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a confusing DS

by allenh » Sun Sep 06, 2015 4:58 am
X=?

1.a^(2x)=b^(x+6)

2.ab=1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..
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by GMATGuruNY » Sun Sep 06, 2015 5:14 am
allenh wrote:X=?

1.a^(2x)=b^(x+6)

2.ab=1

It seems that I should choose C for this one as when you combine these two statements, you will get x=-2. Since a and b are different letters, I assume they represent different numbers. I am just wondering if I need to consider a=b=1, cuz that will change the answer to E..
The problem does not indicate a and b must be distinct values.
Thus, when the statements are combined, it is possible that a=b=1.

Statements combined:
Plugging a=b=1 into a^(2x) = b^(x+6), we get:
1^(2x) = 1^(x+6).
In this case, x can be ANY VALUE.
Since the value of x cannot be determined, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Sun Sep 06, 2015 7:05 am
When it comes to exponent questions with several variables, it's useful to consider what happens when the bases are 0 or 1 and what happens when the variables are 0 or 1.

In this case, we can see that, if a and b both equal 1, the equation a^(2x)=b^(x+6) is true for ANY VALUE of x.

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by Max@Math Revolution » Sun Sep 06, 2015 10:16 pm
X=?

1.a^(2x)=b^(x+6)

2.ab=1

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 equations ensures a solution.

vatiables'number:3 --> needs 3 equations --> E

1) & 2)

if a=b=1, it is possble that 2x is not equal to x+1, therefore the answer is E



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