*Directions (1-5): Read the given information carefully to answer these questions:*

*There are 215 students in a college. The foreign language department offers French, German and Spanish. In a survey we found that*

*(i) 8 students take all the three languages.*

*(ii) 69 students study French.*

*(iii) There are twice as many students who study both French and Spanish (but not German) as those who study both French and German (but not Spanish), and three times as many as those who study all three.***
**

*(iv) 120 students study Spanish.*

*(v) 23 students do not study any foreign language.*

*(vi) The group of students who study both French and Spanish (but not German) is exactly the same size as the group of students who study both German and Spanish.***1. How many students are there who study only French?**

1) 23

2) 24

3) 25

4) 26

5) 27

**2. The number of students who study only Spanish is**

1) 68

2) 72

3) 76

4) 78

5) 82

**3. How many students are there who study at least one foreign language?**

1) 190

2) 192

3) 194

4) 196

5) 198

**4. What is the difference between the number of students who study only Spanish and the number of students who study only German?**

1) 33

2) 34

3) 35

4) 36

5) 37

**5. What is the ratio of the number of students who study Spanish and French but not German to number of students who study Spanish and German but not French?**

1) 3 : 1

2) 1 : 3

3) 3 : 2

4) 2 : 3

5) 1 : 1

*Directions (6-10): Each question below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer-*

*(1) If the question can be answered by using statement I alone but cannot be answered by statement II alone.*

*(2) If the question can be answered by using statement II alone but cannot be answered by statement I alone.*

*(3) If both statements I and II together are required to answer the question.*

*(4) If the answer can be found by using any of the two statements alone.*

*(5) If both the statements together are not sufficient to answer the question.***6. A man sells TV sets at profit of 20%. How much total amount he gains in profit?**

I. He sells 20 TV set.

II. He sells each TV set at Rs 12000.

**7. What is the age of Ravi at present?**

I. His present age is 4 times the present age of Ram.

II. Five years ago Ravi’s age was 7 times the age of Ram.

**8. Area of a rectangle is equal to the area of a right-angled triangle. What is the length and width of the rectangle?**

I. Base of triangle is 10 cm.

II. Height of triangle is 20 cm.

**9. What is the time taken by Ram from point A to other point B?**

I. If he walks 25% faster than his usual speed then he reaches 20 seconds earlier.

II. If he walks half of his usual speed, he takes 100 seconds more to reach the finishing point B.

**10. What is the length of the train?**

I. It crosses a pole in 10 seconds.

II. Speed of the train is 10 m/sec.

**Solutions (1-5):**

1. (3)

2. (2)

3. (2)

4. (5)

5. (3) Ratio

=24/16= 3 : 2

=24/16= 3 : 2

**Solutions (6-10)**

6. 3; Both statements are required for answer.

SP = 12000, Profit = 20%

Cost Price = 1000 ie profit = 2000

Total profit = 2000 × 20 = 40000

7. 3;

**From statement I:**
x = 4y …(i)

**From statement II:**

x – 5 = 7(y – 5)

7y – x = 30 …(ii)

Solving equations (i) and (ii), x

= 40, y = 10

= 40, y = 10

8. 5; Data is not sufficient to find the answer.

9. 4; Both statements alone are sufficient to

answer.

answer.

Let be speed = v, distance = x,

time = t

time = t

t = x/v …(i)

**From statement I:**

x/5v/4=t – 20

4x/5v= t – 20

x/v = 5/4(t – 20) …(ii)

From (i) and (ii), t = 5 / 4(t – 20)

4t = 5t – 100

t = 100 seconds

**From statement II:**

x / v / 2 = t + 100

2x / v = t + 100

t + 100 = 2t

t = 100 seconds

10. 3; Both statements are required to answer the

question.

question.

**From statement I:**

1/v = 10 seconds (1

= length, v = speed)

= length, v = speed)

**From statement II:**

v = 10 m/sec

1 = 10 × v = 100 m