Is the measure of one of the interior angles of : GMAT Data Sufficiency (DS)
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# Is the measure of one of the interior angles of

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Is the measure of one of the interior angles of [#permalink]

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07 Feb 2012, 17:01
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD

[Reveal] Spoiler:
As the OA is not given, I have gone for answer C and this is how I reached. Please let me know whether I am right.

First, we know that the sum of 4 angles of a quadrilateral is 360 degrees.

Now, considering statement 1

Two angles are right angles. Not sufficient as it doesn't say anything about the other two angles.

Considering Statement 2

Not sufficient as it doesn't say anything about the other two angles.

Combining both statements

We can find the 4th angle as below

90+90+90+x = 360
270+x = 360
x = 90. where x is the 4th angle. So the answer is NO the angle won't be 60 degrees.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Sep 2012, 23:48, edited 3 times in total.
Edited the OA
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07 Feb 2012, 17:07
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

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Re: Is the measure of one of the interior angles of [#permalink]

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07 Feb 2012, 22:25
That question was a tricky sucker.
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17 Sep 2012, 20:35
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.
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17 Sep 2012, 23:50
dineesha wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.

Merging similar topics. please refer to the solution above.

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Re: Is the measure of one of the interior angles of [#permalink]

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06 Oct 2012, 05:30
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.
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Re: Is the measure of one of the interior angles of [#permalink]

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06 Oct 2012, 05:49
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chigiwigi wrote:
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.

Consider the diagram below:
Attachment:

Trapezoid.png [ 1.62 KiB | Viewed 8810 times ]
As you can see we can have a quadrilateral with only two right angles.

Hope it helps.
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Re: Is the measure of one of the interior angles of [#permalink]

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06 Oct 2012, 06:31
ok, makes sense. Thanks.
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Re: Is the measure of one of the interior angles of [#permalink]

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28 Jul 2014, 07:52
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Re: Is the measure of one of the interior angles of [#permalink]

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09 Oct 2015, 09:50
Hello from the GMAT Club BumpBot!

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Re: Is the measure of one of the interior angles of [#permalink]

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25 Dec 2015, 01:07
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Hi bunuel

i believe answer should be C
90-90-120-60

Both A & B will result in only above sequence
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Re: Is the measure of one of the interior angles of [#permalink]

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25 Dec 2015, 04:49
varundixitmro2512 wrote:
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Hi bunuel

i believe answer should be C
90-90-120-60

Both A & B will result in only above sequence

The post you quote has TWO possible cases. Please re-read the solution.
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Re: Is the measure of one of the interior angles of [#permalink]

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18 Jan 2016, 07:43
the source of this question is gmatprep and not kaplan
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Re: Is the measure of one of the interior angles of [#permalink]

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18 Jan 2016, 21:13
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD

In the original condition, there are 4 variables(A,B,C,D) and 1 equation(A+B+C+D=180), which should match with the number of equations. So you need 3 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2)
Attachment:

GCDS enigma123 Is the measure of one of the interior (20160119).jpg [ 1.78 MiB | Viewed 3485 times ]

Just like the above, there are both yes and no, which is not sufficient. Therefore, the answer is E.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Is the measure of one of the interior angles of [#permalink]

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05 Sep 2016, 14:51
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

How were you able to get the 45 and 135 pair. I solved for x + 2x = 180 => x = 60. Not sure how you determined x = 45. Please explain. Thanks!
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Re: Is the measure of one of the interior angles of [#permalink]

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06 Oct 2016, 10:41
Can somebody please try explaining how the possibility of 90-90-45 is arrived at?I could only think of x=60
Re: Is the measure of one of the interior angles of   [#permalink] 06 Oct 2016, 10:41
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