Direction:- Below question is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data your knowledge of Mathematics to choose between the possible answers. ΔPQR has anangle equal to 90°. What is the measure of ∠PQR? I. ∠QPR is 50° and ∠QRP is smaller than ∠QPR. II. ∠QRP = ∠QPR

Direction:- Below question is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data your knowledge of Mathematics to choose between the possible answers.

ΔPQR has anangle equal to 90°. What is the measure of ∠PQR?

I. ∠QPR is 50° and ∠QRP is smaller than ∠QPR.

II. ∠QRP = ∠QPR

A The statement I alone is sufficient to answer the question but the statement II alone is notsufficient

B The statement II alone is sufficient to answer the question but the statement I alone is notsufficient

C Both statements I and II together are needed to answer the question

D Either statement I alone or statement II alone is sufficient to answer the question

E You cannot get the answer from the statement I and II together but need even more data

Solution

Correct Answer: Option D

In a triangle, sum of angles = 180°

From statement I,

∠QPR is 50° and ∠QRP is smaller than ∠QPR

Since ∠QPR is 50°, sum of remaining two angles = 180° – 50° = 130°

Since one of the remaining angles is 90° , the third angle must be: 130° – 90° = 40°

Since ∠QRP is smaller than ∠QPR, ∠QRP cannot be 90°.

∴ ∠PQR must be 90°.

∴ The statement I alone is sufficient to answer the question

From statement II,

Given: ∠QRP = ∠QPR

Since both angles except ∠PQR are equal therefore none of them can be 90°, because sum of all three angles must be equal to 180°

Thus, ∠PQR is 90°

∴ The statement II alone is sufficient to answer the question

Solution

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