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M70-07

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Math Expert
Joined: 02 Sep 2009
Posts: 59724

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03 Sep 2018, 02:51
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45% (medium)

Question Stats:

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

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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
Joined: 02 Sep 2009
Posts: 59724

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03 Sep 2018, 02:51
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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Joined: 03 Dec 2018
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06 Dec 2018, 10:41
Isn't that the smallest number of adjacent angles? Largest number should be 3 (x + 2x + 3x).
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Joined: 28 Aug 2018
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20 Mar 2019, 15:12
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).
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Joined: 05 Aug 2019
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05 Aug 2019, 12:12
Intern
Joined: 29 Jul 2019
Posts: 4

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20 Sep 2019, 20:57
1
Rashi18 wrote:

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.

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Re: M70-07   [#permalink] 20 Sep 2019, 20:57
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