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If y >= 0, What is the value of x?

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If y >= 0, What is the value of x?

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If y >= 0, What is the value of x?

(1) |x-3| >= y
(2) |x-3| <= -y

OA B

Source: GMAT Prep

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BTGmoderatorDC wrote:
If y ≥ 0, What is the value of x?

(1) |x - 3| ≥ y
(2) |x - 3| ≤ -y
Target question: What is the value of x?

Given: y ≥ 0

Statement 1: |x - 3| ≥ y
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 10 and y = 2. We get |10 - 3| ≥ 2, which evaluates to be 7 ≥ 2, which satisfies statement 1. In this case, the answer to the target question is x = 10
Case b: x = 9 and y = 2. We get |9 - 3| ≥ 2, which evaluates to be 6 ≥ 2, which satisfies statement 1. In this case, the answer to the target question is x = 9
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x - 3| ≤ -y
IMPORTANT: We're told that y ≥ 0
This means -y ≤0
In other words, -y is less than or equal to zero
Hmmm, we know that |x - 3| must be greater than or equal to zero for all values of x
So, statement 2 essentially tells us: (some number that's GREATER THAN or equal to zero) ≤ (some number that's LESS THAN or equal to zero)
The only way this inequality can be true is when both sides equal zero
So, it must be the case that |x - 3| = 0, which means x must equal 3
In other words, the answer to the target question is x = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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