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In the figure above, ΔPQR has angle measures as shown. Is x < y? – OG 2020 Question #289 with Solution

A 2 min read

 

 

 

In the figure above, ΔPQR has angle measures as shown. Is x < y?

  1. PQ = QR
  2. PR > QR
Source OG 2020
Type Data Sufficiency
Topic Geometry
Sub-Topic Triangles
Difficulty Medium

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

  • The figure of a triangle PQR, where angle P = x°, angle Q = y° and angle R = 58°

From this information, we need to determine

  • If x < y or not.

As PQR is a triangle, the sum of the three angles must be equal to 180°

  • x° + y° + 58° = 180°
  • Or, x° + y° = 180° – 58° = 122°

Hence, to determine whether x < y, we need to know the value of either x or y.

With this information, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

As per the information given in statement 1, PQ = QR.

  • Therefore, we can say angle QPR = angle QRP
  • Or, x° = 58°

As we can determine the value of x, we can also determine the value of y and find out whether x < y or not.

Hence, statement 1 is sufficient to answer the question.

 

Step 4: Analyse Statement 2

As per the information given in statement 2, PR > QR.

  • Therefore, the angle opposite to PR > the angle opposite to QR
  • Or, y > x

As we can determine whether x < y or not, statement 2 is sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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