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Math Expert V
Joined: 02 Sep 2009
Posts: 59724

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Difficulty:   45% (medium)

Question Stats: 62% (01:51) correct 38% (02:09) wrong based on 13 sessions

### HideShow timer Statistics In the figure above, what is the largest number of adjacent angles that can be combined to create a sum of 120 degrees?

A. 1
B. 2
C. 3
D. 4
E. 5

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Math Expert V
Joined: 02 Sep 2009
Posts: 59724

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1
Official Solution: In the figure above, what is the largest number of adjacent angles that can be combined to create a sum of 120 degrees?

A. 1
B. 2
C. 3
D. 4
E. 5

We’ll go for LOGICAL because there is a simple logic behind the question.

All the angles together make up a circle, which equals 360 degrees: $$24x = 360$$. Since we are looking for 120 degrees, we can divide the equation by 3 and arrive at $$8x = 120$$. There aren’t any adjacent angles that can be added to up to create 8, except the angle $$8x$$ itself. So the largest number of adjacent angles is 1.

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Intern  Joined: 03 Dec 2018
Posts: 1

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Isn't that the smallest number of adjacent angles? Largest number should be 3 (x + 2x + 3x).
Intern  Joined: 28 Aug 2018
Posts: 1

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Those would be less than 120 degrees (as x=15 --> x+2x=3x=6*15=90). The question asks for a sum of exactly 120 degrees (i.e. only 8x works).
Intern  Joined: 05 Aug 2019
Posts: 1

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i still don't understand the question, can someone please help me with this Intern  B
Joined: 29 Jul 2019
Posts: 4

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1
Rashi18 wrote:
i still don't understand the question, can someone please help me with this The question asks for the largest number of "adjacent" angles that'll help us get extra my 120°.

The angles here are x, 2x, 3x, 4x, 6x, and 8x (sequentially)

If we are to choose any adjacent angles they have to be next to each other in the above sequence. (eg. X, 2x, and 3x are adjacent but x, 3x and 4x are not all adjacent)

Now, we are supposed to tell how many such angles (maximum) can make up 120°.

From the official solution, I believe you understand how 24x = 360° and hence 8x = 120°.

So can you form a sum of 8x from the sequential list that we prepared (x, 2x, 3x, 4x, 6x and 8x) such that all such angles are adjacent.

No. You cannot. Try it out.

X+2X+4x= 8x but these angles aren't adjacent.

Hence, we find only 8x (one angle) that forms EXACTLY 120°. Hence the answer is 1.

Posted from my mobile device Re: M70-07   [#permalink] 20 Sep 2019, 20:57
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# M70-07

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