Data Sufficiency

Is a>|b|?

(1) 2^(a−b)>16
(2) |a-b|<b

Source:e-gmat

Mo2men wrote:Is a>|b|?

(1) 2^(a−b)>16
(2) |a-b|<b

Source:e-gmat

(1) a - b must be greater than 4. If a & b are both positive, then a must be greater than b (and so a>|b|). If a & b are both negative, then |b| > a. Insufficient.

(2) Not sufficient. |a-b| < b. Picking values -- A could be 3 and b 2, in which case 1<2; or A could be 2 and b 3, in which case 1<2. In case (1), a>|b|, while in case (2) a<|b|. Note importantly, since |a-b| must be greater than or equal to 0, this implies b must be greater than or equal to 0.

(1) & (2) combined: B must be greater than or equal to zero, and a-b>4. Thus, a>b+4. Since b must be greater than or equal to zero, |b|=b. It follows that, since a>b+4, a>b and a>|b|.

Therefore, it would appear the answer is C.

[email protected] wrote:Hi Mo2men,

This DS question can be solved by TESTing VALUES.

We're asked if A > |B|. This is a YES/NO question.

1) 2^(A - B) = 16

The only 'power of 2' that equals 16 is the 4th power, so from this Fact we know that A - B = 4

IF....
A = 4
B = 0
Then the answer to the question is YES.

IF...
A = 0
B = -4
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) |A - B| < B

IF...
A = 3
B = 2
Then the answer to the question is YES.

IF...
A = 2
B = 3
Then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
A - B = 4
|A - B| < B

So.... 4 < B, which means that B MUST be positive.
The first equation can then be rewritten as A = B + 4, which means that A MUST be greater than B.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Thanks Rich

I'd like to draw your attention that The 1 statement is 2^(A - B) > 16. I know that the final answer won't change. we can change values to be

A - B > 4

A = 5
B = 0
Answer: Yes

A= 0
B= -5

Answer: No

Insufficient

Hi, Although I am not expert, and very brand new to Beat the GMAT community and I just started to see what is going on before even I started buying my study material. Based on what I have reviewed yesterday from the DS videos. I think I would use the table method to answer this question. I have chosen two values of a, and b to plug it in statement 1. to see if the answer is greater than 16. I picked a=1, b=1 the answer is no so I kept going between positive and negative numbers that gave me answer no; however, when I chose the a=6, b=0 I got the answer yes. so I have two contradictory answers for statement 1; therefore it is insufficient to answer the target question.
I used the table method as well and picked up value for a=1, b=1 so the answer yes. for the values a=-1 b=-1 the answer is no so I concluded that statement 2 is insufficient as well. If both 1, and 2 are insufficient the answer would be E based on the the videos I review here at Beat the GMAT.

[email protected] wrote:Hi Mo2men,

This DS question can be solved by TESTing VALUES.

We're asked if A > |B|. This is a YES/NO question.

Combined, we know...
A - B > 4
|A - B| < B

So.... 4 < B, which means that B MUST be positive.
The first inequality can then be rewritten as A > B + 4, which means that A MUST be greater than B.
Combined, SUFFICIENT


assassins aren't born, they're made,
Rich

Dear Brent while considering both the statements, how did you reach the conclusion that
(a-b) > 4 from the first statement,
(a-b)^2 > 16
After rooting both LHS RHS
shouldn't it be (a-b)>+4 or (a-b)<-4

Please correct me where am I going wrong
Thanks
Teja

evs.teja wrote: Dear Brent while considering both the statements, how did you reach the conclusion that
(a-b) > 4 from the first statement,
(a-b)^2 > 16
After rooting both LHS RHS
shouldn't it be (a-b)>+4 or (a-b)<-4

Please correct me where am I going wrong
Thanks
Teja

Teja, I think you've got it upside down. S1 says 2ᵃ−ᵇ > 16, not (a - b)² > 16. (But otherwise, you're right, we would have two sets of solutions! ^_^)