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# What is the value of y? 1.3|x^2-4|=y-2 2.|3-y|=11 I find

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What is the value of y? 1.3|x^2-4|=y-2 2.|3-y|=11 I find [#permalink]  16 Jun 2011, 21:31
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What is the value of y?
1.3|x^2-4|=y-2
2.|3-y|=11
I find inequality + absolute value (modulus) questions so much troublesome.There's just no end to them.Please help me overcome them.
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Re: inequality! [#permalink]  16 Jun 2011, 22:51
st 1 not sufficient as diff values of x give diff answer to y
solving st 2 we get y = 14 or -8 so st 2 is also insufficient
Now consider both statements together from st2 we 2 values of y
for st1 RHS is positive but when we use y=-8 we get negative so we eliminate it
so we are now left with only one value of y, y=14 so C is the answer
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Re: inequality! [#permalink]  16 Jun 2011, 23:02
AnkitK wrote:
What is the value of y?
1.3|x^2-4|=y-2
2.|3-y|=11
I find inequality + absolute value (modulus) questions so much troublesome.There's just no end to them.Please help me overcome them.

st1. Mod value of X will give you 2 different values for Y. Not sufficicient
St2: Mod Y will give a+ve and -ve value for Y. Insufficient

St1 and 2
From stat 1. we know 3|X^2-4| has to be postive . so we cant have a negative value for Y .
Hence from st 2 take the +ve for Y and solve

thus its C
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Re: inequality! [#permalink]  17 Jun 2011, 00:40
AnkitK wrote:
What is the value of y?
1.3|x^2-4|=y-2
2.|3-y|=11
I find inequality + absolute value (modulus) questions so much troublesome.There's just no end to them.Please help me overcome them.

1. 3|x^2-4|=y-2
y=3|x^2-4|+2
Thus y>=2 because |x^2-4|>=0
Not Sufficient.

2. |3-y|=11
-3+y=11
y=14

OR

3-y=11
y=-8
Not Sufficient.

Combined:
We know y>=2; thus y must be 14.
Sufficient.

Ans: "C"
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MGMAT DS [#permalink]  20 Jun 2011, 05:20
What is the value of y?

(1) 3|x2 – 4| = y – 2

(2) |3 – y| = 11
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Re: MGMAT DS [#permalink]  20 Jun 2011, 05:46
siddhans wrote:
What is the value of y?

(1) 3|x2 – 4| = y – 2

(2) |3 – y| = 11

guess expression in statement 1 is 3|$$x^2$$ – 4| = y – 2

statement 1 - we don't know the value of x and so cannot calculate y. hence insuff

statement 2 - y can be -8 or 14. Again insuff

taking together we know y is either -8 or 14

3|x2 – 4| = y – 2 => |x2 – 4| = (y – 2)/3

we know |x2 – 4| is always positive so y will be 14.

Hence suff

Ans C
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Re: MGMAT DS [#permalink]  20 Jun 2011, 07:27
kp1811 wrote:
siddhans wrote:
What is the value of y?

(1) 3|x2 – 4| = y – 2

(2) |3 – y| = 11

guess expression in statement 1 is 3|$$x^2$$ – 4| = y – 2

statement 1 - we don't know the value of x and so cannot calculate y. hence insuff

statement 2 - y can be -8 or 14. Again insuff

taking together we know y is either -8 or 14

3|x2 – 4| = y – 2 => |x2 – 4| = (y – 2)/3

we know |x2 – 4| is always positive so y will be 14.

Hence suff

Ans C

When you have question with mod how do you deal with them? In other words what is the important of mod in |x^2 -4| ...Does this mean if a question has mod we need to take out mod inorder to solve it further or it means that the values of that expression will always be +ve ...therefore x will always be positive???
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Re: inequality! [#permalink]  20 Jun 2011, 07:44
(1)

you get 2 equations: 3x^2-10=y and -3x^2-14=y

since you don't know x, these are insufficient.

(2) gives you 2 values for y = -8 and 14

again this is insuff.

Together:
plugin the value of y and you get x=root 8

plugin x=root 8 and you get y = 14

hence sufficient.

(c)
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Re: inequality! [#permalink]  20 Jun 2011, 21:46
When you have question with mod how do you deal with them? In other words what is the important of mod in |x^2 -4| ...Does this mean if a question has mod we need to take out mod inorder to solve it further or it means that the values of that expression will always be +ve ...therefore x will always be positive???
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Re: inequality! [#permalink]  20 Jun 2011, 23:31
From statement 1: y is positive
From statement 2: y = -8 or 14
From 1+2) y must be 14
Re: inequality!   [#permalink] 20 Jun 2011, 23:31
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