BTG Community, Please help me clarify the solution to this problem.
Is |x| = y-z?
(1) x + y = z
(2) x < 0
Solution:
I got so far:
Question Rephrase:
Is x = y -z OR Is x = z -y ? (Solving the absolute value - 2 Possibilitues)
Statement1:
x+y=z
=> Case1: Is x = y-z?
Using x+y=z to answer the above
I got y=z?
NO
=> Case2: Is x = z -y?
Using x+y=z
I got 0=0
YES
Yes & NO == Insufficient
Statement2: x < 0
If x < 0
Does not tell me much about y and z. Insufficient.
Statement1 & 2 Together
If x<0 and y=z 0 </ 0 NO. Sufficient. (I have a jambled logic here)
Please help with some details.
Absolute Inequality
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- iwillsurvive101
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Hi,iwillsurvive101 wrote:BTG Community, Please help me clarify the solution to this problem.
Is |x| = y-z?
(1) x + y = z
(2) x < 0
Solution:
I got so far:
Question Rephrase:
Is x = y -z OR Is x = z -y ? (Solving the absolute value - 2 Possibilitues)
I just want to check if you know when is x = y - z and when is x = z - y?
Well, this comes from the definition of modulus of which says that:
|x| = x when x > 0,
|x| = - x when x < 0
So,
x = y - z when x > 0 and
x = z - y when x < 0.
Let me take over from you from the part where you tried combining the statements and got confused.
When you combine the two statements we know that x < 0 and x = z - y.
And, the question which was 'Is |x| = y - z?' before simplifies to 'Is x = z - y?' now because x < 0.
So, Is x = z - y?
YES, Statement(1) tells us exactly that.
SUFFICIENT
Please let me know if this makes sense.
Aneesh Bangia
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Since |x| = y - z, so y - z ≥ 0
We have to find if y - z ≥ 0 and if y - z = |x|
(1) x + y = z
-x = y - z
If x > 0, then y - z = negative
If x ≤ 0, then y - z = positive
No definite answer; NOT sufficient.
(2) x < 0 is definitely NOT sufficient as we have to find if y - z is equal to |x| or not.
Combining (1) and (2), we get the answer to the question; SUFFICIENT.
The correct answer is C.
We have to find if y - z ≥ 0 and if y - z = |x|
(1) x + y = z
-x = y - z
If x > 0, then y - z = negative
If x ≤ 0, then y - z = positive
No definite answer; NOT sufficient.
(2) x < 0 is definitely NOT sufficient as we have to find if y - z is equal to |x| or not.
Combining (1) and (2), we get the answer to the question; SUFFICIENT.
The correct answer is C.
Anurag Mairal, Ph.D., MBA
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