To any Expert..Modulus question

[Mo2men]

Is a>|b|?

(1) 2^(a−b)>16
(2) |a-b|<b

Source:e-gmat

[[email protected]]

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 = 5
B = 0
Then the answer to the question is YES.

IF...
A = 0
B = -5
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 inequality 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

[800_or_bust]

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.

[Mo2men]

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

[sufi]

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]]

Hi Mo2men,

Good catch! I've updated my original explanation accordingly.

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

[[email protected]]

Hi sufi,

When TESTing VALUES on a DS question, you have pay attention to the 'restrictions' that exist in each of the two Facts that appear beneath the prompt.

In Fact 1, we're told that (A-B)^2 > 16....

You MUST choose an A and a B that will "fit" that inequality. If you used A=1, B=1, then you would end up with (1-1)^2 = 0, but that is NOT greater than 16. This means that you cannot use that specific pair of values (since they don't fit what you were told).

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

[evs.teja]

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

[Matt@VeritasPrep]

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! ^_^)