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|Equations| with |A|bsolute value

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|Equations| with |A|bsolute value

by aditya.j » Wed Apr 11, 2012 7:00 pm
Is 5|x| = y - 2z?

5x + y = 2z
x < 0

(A)

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B)

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C)

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D)

EACH statement ALONE is sufficient.

(E)

Statements (1) and (2) TOGETHER are NOT sufficient.

OA

C

[spoiler] Whats the easiest way to solve this sum?..[/spoiler]
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Source: — Data Sufficiency |
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by rijul007 » Wed Apr 11, 2012 8:49 pm
aditya.j wrote:Is 5|x| = y - 2z?

5x + y = 2z
x < 0

(A)

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B)

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C)

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D)

EACH statement ALONE is sufficient.

(E)

Statements (1) and (2) TOGETHER are NOT sufficient.

OA

C

[spoiler] Whats the easiest way to solve this sum?..[/spoiler]

Statement 1
5x + y = 2z
5x = 2z-y

If x is positive
5|x| = 2z-y
If x is negative
5|x| = y-2z
Not sufficient


Statement 2
x<0

Clearly, not sufficient. You need more info


Combining statement 1 and 2
5|x| = y-2z?
Yes


Sufficient


Option C
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by GMATGuruNY » Wed Apr 11, 2012 10:40 pm
aditya.j wrote:Is 5|x| = y - 2z?

5x + y = 2z
x < 0

[spoiler] Whats the easiest way to solve this sum?..[/spoiler]
Statement 1: 5x + y = 2z
5x = 2z-y

If x>0, then 2z-y>0.
Thus:
5|x| = 2z-y.

If x<0, then 2x-y<0.
Since 5|x| cannot be negative:
5|x| = -(2z-y)
5|x| = y-2z.

Since it's possible that 5|x| = 2z-y or that 5|x| = y-2z, INSUFFICIENT.

Statement 2: x<0
No way to determine whether 5|x| = y-2z.
INSUFFICIENT.

Statements 1 and 2 combined:
When x<0 in statement 1, 5|x| = y-2z.
SUFFICIENT.

The correct answer is C.
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by aditya.j » Thu Apr 12, 2012 7:08 pm
Hey Mitch,

Thanks a lot for the reply!

For some reason, i am finding it difficult to understand this sum. For eg you mentioned:

If x<0, then 2x-y<0.

Since 5|x| cannot be negative:

5|x| = -(2z-y)
5|x| = y-2z.

Isn't |x| always positive, ie. the distance from 0, and if it's positive then if we equate it with another term, isn't that going to be positive also?

In addition even if we plug terms:

5 |+2| = 2(8) - 6 //(5 |X| = 2Z - Y)----------------a

Now if we plug in x<0

5 |-2| = isn't this going to be the same as---a? (because the Mod term becomes positive)

I have understood that if x>0 then 5x = 2z-y and if x<0 then 5x =y-2z :

But what happens when we make 5x =y-2z into 5 |x| = y- 2z ?


Any help would be appreciated!


Regards,

aJ
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by GMATGuruNY » Thu Apr 12, 2012 7:44 pm
aditya.j wrote:Hey Mitch,

Thanks a lot for the reply!

For some reason, i am finding it difficult to understand this sum. For eg you mentioned:

If x<0, then 2x-y<0.

Since 5|x| cannot be negative:

5|x| = -(2z-y)
5|x| = y-2z.

Isn't |x| always positive, ie. the distance from 0, and if it's positive then if we equate it with another term, isn't that going to be positive also?

In addition even if we plug terms:

5 |+2| = 2(8) - 6 //(5 |X| = 2Z - Y)----------------a

Now if we plug in x<0

5 |-2| = isn't this going to be the same as---a? (because the Mod term becomes positive)

I have understood that if x>0 then 5x = 2z-y and if x<0 then 5x =y-2z :

But what happens when we make 5x =y-2z into 5 |x| = y- 2z ?


Any help would be appreciated!


Regards,

aJ
Statement 2: x<0
Thus:
|x| = -x.
5|x| = -5x.

Statement 1: 5x + y = 2z
Thus:
5x = 2z-y
-5x = y-2z

Statements 1 and 2 combined:
Substituting -5x = y-2z into 5|x| = -5x, we get:
5|x| = y-2z.
SUFFICIENT.
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by icemanKK » Thu Apr 12, 2012 11:43 pm
I believe we can also solve the problem in the following method (but need suggestions) :

From the properties of Absolute value, we know that :
|x| = (y-2z)/5 -----> eq 1
and
|x| = -(y-2z)/5 -----> eq 2

So the above 2 equations are the ones that we should set out to prove using the statements in the question.

Since this is an absolute value equation problem 'x' can take 2 values - one > 0 and one < 0

Now, coming to the statements :

Statement 1 :

Only states equation 2 and does not indicate the side on which 'x' lies on.

Statement 2 :

Only states the possible ranges of values of 'x' and nothing in relation to what we need to prove.

Combining the statements - we can prove eq 2 (stated above)

C

However, I am not sure whether not proving eq 1 (stated above) is OK by this question .....Is this ok in a data sufficiency question ???
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