Data Sufficiency

ziyuenlau wrote:Is √x a prime number?

(1) |3x − 7| = 2x + 2

(2) x² = 9x

Target question: Is √x a prime number?

Statement 1: |3x − 7| = 2x + 2
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

So, we get two equations: 3x − 7 = 2x + 2 or 3x − 7 = -(2x + 2)

If 3x − 7 = 2x + 2, then we get x = 9. When we plug this x-value into the original equation, it WORKS.
If x = 9, then √x = √9 = 3, and 3 IS a prime number.

If 3x − 7 = -(2x + 2), then we get x = 1. When we plug this x-value into the original equation, it WORKS.
If x = 1, then √x = √1 = 1, and 1 is NOT a prime number.

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x² = 9x
Rearrange to get: x² - 9x = 0
Factor: x(x - 9) = 0

So, EITHER x = 0 OR x = 9
If x = 0, then √x = √0 = 0, and 0 is NOT a prime number.
If x = 9, then √x = √9 = 3, and 3 IS a prime number.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 9 or x = 1
Statement 2 tells us that x = 9 or x = 0
Since BOTH equations are TRUE, it MUST be the case that x = 9.
Since x = 9, then √x = √9 = 3, and 3 IS a prime number.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

ziyuenlau wrote:Is √x a prime number?

(1) |3x−7|=2x+2

(2) x^2=9x

OFFICIAL ANSWER : C

One of the common mistakes is committed while handling x^2=9x. Usually, one gets tempted to cancel x from both the sides, rendering x = 9; however, it is incomplete. One must deal x^2=9x as x^2 - 9x = 0 => x(x - 9) = 0 => x = 0 or 9.

Hope this helps!

-Jay
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