A question and a set of statements are given. Find which of the given statements is/are sufficient to answer the given question. Question :
Find x° and y°.
Statements :
I. P° = 125° and Q° = 85°.
II. P° > Q°.
In the figure, the two horizontal lines are parallel and the slanting lines act as transversals. Therefore, angle relationships such as supplementary angles can be used.
Using Statement I:
Statement I gives:
p = 125° and Q = 85°
From the left transversal, angles p and y are supplementary.
So,
y + p = 180°
Substituting the value of p:
y + 125° = 180°
Therefore,
y = 180° - 125° = 55°
From the right transversal, angles x and Q are supplementary.
So,
x + Q = 180°
Substituting the value of Q:
x + 85° = 180°
Therefore,
x = 180° - 85° = 95°
Hence, Statement I gives exact values of both x and y. So, Statement I alone is sufficient.
Using Statement II:
Statement II only says:
p > Q
This only gives a comparison between p and Q. It does not give the exact value of either angle. Therefore, exact values of x and y cannot be found from Statement II alone.
Conclusion:
Statement I alone is sufficient to find x and y, while Statement II alone is not sufficient.
Therefore, the correct answer is — Only Statement I is sufficient.
Important Questions from Data Sufficiency (Notes)
In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.
Q. Five students – Isha, Kavita, Meenal, Nisha, and Priti – scored different marks.Who scored the second highest?
(I) Meenal scored more than Isha but less than Nisha.
(II) Priti scored more than Meenal but less than Nisha.- In light of the statements I and II choose the most appropriate option.
If a group comprises of five persons A, B, C, D and E, then how many persons are taller than E?
Statement (I) A is taller than B and B is shorter than A and E only.
Statement (II) C is shorter than A and A is shorter than E. - In light of the statements I and II choose the most appropriate option.
Eight boxes- A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I) Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II) Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R. - A question along with a set of statements is given. Find which of the given statements is/are sufficient to answer the given question.
Question:
Find the perimeter of a triangle given that:
Statements:
I. Area of the triangle is 24 sq. units.
II. Height of the triangle is 4 units. A question along with a set of statements is given below. We have to find which of the given statements is/are sufficient to answer the given question.
Question : Find the area of the triangle PQR.
Statements :
I. PQ = 5 m., PR = 5 m.
II. Length of PO is 4 m.
