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From the two figures above, which of the following can be determined?

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From the two figures above, which of the following can be determined? [#permalink]

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New post Updated on: 23 May 2017, 13:58
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From the two figures BELOW, which of the following can be determined?
Attachment:
12345FDS.jpg
12345FDS.jpg [ 7.54 KiB | Viewed 426 times ]


I. x = 60˚
II. 7s = 180˚
III. 2s < x

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Source: Nova GMAT

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Originally posted by SajjadAhmad on 23 May 2017, 13:52.
Last edited by Bunuel on 23 May 2017, 13:58, edited 1 time in total.
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Re: From the two figures above, which of the following can be determined? [#permalink]

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New post 23 May 2017, 15:48
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SajjadAhmad wrote:
From the two figures BELOW, which of the following can be determined?
Attachment:
12345FDS.jpg


I. x = 60˚
II. 7s = 180˚
III. 2s < x

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Source: Nova GMAT


From figure (i);
s + 2s + 4s = 180
7s = \(180^{\circ}\) ------ (Option II)

From figure (ii)
x + x + x = 180
3x = 180
x = \(60^{\circ}\) ----------- (Option I)

7s = \(180^{\circ}\)
s = \(\frac{180}{7}\)
2s = \(\frac{180}{7}\) x 2 = \(51.428^{\circ}\) (Which is less than \(60^{\circ}\))
That is; 2s is less than x. (2s < x)------- (Option III)

All 3 options can be determined.
Answer E...
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From the two figures above, which of the following can be determined? [#permalink]

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New post 23 May 2017, 19:25
Figure (1)
Sum of angles of triangle is \(180^{\circ}\)
s+2s+4s=\(180^{\circ}\)
7s= \(180^{\circ}\)
Thus option (II) is determined

7s=180; s=\(\frac{180}{7}\); 2s=\(\frac{180}{7}\)*2 (which is less than \(60^{\circ}\))

Figure (2)
x+x+x=180
3x=180
x=\(\frac{180}{3}\)= \(60^{\circ}\)
Thus option (I) is determined

Also 2s<x
Thus option (III) is determined

Answer: E.

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From the two figures above, which of the following can be determined?   [#permalink] 23 May 2017, 19:25
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From the two figures above, which of the following can be determined?

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