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if a & B are consteants MGMAT

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Source: — Data Sufficiency |

by Uva@90 » Thu Aug 20, 2015 8:41 am
rommysingh wrote:If a and b are constants, what is one solution of the equation (x + a)(x - b) = 0?

(1) a = 4

(2) b = 3
IS OA E ?

Pls post OA

Regards,
Uva
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by Brent@GMATPrepNow » Thu Aug 20, 2015 8:47 am
rommysingh wrote:If a and b are constants, what is one solution of the equation (x + a)(x - b) = 0?

(1) a = 4
(2) b = 3
Target question: What is one solution of the equation (x + a)(x - b) = 0

Statement 1: a = 4
This means the equation is (x + 4)(x - b) = 0
So, x = -4, is one possible solution to the equation.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The b = 3
This means the equation is (x + a)(x - 3) = 0
So, x = 3, is one possible solution to the equation.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Aside: I don't think I've seen an official GMAT question ask for ONE solution to a quadratic equation. Typically, we're either asked for the value of a variable or asked some yes/no question about the value of the variable (e.g., "Is x > 3?). What's the source?

Cheers,
Brent
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by Max@Math Revolution » Fri Aug 21, 2015 8:12 pm
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 equations ensures a solution.


If a and b are constants, what is one solution of the equation (x + a)(x - b) = 0?

(1) a = 4

(2) b = 3

==> In the original condition, x=-a, and thus we have 2 variables -a,b, meaning we need 2 equations to match the number of variables. Since we have 1 each for both (1), (2) the answer is likely C. Using both (1) & (2) together, x=-4,3 is our solution yet it is not unique, and thus NOT sufficient. Therefore the best answer is E



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