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# In the figure shown, if ABCD is a parallelogram, what is the value of

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
In the figure shown, if ABCD is a parallelogram, what is the value of  [#permalink]

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13 Apr 2018, 00:56
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Difficulty:

5% (low)

Question Stats:

95% (01:00) correct 5% (01:14) wrong based on 49 sessions

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In the figure shown, if ABCD is a parallelogram, what is the value of y?

(1) w = 125
(2) z = 55

Attachment:

2018-04-13_1252.png [ 8.57 KiB | Viewed 973 times ]

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Re: In the figure shown, if ABCD is a parallelogram, what is the value of  [#permalink]

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13 Apr 2018, 07:33
St 1 w=125 so x = 55
Adjecent angle of parelle. Are supplimentry

X+5y= 180
Y= 25

St2 z=55 so angle B = 125
We know opposite angle of parelle. Are eqaul so 5y = 125
Y= 25
Sufficient

Ans = D

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Re: In the figure shown, if ABCD is a parallelogram, what is the value of  [#permalink]

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16 Apr 2018, 06:40
Bunuel wrote:

In the figure shown, if ABCD is a parallelogram, what is the value of y?

(1) w = 125
(2) z = 55

Attachment:
2018-04-13_1252.png

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.

We have the following equations from the figure.
x + w = 180
x + 5y = 180
x = z

Since we have 4 variables and 3 equations, D is most likely to be the answer.

1) w = 125
x = 55
5y = 180 - x = 180 - 55 = 125
y = 25
The condition 1) is sufficient.

2) z = 55
x = 55
5y = 180 - x = 180 - 55 = 125
y = 25
The condition 2) 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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Re: In the figure shown, if ABCD is a parallelogram, what is the value of  [#permalink]

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28 Apr 2018, 04:57
Two important properties of parallelogram is utilized here

Opposite angles of parallelogram are equal.

Both these properties are used to find angle y

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Re: In the figure shown, if ABCD is a parallelogram, what is the value of &nbs [#permalink] 28 Apr 2018, 04:57
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