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09 Jun 2025, 09:49
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
99% (00:40) correct
0% (00:00) wrong based on 7 sessions
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In triangle XYZ not given, the measure of angle X equals the measure of angle Y.
Quantity A
The degree measure of angle Z
Quantity B
The degree measure of angle X plus the degree measure of angle Y
Quantity A
The degree measure of angle Z
Quantity B
The degree measure of angle X plus the degree measure of angle Y
11 Jun 2025, 00:32
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Given:
To compare: Angle Z with Angle X + Y
Solution:
Let's place a '?' between the two sides. It could be >, <, or =. We will do the same operation on both sides (just like in any equation or inequality) to simplify this comparison.
Correct Answer: D
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
- Triangle XYZ
- Angle X = angle Y
To compare: Angle Z with Angle X + Y
Solution:
- In any triangle, the sum of the three angles is 180°.
- If we take Angle X = Angle Y = a° (since they are equal), we have:
- 2a + Z = 180°, which gives Z = 180 − 2a.
- We need to compare:
- Quantity A: Z = 180 − 2a
- Quantity B: X + Y = 2a
Let's place a '?' between the two sides. It could be >, <, or =. We will do the same operation on both sides (just like in any equation or inequality) to simplify this comparison.
- 180 − 2a ? 2a
- 180 ? 4a
- 45 ? a
- If a < 45°, then Quantity A > Quantity B. [40-40-100 triangle]
- If a > 45°, then Quantity B > Quantity A. [50-50-80 triangle]
- If a = 45°, then Quantity B = Quantity A. [45-45-90 triangle]
- Since a is not known, the relationship cannot be determined.
Correct Answer: D
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
14 Jun 2025, 06:51
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OE
Because angle X = angle Y, at least two sides of the triangle are equal. You can draw two diagrams with X and Y as the base angles of a triangle. In one diagram, make the triangle tall and narrow so that angle X and angle Y are very large and angle Z is very small. In this case, Quantity B is greater. In the second diagram, make the triangle short and wide so that angle Z is much larger than angle X and angle Y. In this case, Quantity A is greater. Because more than one relationship between the quantities is possible, the correct answer is (D).
GMAT-Club-Forum-buwe7f6t.png [ 29.11 KiB | Viewed 522 times ]
Because angle X = angle Y, at least two sides of the triangle are equal. You can draw two diagrams with X and Y as the base angles of a triangle. In one diagram, make the triangle tall and narrow so that angle X and angle Y are very large and angle Z is very small. In this case, Quantity B is greater. In the second diagram, make the triangle short and wide so that angle Z is much larger than angle X and angle Y. In this case, Quantity A is greater. Because more than one relationship between the quantities is possible, the correct answer is (D).
Attachment:
GMAT-Club-Forum-buwe7f6t.png [ 29.11 KiB | Viewed 522 times ]
