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# In the triangle above, x and y are integers. If 30 < y < 40, what is

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Posts: 55274
In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 00:37
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In the triangle above, x and y are integers. If 30 < y < 40, what is one possible value of x?

(A) 95
(B) 100
(C) 105
(D) 110
(D) 115

Attachment:

2017-09-01_1133.png [ 11.44 KiB | Viewed 992 times ]

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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 02:13
1
Bunuel wrote:

In the triangle above, x and y are integers. If 35 < y < 40, what is one possible value of x?

(A) 95
(B) 100
(C) 105
(D) 110
(D) 115

Attachment:
2017-09-01_1133.png

Hi Bunuel,

If the value of y is between 35 and 40, then neither of the answer options are possible
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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 02:21
pushpitkc wrote:
Bunuel wrote:

In the triangle above, x and y are integers. If 35 < y < 40, what is one possible value of x?

(A) 95
(B) 100
(C) 105
(D) 110
(D) 115

Attachment:
2017-09-01_1133.png

Hi Bunuel,

If the value of y is between 35 and 40, then neither of the answer options are possible

Yes. It should be "If 30 < y < 40". Edited. Thank you.
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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 02:28
If the value is between 30 and 40, y could be 35.

Since, the sum of three angles in the triangle is 180,
and x + 2y = 180, the third angle can be 180 - (35*2) = 110(Option D)
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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 03:37
The value will be between 35 and 40..and x + 2y =180
We get max value of y as 39 and minimum value as 36..so the equation will be as follows
x + 2 X 39= 180
Gives x= 102
Similarly
X + 2 X 36= 180
Gives x = 108
It implies
X will be between 102~108

Correct ans = 105
Option C

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In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 11:03
The sum of angles of a triangle is 180, so x + 2y = 180
Then taking into account that y<40 we have x > 100 and we eliminate A and B

From the formula x + 2y = 180 we can have y = 90 - x/2
In the question it is mentioned that x is integer, so x must be even. So the answer is 110 (D)
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In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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01 Sep 2017, 16:22
Bunuel wrote:

In the triangle above, x and y are integers. If 30 < y < 40, what is one possible value of x?

(A) 95
(B) 100
(C) 105
(D) 110
(D) 115

Attachment:
2017-09-01_1133.png

Working from answer choices sometimes sparks the right thought.

Subtract the answer choice (x) from 180, and then divide by 2.

I didn't write all the algebra down but you could.*:

180 - 105 = 95, which, divided by 2, does not yield an integer, which y must be. All answers with odd numbers are out.

That leaves B and D. It takes seconds to calculate if you don't happen to see that if 2y cannot be greater than 80, x cannot be smaller than 100. B gives

2y = 80. y = 40. Not permissible.

By POE, if you're brave, choose D and move on. Or

Answer D) 110: (180 - 110) = 70, y = 35. Correct

*x + 2y = 180
2y = 180 - x
y = $$\frac{180 - x}{2}$$
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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is  [#permalink]

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07 Sep 2017, 07:12
Bunuel wrote:

In the triangle above, x and y are integers. If 30 < y < 40, what is one possible value of x?

(A) 95
(B) 100
(C) 105
(D) 110
(D) 115

Attachment:
2017-09-01_1133.png

We see that x = 180 - 2y and y = (180 - x)/2.

Since 30 < y < 40, 60 < 2y < 80. Thus, the “minimum” value of x is 180 - 80 = 100 and the “maximum” value of x is 180 - 60 = 120. In other words, 100 < x < 120.

We see that three answer choices, C, D, and E, satisfy this inequality. However, let’s say x = 105; then y = (180 - 105)/2 = 75/2 = 37.5 would not be an integer. The same can be said when x = 115. In other words, if x is odd, then y will not be integer. Thus, x must be even. So x must be 110. In fact, when x = 110, y = (180 - 110)/2 = 70/2 = 35, which is an integer.

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Re: In the triangle above, x and y are integers. If 30 < y < 40, what is   [#permalink] 07 Sep 2017, 07:12
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