Statement 1 is not sufficient because x could also equal -4:
$$\sqrt{\left(-4\right)^2}=\sqrt{16}=4\ $$
Keep an eye out for negative options unless the question specifically states that x is positive! Similarly, look for non-integer options unless the question specifically states that the answer is an integer, etc.
Is x = 4 ?
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Source: Beat The GMAT — Data Sufficiency |
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As for why B is correct, knowing that the absolute value of x (which must be positive) is equal to negative x tells us that x itself must be negative. The negative of a negative number is positive
- (-n) = n
If x is a negative number, it cannot be a positive number, like 4. So this statement is sufficient to answer "no, x does not equal 4".
- (-n) = n
If x is a negative number, it cannot be a positive number, like 4. So this statement is sufficient to answer "no, x does not equal 4".
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Hi M7MBA,
We're asked if X is equal to 4. This is a YES/NO question. We can solve it with a mix of 'math' and some Number Properties.
$$\left(1\right)\ \sqrt{x^2}=4.$$
According to the "Order of Operations" rules, we have to square the value of X BEFORE we square-root the result. Thus, there are 2 values that 'fit' the equation in Fact 1: +4 (which would give us a YES answer) and -4 (which would give us a NO answer).
Fact 1 is SUFFICIENT
$$\left(2\right)\ \left|x\right|=-x\ .$$
The result absolute value on the 'left' side of the equation can either be positive or 0. Since that value equals NEGATIVE X, then X must either be a NEGATIVE number or 0. By extension, it can NEVER be 4, so the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're asked if X is equal to 4. This is a YES/NO question. We can solve it with a mix of 'math' and some Number Properties.
$$\left(1\right)\ \sqrt{x^2}=4.$$
According to the "Order of Operations" rules, we have to square the value of X BEFORE we square-root the result. Thus, there are 2 values that 'fit' the equation in Fact 1: +4 (which would give us a YES answer) and -4 (which would give us a NO answer).
Fact 1 is SUFFICIENT
$$\left(2\right)\ \left|x\right|=-x\ .$$
The result absolute value on the 'left' side of the equation can either be positive or 0. Since that value equals NEGATIVE X, then X must either be a NEGATIVE number or 0. By extension, it can NEVER be 4, so the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
