Directions (1-15): Each of the questions given below is followed by two statements numbered I and II. Decide whether the data provided in the statements are sufficient to answer the questions.
Given answer
(a) If the statement I alone is sufficient to provide the answer
(b) If the statement II alone is sufficient to provide the answer
(c) If both statements are required to provide the answer
(d) If neither statement I nor II is sufficient to provide the answer
(e) If either statement I or II is sufficient to provide the answer
Q1. Amongst five students A, B, C, D and E who got the maximum marks?
I. D got more than A and C.
II. B got less than E but more than D.
Q2. A toy was initially listed at a price to give the shopkeeper 20% profit of the wholesale cost. What is the wholesale cost?
I. After reducing the listed price by 10%, the toy sold for a profit of Rs. 10.
II. The toy sold for Rs. 50.
Q3. Is a < b?
I. a^2-4a + 4 = 0
II. b^2-6b + 9 = 16
Q4. What is the value of a two-digit number?
I. The sum of the two digits is 6.
II. The difference of the two digits is 2.
Q5. What percentage rate of simple interest per annum did Ashok pay to Sudhir?
I. Ashok borrowed Rs. 8000 from Sudhir for 4 year.
II. Ashok returned Rs. 8800 to Sudhir at the end of 2 year and settled the loan.
Q6. What is the length of the train which crosses a stationary man in 5 s?
I. The train crosses a 150 m long platform in 20s.
II. The speed of the train is 36 km/h.
Q7. Find the ratio of the number of boys to that of girls in a school.
I. Number of boys is 30 more than girls.
II. Number of girls is 75% of the number of boys.
Q8. A shopkeeper sells some articles, making profit of 20% on the cost price. Find the amount of profit.
I. Cost price of the article is Rs. 1200.
II. Selling price of the article is Rs. 240 more than the cost price.
Q9. Is the quadrilateral ABCD cyclic?
I. AC = BD
II. ÐBAD + ÐBCD = 180°
Q10. Is the ABC right angled?
I. ÐA = 2ÐB
II. ÐB = 2/3
Q11. Four circles of equal radii are inscribed in a square touching each other. What is the area covered by the four circles?
I. The perimeter of the square is 32 cm.
II. The ratio of sums of areas of four circles to that of the square is 3 : 4.
Q12. What is the cost of painting a room which is of the form of a cube?
I. The base area of the room is 144 sq. ft.
II. The room has one door is size 6’ × 4’ and has no window.
Q13. If a, b and c are positive integers. Is the product of abc even?
I. a + b + c is odd
II. a + c is odd
Q14. Find the value of x.
I. y = 120°
II. z = 87°
Q15. x, y and z are integers. Is x an odd number?
I. An odd number is obtained when x is divided by 5.
II. (x + y) is an odd number.
Solutions
S1. Ans.(c)
Sol. Statement I, D > A and D > C but there is no information about other students. So, statement I alone is not sufficient to answer the question.
Statement II, E > B > D, again there is no information about other students. So, statement II alone is also not sufficient to answer the question.
Combining the two statements,
E > B > D > A and C, so E got the maximum marks.
S2. Ans.(a)
Sol. Let the cost price of a toy be Rs. x
So, the list price of a toy be Rs. 1.2x
Statement I.
List price after the reduction = 1.2x – 10% of 1.2x
= Rs. 1.08x
Now, 1.08x – x = 10
⇒ x = 10/0.08 = 125
So, statements I alone is sufficient to answer the question, statement II will not give any solid information. So, statement II alone is not sufficient to answer the question.
S3. Ans.(d)
Sol. From statement I,
a^2-4a + 4 = 0
⇒ (a-2)^2 = 0
⇒ a = 2
Nothing can be said about ‘b’.
From statement II,
b^2-6b + 9 = 19
⇒ b^2-6b-7 = 0
⇒ b = −1 or 7
Nothing can be said about ‘a’.
Combining the two statements will not give any unique answer.
S4. Ans.(d)
Sol. Let the two-digit number = xy
Statement I, x + y = 6. This is a single equation with two variables. So, statement I alone is not sufficient to answer the question.
Statement II, x – y = 2 or y – x = 2. This is again single equation with two variables. So, statement II is also not sufficient to answer the question.
On combining the two statements,
x = 4, y = 2 or x = 2, y = 4
The two-digit number can be 42 or 24.
Therefore, combing the two statement will not give any unique answer.
S5. Ans.(c)
Sol. From statement I, we get principal and from statement II, we get amount and time.
Hence, from I and II, we can find out the rate of SI.
S6. Ans.(c)
Sol. Let the length of the train be x.
Then, speed = x/5 m/s …(i)
From statement I, speed = (x + 150)/20 m/s …(ii)
From statement II, speed = 36 km/h
= 36 × 5/18 = 10 m/s
Now putting the value of speed in either of the equation (i) and (ii) we can calculate the length of train
∴ speed = x/5
10 ms = x/5
⇒ x = 50 m
S7. Ans.(b)
Sol. Let the number of boys be x and number of girls be y.
Statement I is insufficient to answer as the information required to get the answer is not available.
From statement II,
y = 75/100x
⇒ y = 0.75x
⇒x/y=1/0.75=4/3
S8. Ans.(e)
Sol. By both the statements individually we can find out the CP & SP and profit.
S9. Ans.(b)
Sol. From statement I, AC = BD
From statement II, ÐBAD + Ð BCD = 180°
Statement II satisfies the conditions of the cyclic quadrilateral.
S10. Ans.(c)
Sol. From statement I, ÐA = 2ÐB
ÐA + ÐB + ÐC = 180°
⇒ 2ÐB + ÐB + ÐC = 180°
From statement II, ÐB =
∴ ÐC =
⇒ 2ÐB + ÐB +
⇒ ÐB = 40°
⇒ ÐA = 80° and ÐC = 60°
S11. Ans.(a)
Sol. From statement I:
∵ Perimeter of square = 32 cm
∴ Length of side = 32/4 = 8 cm
⇒ Diameter of each circle
=(Length of side of square)/2=8/2=4 cm
So, radius of circle = 2 cm
And area of the circle = 4πr^2 = 4𝜋 × 4 = 16𝜋
From statement II, does not give any solid information.
S12. Ans.(d)
Sol. Both the statements are not sufficient to answer.
Additional data is required.
S13. Ans.(b)
Sol. Form statement II, If a + c is odd then one of a and c must be even because as we know, addition to two add numbers will always give an even number while addition of one even and one odd number is an odd number. So, if one of a and c is even then the product of abc is even.
S14. Ans.(c)
Sol.
From I and II, y = 120° and z = 87°
⇒ x = 180° − 120° + 87°
x = 147°
S15. Ans.(a)
Sol. From statement I, Let number obtained when x is divided by 5 be a.
Then, x = 5a
When, a is an odd number.
We know that, multiplication of two odd number is always odd number.
So, x is an odd number.
From statement II, If any of x or y is an odd number and other is even, then the result will be an odd number.
∴ (x + y) may or may not be an odd number.
So, be statement II, we cannot say that x is an odd number.
No comments:
Post a Comment