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Absolute value of X

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Source: — Data Sufficiency |
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by hemant_rajput » Tue Jan 29, 2013 8:49 am
nisagl750 wrote:Is |x| = y - z?

1)x+y = z

2)x < 0
I think y-z will equal to |x| iff x = 0. So the real question is asking is y-z = 0

so now take statement 1
can't say

now statement 2
x<0 but y-z is either equal to -x or x. so we know that y-z is not equal to 0

so yes

answer is B
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by ceilidh.erickson » Tue Jan 29, 2013 12:19 pm
With a DS question like this, it's best to start with the easier statement. Statement (2) is clearly easier. x < 0 tells us nothing about y or z, so this is insufficient. We can eliminate B and D.

Statement (1): x + y = z
This means that x = -y + z. With absolute value questions, it's often good to test values.

Scenario 1: y=5, z=4, x=-1. This satisfies the statement: -1 = -5 + 4
If we plug these into the question, |-1| = 5 - 4
True!

Scenario 2: y=4, z=5, x=1. This satisfies the statement: 1 = -4 + 5
Plug these values into the question: |1| = 4 - 5
Not true!

If we can get a "yes" or a "no" answer to the question, it's INSUFFICIENT.

Put the statements together. If x < 0, that eliminates scenario 2. Whenever x is negative, the absolute value of x will have the opposite sign. Therefore, if x = -y + z, then |x| must equal y - z. SUFFICIENT.

The answer is C.
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by nisagl750 » Tue Jan 29, 2013 9:44 pm
ceilidh.erickson wrote:With a DS question like this, it's best to start with the easier statement. Statement (2) is clearly easier. x < 0 tells us nothing about y or z, so this is insufficient. We can eliminate B and D.

Statement (1): x + y = z
This means that x = -y + z. With absolute value questions, it's often good to test values.

Scenario 1: y=5, z=4, x=-1. This satisfies the statement: -1 = -5 + 4
If we plug these into the question, |-1| = 5 - 4
True!

Scenario 2: y=4, z=5, x=1. This satisfies the statement: 1 = -4 + 5
Plug these values into the question: |1| = 4 - 5
Not true!

If we can get a "yes" or a "no" answer to the question, it's INSUFFICIENT.

Put the statements together. If x < 0, that eliminates scenario 2. Whenever x is negative, the absolute value of x will have the opposite sign. Therefore, if x = -y + z, then |x| must equal y - z. SUFFICIENT.

The answer is C.
Thanks,

I have a doubt.

question asks is |x| = y-z?

which means

Is x=y-z (If x is positive)
Is x=z-y (If x is negative)

Statement 1: x+y=z

i.e. x=z-y
does this not show that x=z-y and hence is sufficient?

What am I missing here?
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by ceilidh.erickson » Wed Jan 30, 2013 5:21 am
nisagl750 wrote: question asks is |x| = y-z?

which means

Is x=y-z (If x is positive)
Is x=z-y (If x is negative)

Statement 1: x+y=z

i.e. x=z-y
does this not show that x=z-y and hence is sufficient?

What am I missing here?
Yes, statement 1 shows that x = z - y. But as you said, our question is twofold: is x = y - z if x is positive, or x = z - y if x is negative. If we don't know whether x is positive or negative, we don't know which question we're answering. So x = z - y. If z is negative, we'd get a "yes" answer to the question. If x is positive, though, we'd get a "no" answer to the question.

We need statement 2, which tells us that x is negative, to answer both parts of the question.
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by nisagl750 » Wed Jan 30, 2013 5:32 am
Got it. Thanks!
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