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 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 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 select the most appropriate answer.
C, I, L, N, R, and Y live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on, till the topmost floor is numbered 6. Who among them lives immediately above Y?
(I) Only four people live between N and I. C lives immediately below I.
(II) Only one person lives between C and R. Y lives immediately above N.P and Q are children of S. Who is the father of P? To answer this question which of the statements (1) and (2) is/are necessary?
(1) R is the brother of P and the son of T.
(2) U is the mother of Q.Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question.
Question:
Rajesh's salary is Rs. 12,500. What is Arvind's salary?
Statements
I. Arvind gets $\frac{3}{5}$th of the total salary of his and Rajesh'
II. Two-thirds of Arvind's salary is equal to the average salary of both.
