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# In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100

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Math Expert
Joined: 02 Sep 2009
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In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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13 Nov 2017, 00:26
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In ΔPQR above, what is the value of y?

(1) (3/2)x = 120

(2) x + y = 100

[Reveal] Spoiler:
Attachment:

20120326004943723_3577.jpg [ 5.05 KiB | Viewed 673 times ]
[Reveal] Spoiler: OA

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Joined: 25 Sep 2017
Posts: 16
Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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13 Nov 2017, 00:32
It must be D

A: x= 120 * 2/3 => 80

B:2x+y=180
=> x+(x+y) = 180
=> x+100 = 180
=> x = 80
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Joined: 08 Aug 2017
Posts: 11
Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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13 Nov 2017, 02:04
2x+y = 180

st 1 - we will get the value of x.
st 2 - x=100-y
substitute in 2x+y = 180.

therefore, D.
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Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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14 Nov 2017, 00:52
Bunuel wrote:

In ΔPQR above, what is the value of y?

(1) (3/2)x = 120

(2) x + y = 100

[Reveal] Spoiler:
Attachment:
20120326004943723_3577.jpg

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

$$2x+y = 180$$
Since we have 2 variables and 1 equation, D is most likely to be the answer.
Thus we should check each of conditions first.

Condition 1)
$$\frac{3}{2}x = 120$$
$$x = 80$$.
$$2 \cdot 80 + y = 180$$
$$y = 20$$
This is sufficient.

Condition 2)
$$x + y = 100$$
$$2x + y = 180$$
$$x = 80$$
$$y = 20$$
This is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59 % chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Joined: 30 Sep 2017
Posts: 36
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
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Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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14 Nov 2017, 07:28
St1:
3x/2 = 120
x= 80, hence y can be found, since sum of angle of a triangle = 180.
St2
x+y = 100
As sum of angles of a triangle is 180
2x+y =180, solving we can found y .
hence sufficient,
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Joined: 11 Oct 2016
Posts: 90
Location: India
GMAT 1: 610 Q47 V28
Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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14 Nov 2017, 21:28
D

From 1 > A = 80
X+X+Y=180
160+Y=180
Y=20

From 2 > X+Y=100
2X+Y=180
X=80
Hence B = 20
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Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 [#permalink]

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16 Nov 2017, 11:08
Bunuel wrote:

In ΔPQR above, what is the value of y?

(1) (3/2)x = 120

(2) x + y = 100

[Reveal] Spoiler:
Attachment:
20120326004943723_3577.jpg

From statement 1 we can find the value of X=80

Now since the given triangle is an voiceless trialed, so X+X+y=180

Since we know the value of X from statement 1 we can find the value of Y.

Now as per the statesmen 2 ; X+Y=180

Also X+X+Y=180 (Property of a triangle)
so using 2 statement we can find the value of X and Thus Y

Re: In ΔPQR above what is the value of y? (1) (3/2)x = 120 (2) x + y = 100   [#permalink] 16 Nov 2017, 11:08
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