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If b is an Integer is a*IaI<2^b? (1)b<0 (2)a=b

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If b is an Integer is a*IaI<2^b? (1)b<0 (2)a=b

by GMATinsight » Wed Oct 14, 2015 8:37 am
If b is an Integer is a*IaI<2^b?

(1)b<0
(2)a=b

Answer: option C
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Source: — Data Sufficiency |
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by GMATinsight » Wed Oct 14, 2015 8:37 am
GMATinsight wrote:If b is an Integer is a*IaI<2^b?

(1)b<0
(2)a=b

Answer: option C
Statement 1: b < 0

Case 1: @a=0.1, b=-1, a*IaI=0.01 and 2^b = 1/2, i.e. a*IaI < 2^b
Case 2: @a=1, b=-1, a*IaI=1 and 2^b = 1/2, i.e. a*IaI > 2^b

NOT SUFFICIENT

Statement 2: a=b
Case 1: @a=2, b=2, a*IaI=4 and 2^b = 4, i.e. a*IaI is NOT less than 2^b
Case 2: @a=-1, b=-1, a*IaI=-1 and 2^b = 1/2, i.e. a*IaI < 2^b
NOT SUFFICIENT

Combining the Two statements
if a=b and b < 0
then LHS i.e. a*IaI will always be Negative and RHS i.e. 2^b will always be positive hence,
a*IaI < 2^b
SUFFICIENT

Answer: Option C
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by Max@Math Revolution » Wed Oct 21, 2015 11:29 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If b is an Integer is a*IaI<2^b?

(1)b<0
(2)a=b


In the original condition, there are 2 variables (a,b) and 2 equations in the conditions, so there is high chance (C) will be our answer. If we combine the 2 conditions,
a=b<0, so |a|=-a. Then a|a|=a(-a)=-a^2, and the answer becomes 'yes' always at -a^2<2^b, so this is a sufficient set of conditions, and the answer becomes (C)

For cases where we need 2 more equation, such as original conditions with "2 variables", or "3 variables and 1 equation", or "4 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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