Is a − b 9 ? (1) a − √400 0 (2) 0

Question

Is a − b > 9 ?

(1) a − √400 > 0
(2) 0 < b − √121

BrentGMATPrepNow · Answer

Target question : Is a − b > 9 ? Statement 1 : (1) a − √400 > 0 Simplify to get: a − 20 > 0 Add 20 to both sides to get: a > 20 Since we have no information about the value of b, statement 1 is NOT SUFFICIENT Statement 2 : 0 < b − √121 Simplify to get: 0 < b − 11 Add 11 to both sides to get: 11 < b Since we have no information about the value of a, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that a > 20 Statement 2 tells us that b > 11 There are several values of a and b that satisfy BOTH statements. Here are two: Case a : a = 30 and b = 12. In this case, a - b = 30 - 12 = 18, which means the answer to the target question is YES, a - b is greater than 9 Case b : a = 30 and b = 30. In this case, a - b = 30 - 30 = 0, which means the answer to the target question is NO, a - b is not greater than 9 Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent

Showmeyaa · Answer

1) a > √400
a > 20. No info on b - Insufficient!
2) b > √121
b > 11. No info on a - Insufficient!
Combining 1 & 2:
Case1: a = 21, b = 12
a - b > 9? No!
Case2: a = 30, b = 15
a - b > 9? Yes!
IMO, (E)

Makesh89 · Answer

Why are we not considering the squareroot of 400=-20 and 121 to be - 11. 
In simple terms why are we not considering the negative square roots. 
Kindly make me understand.

1) a > √400
a > 20. No info on b - Insufficient!
2) b > √121
b > 11. No info on a - Insufficient!
Combining 1 & 2:
Case1: a = 21, b = 12
a - b > 9? No!
Case2: a = 30, b = 15
a - b > 9? Yes!
IMO, (E)

Posted from my mobile device

Showmeyaa · Answer

Posted from my mobile device    
Hi  Makesh89 
 \sqrt{Number}  is always positive.
 \sqrt{Variable}  can be positive or negative.
For ex:
 \sqrt{25}  = 5
 \sqrt{x^2}  = |x| = +x, -x.

bumpbot · Answer

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Is a − b > 9 ? (1) a − √400 > 0 (2) 0 < b − √121

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