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In triangle ABD above, if 25 < y < 45, which of the
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20 Aug 2020, 10:33
20 Aug 2020, 10:33
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65% (01:05) correct
35% (01:13) wrong based on 20 sessions
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GRE which of the following are possible values for.png [ 6.69 KiB | Viewed 1868 times ]
In \(\triangle ABD\) above, if \(25 < y < 45\), which of the following are possible values for z?
Indicate all such values.
A. 25
B. 30
C. 35
D. 40
E. 45
F. 50
G. 55
H. 60
Re: In triangle ABD above, if 25 < y < 45, which of the
[#permalink]
20 Aug 2020, 12:49
20 Aug 2020, 12:49
1
ABC is a triangle so we know the sum of all the interior angles will be 180°. Denoting angles by ^ we have z + y + ^ACB=180.
Then ^BCD is a flat angle so we also know ^ACD + ^ACB=180 that is 80 + ^ACB = 180. So one info we have is that angle ^ACB=100°
Then we substitute and have z+y=80 so z=80-y.
But we know 25 < y < 45
Multiplying all sides by -1 we have -45 < -y < -25
Adding 80 we now have 80-45 < z = 80 - y < 80 - 25
Thus 35 < z < 55 and we can tick boxes D, E and F.
Then ^BCD is a flat angle so we also know ^ACD + ^ACB=180 that is 80 + ^ACB = 180. So one info we have is that angle ^ACB=100°
Then we substitute and have z+y=80 so z=80-y.
But we know 25 < y < 45
Multiplying all sides by -1 we have -45 < -y < -25
Adding 80 we now have 80-45 < z = 80 - y < 80 - 25
Thus 35 < z < 55 and we can tick boxes D, E and F.
gmatclubot
Re: In triangle ABD above, if 25 < y < 45, which of the [#permalink]
20 Aug 2020, 12:49
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