1|, the answer to the target question is YES, it's true that a > |b|
Case b: a = -1 and b = -6. Since -1 < |-6|, the answer to the target question is NO, it's not true that a > |b|
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: \(|a – b| < b\)
|a – b| is always greater than or equal to 0.
Since b is greater than |a – b|, we know that b is POSITIVE

----ASIDE------------------
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
------------------------------

From Rule #1, we can write: -b < a – b < b
Add b to all sides of the inequality to get: 0 < a < 2b
There are several values of a and b that satisfy the inequality 0 < a < 2b. Here are two:
Case a: a = 4 and b = 3. Since 4 > |3|, the answer to the target question is YES, it's true that a > |b|
Case b: a = 1 and b = 3. Since 3 < |1|, the answer to the target question is NO, it's not true that a > |b|
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that 0 < a < 2b.
This is very useful because it tells us that a and b are both POSITIVE

Statement 1 tells us that a - b > 4
Add b to both sides of the inequality to get: a > b + 4
Rewrite as: b + 4 < a
Since we also know that b < b + 4, AND that 0 < b, we can write: 0 < b < b + 4 < a
Since b is POSITIVE, and since b < a, we can be absolutely certain that a > |b|
So, the answer to the target question is YES, it's true that a > |b|
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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Is a > |b|? (1) 2^(a - b) > 16 (2) |a b| < b 13 Nov 2025, 07:48
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