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Retired Moderator
Joined: 16 Apr 2020
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Integers x, y and z are interior angles of a triangle ABC.
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27 Sep 2021, 08:58
27 Sep 2021, 08:58
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Question Stats:
29% (01:42) correct
70% (01:58) wrong based on 27 sessions
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Integers x, y and z are interior angles of a triangle ABC.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Total number of possible values of x – y + z, which are less than zero |
89 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: Integers x, y and z are interior angles of a triangle ABC.
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07 Oct 2021, 00:34
07 Oct 2021, 00:34
3
Explanation:
In a traingle, sum of all interior angles is 180°
i.e. x + y + z = 180°
x + z = 180° - y
Now we have been given that, x – y + z < 0
i.e. 180° - y - y < 0
180° < 2y
90° < y
In order to form a triangle with interior angles (integers), the minimum value of x and z is 1°
i.e. 1° + y + 1° = 180°
y (max.) = 178°
Therefore, 91° ≤ y ≤ 178°
Number of possible values (inclusive) = 178 - 91 + 1 = 88
Col. A: 88
Col. B: 89
Hence, option B
In a traingle, sum of all interior angles is 180°
i.e. x + y + z = 180°
x + z = 180° - y
Now we have been given that, x – y + z < 0
i.e. 180° - y - y < 0
180° < 2y
90° < y
In order to form a triangle with interior angles (integers), the minimum value of x and z is 1°
i.e. 1° + y + 1° = 180°
y (max.) = 178°
Therefore, 91° ≤ y ≤ 178°
Number of possible values (inclusive) = 178 - 91 + 1 = 88
Col. A: 88
Col. B: 89
Hence, option B
General Discussion
Re: Integers x, y and z are interior angles of a triangle ABC.
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28 Sep 2021, 07:20
28 Sep 2021, 07:20
1
KarunMendiratta wrote:
Integers x, y and z are interior angles of a triangle ABC.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Total number of possible values of x – y + z, which are less than zero |
89 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
In a triangle, sum of any 2 angle is larger than the third one.
So x + z > y
=> x+z -y > 0.
Therefore Quantity B is greater.
