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# 3 lines intersect at point P, so that 6 angles are created. What is th

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3 lines intersect at point P, so that 6 angles are created. What is th  [#permalink]

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19 Jun 2018, 08:31
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65% (hard)

Question Stats:

49% (01:35) correct 51% (01:42) wrong based on 49 sessions

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3 lines intersect at point P, so that 6 angles are created. What is the sum of two randomly selected angles?

(1) The sum of one pair of adjacent angles is 120 degrees.
(2) At least 3 of the 6 angles are 60 degrees each.

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3 lines intersect at point P, so that 6 angles are created. What is th  [#permalink]

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19 Jun 2018, 21:42
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gmatbusters wrote:
3 lines intersect at point P, so that 6 angles are created. What is the sum of two randomly selected angles?

(1) The sum of one pair of adjacent angles is 120 degrees.
(2) At least 3 of the 6 angles are 60 degrees each.

Refer to the attached picture. So we have three angles x, y and z. And 3 pairs of vertically opposite angles also as x, y and z. Here sum of any three adjacent angles would be 180 degrees (since they lie on a line). To answer this question, we should be able to answer the sum of any two adjacent angles. So we should be able to answer the sum of x+y, and that of y+z and also that of x+z.

(1) Lets say x+y=120. This gives z=60 (since x+y+z=180), so two vertically opposite angles z are 60 each. But since we dont know individual values of x and y, we cant say what is x+z or what is y+z. Not sufficient.

(2) At least 3 angles are 60. Lets say z=60. So two angles here z each are 60 each. Now another angle has to be 60. If x=60, then we have x=z=60, and since x+y+z=180, so definitely y will also be = 60. So all angles will be 60 and thus sum of any two randomly selected angles, will be 120 degrees only. Sufficient.

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Re: 3 lines intersect at point P, so that 6 angles are created. What is th  [#permalink]

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01 Dec 2019, 05:07
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Re: 3 lines intersect at point P, so that 6 angles are created. What is th   [#permalink] 01 Dec 2019, 05:07
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