Directions (1-5): Each question below is followed by two statements A and B. You are to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.
Give answer (a) if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
Give answer (b) if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.
Give answer (c) if both statements A and B together are needed to answer the question.
Give answer (d) if either the statements A alone or statement B alone is sufficient to answer the question
Give answer (e) if you cannot get the answer from the statements A and B together, but need even more data.
Q1. Triangle ABC has angle BAC equal to 90°. What is the measure of the angle ABC?
A. The angle ACB is 35°.
B. The angle CBA is 55°.
Q2. X, Y and Z are three consecutive even numbers (not necessarily in this order). What is the sum of these numbers?
A. The difference between X and Z is 4.
B. One-third of Y is 14.
Q3. What is the salary of P, in a group of P, Q, R, S, T and U, whose average salary is Rs. 35,000?
A. Total of the salary of Q and S is Rs. 54000.
B. Total of the salary of T and U is Rs. 58000.
Q4. What is the rate p.c.p.a. on an amount of Rs. 6,000 deposited in a Bank?
A. The simple interest for four years is Rs. 3600.
B. The difference between the simple interest and compound interest is Rs. 894.0375.
Q5. What is the number?
A. 20% of that number is one fifth of that number.
B. 5/6th of that number is less than that number by 15.
Directions (6-10): Each of the questions consists of a question followed by three statements. You have to study the questions and the statements and decide which of the statements(s) is/are necessary to answer the question.
Q6. What is the area of the hall?
I. Material cost of flooring per sq metre is Rs. 250
II. labour cost of flooring the hall is Rs. 3,500
III. Total cost of flooring the hall is Rs. 14,500
(a) I and II only
(b) II and III only
(c) All I, II and III
(d) Any two of the three
(e) None of these
Q7. What was the percentage of discount offered?
I. Profit earned by selling the article for Rs. 252 after giving discount was Rs. 52.
II. Had there been no discount the profit earned would have been Rs. 80
III. Had there been no discount the profit earned would have been 40%.
(a) I and II only
(b) II and either I or III only
(c) I and III only
(d) I and either II or III only
(e) None of these
Q8. What is the speed of the train?
I. The train crosses a signal pole in 13 sec.
II. The train crosses a platform of length 250 m in 27 seconds.
III. The train crosses another train running in the same direction in 32 seconds.
(a) I and II only
(b) I and III only
(c) II and III only
(d) Any two of the three
(e) None of these
Q9. What is the population of State ‘A’?
I. After increasing the population of State A by 15% it becomes 1.61 lakhs
II. Ratio of population of State A to that of State B is 7 : 8 respectively
III. Population of State B is 1.6 lakhs
(a) I only
(b) II and III only
(c) I and II only
(d) Either only I or II and III
(e) All I, II and III
Q10. How many workers are required for completing the construction work in 10 days?
I. 20% of the work can be completed by 8 workers in 8 days
II. 20 workers can complete the work in 16 days
III. One eighth of the work can be completed by 8 workers in 5 days
(a) I and II only
(b) II and III only
(c) I only
(d) III only
(e) Any one of three
Directions (11-15): In the following questions two equations numbered I and II are given. You have to solve both the equations and–
Give answer (a) if x>y
Give answer (b) if x≥y
Give answer (c) if x<y
Give answer (d) if x≤y
Give answer (e) if x = y or the relationship cannot be established.
Solution:
S1. Ans.(d)
Sol.
From statement A
∠ABC = 180 – (∠BAC + ∠ACB)
= 180 – (90+ 35) = 55°
From statement B, ∠ABC = 55°
S2. Ans.(c)
Sol.
A. x-z=4 or z-x=4
B. y/3=14⇒y=42
So, no. are 40, 42, 44
So, both statements together are required to answer the question
S3. Ans.(e)
Sol.
P + Q + R+ S +T +U = 6 × 35000 = 210000
A. Q +S = 54000
B. T + U = 58000
P + R = 210000 – (54000 + 58000)
= 210000 – 112000
=98000
We can not find salary of P from given data
S5. Ans.(b)
Sol.
A. Let no. is x
x ×20% =x/5
B. 5x/6=x-15
⇒ x=90
So, statement A is insufficient whereas statement B alone is sufficient to answer the question.
S6. Ans.(c)
Sol.
Let area = x m²
Then,
250x + 3500 = 14500
By this equation, we can find x
So all three statements are required
S7. Ans.(d)
Sol.
I. S.P. = 252
Profit = 52
C.P. = 252 – 52 = 200
II. Profit = 80 (when no discount)
So, M.P =200+80=280
III. When discount = 0
Profit = 40%
Profit =200×40/100=80
So, we can calculate M.P. and consequently discount percentage.
So, statement I with either II or III is necessary to answer the question
So from above equations, we can see statement I & II are sufficient to find out speed of train.
S9. Ans.(d)
Sol.
I. A ×115/100=1.61 lakh
II. A∶B=7∶8
III. B=1.6 lakh
So, we can see, population of A can be find out either only by statement I or statement II & III together.
S10. Ans.(e)
Sol.
I. n×10=8×8×5
II. n×10=20×16
III. n×10=8×5×8
So, from any of the three statements, we can get the answer.
S11. Ans.(e)
Sol.
I.
x^2-1200=244
x^2=1444
x= ±38
II. y+122=159
y=159-122=37
∴ No relation can be established between x & y
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