What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
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sparkles3144
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(1) you will get two y values. y = 11 and y = 14
Insufficient
(2) you will get two y values. y = -8 and y = 14
Insufficient
(C) Sufficient. y = 14
Insufficient
(2) you will get two y values. y = -8 and y = 14
Insufficient
(C) Sufficient. y = 14
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GMATGuruNY
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Statement 1: 3|x^2 - 4| = y - 2What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
No way to determine the value of y.
INSUFFICIENT.
Statement 2: |3 - y| = 11
Case 1: 3-y = 11
-y = 8
y = -8.
Case 2: -3+y = 11
y = 14.
Since it's possible that y=-8 or y=14, INSUFFICIENT.
Statements combined:
If y=-8 in statement 1, we get:
3|x^2 - 4| = -8 - 2
|x^2 - 4| = -10/3.
Not possible: an absolute value expression cannot be equal to a negative value.
Thus, the only value that satisfies both statements is y=14.
SUFFICIENT.
The correct answer is C.
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Brent@GMATPrepNow
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himu wrote:What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
Target question: What is the value of y?
Statement 1: 3|x^2 - 4| = y - 2
There are many pairs of values that meet this condition. Here are two:
Case a: x = 0 and y = 14
Case b: x = 1 and y = 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |3 - y| = 11
There are EXACTLY TWO solutions to this equation
Case a: y = -8
Case b: y = 14
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 essentially tells us that y MUST be positive. We know this because we have 3|something| = y - 2
In other words, y = 3|something| + 2
Since |something| is always greater than or equal to zero, y must be positive.
Statement 2 tells us that y MUST equal EITHER -8 or 14
Since y must be positive, we can be certain that y = 14
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
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Brent
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