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Source: — Data Sufficiency |
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by niketdoshi123 » Fri Apr 13, 2012 10:34 pm
considering statement 1
taking x = 0
|0| + |0-1| = 1 (yes)
taking x = 2
|2| + |2-1| = 3 (no)
so statement 1 is insufficient

considering statement 2
taking x = 1
|1| + |1-1| = 1 (yes)
taking x = -1
|-1| + |-1-1| =3 (no)
so statement 2 is insufficient

considering both the statements together
taking any value of x in the range, 0<=x<=1,
will satisfy the equation.

The correct answer is C
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by killer1387 » Fri Apr 13, 2012 10:34 pm
i am also getting C
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by Shalabh's Quants » Sat Apr 14, 2012 5:10 am
sam2304 wrote:Is |x| + |x-1| = 1 ?
1. x >= 0
2. x <= 1

[spoiler]No OA for this question. I came up with C. Is it right ?[/spoiler]
Stat. 1...

Set of x will be x = {0, 1, 2, 3,.....}; It will also include fractions/real nos. too.

A Can't be an answer as for x = 0 or 1, we get yes and for other values, we get NO.Not Suff.

Stat. 2...

Set of x will be x = {.....-3, -2, -1, 0, 1}; It will also include fractions/real nos. too.

B Can't be an answer as for x = 0 or 1, we get yes and for other values, we get NO.Not Suff.

Combining 2 statements.

Since from stat. 1, we get x = {0, 1, 2, 3,.....} & from stat. 1, we get x = {.....-3, -2, -1, 0, 1}

So we need to check if x lies between 0 & 1, do we get the answer?

Lets try for some random values for x = 0, 1/3, 1/2, 9/10, 1... In each case, we get result as |x| + |x-1| = 1. Ans. C.
Shalabh Jain,
e-GMAT Instructor
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