**DIRECTIONS**You have to decide whether the data given in the statements is sufficient to answer the question or draw the conclusion of the statement in the question.

*for following questions 1 to 10:***Mark 1 if statement A alone is sufficient but B alone is not sufficient**

**Mark 2 if statement B alone is sufficient but statement A alone is not sufficient**

**Mark 3 if both statements A and B are needed**

**Mark 4 if either of statement A or statement B alone is sufficient.**

**Mark 5 if both of them together are not sufficient**

- Is X greater than Y?
- X
^{2}+5X+6=0. - Y
^{2}+16Y+63=0.

- X

**Answer Option: 3**

**Statement (A) alone can be translated as**

**X2+5X+6=0**

**X2+3X+2X+6=0.**

**(X+3)(X+2)=0**

**X= -3, -2**

**We can’t conclude with only statement A.**

**Statement (B) alone can be translated as**

**Y2+16Y+63=0**

**Y2+9Y+7Y+63=0.**

**(Y+9)(Y+7)=0**

**Y= -9, -7**

**We can’t conclude with only statement B. By combining both the statements we can say X(= -3,-2) is greater than Y(= -9,-7).**

**So,both statements are necessary to determine the right answer. So, the answer is option 3.**

**2. What is the total population of town A ?**

- 40% of total population of town A are males.
- Total numbers of females in town A is 6000

**Answer Option: 3**

**Statement (A) alone can be translated as 40% of total population of town A is males. That is still not enough to tell us the total number of population in Town A.**

**Statement (B) alone can be translated as total population of females in town A is 6000. That is also not enough to tell us the result.**

**Combining both statements,**

**From the 1**

^{st}, 60% of Total population are females which is 6000 from the 2^{nd}statement.**60% of total population= 6000**

**Total population= 10000**

**Both statements are necessary to determine the right answer. So, the answer is option 3.**

**3. Is the smallest of five consecutive integers even?**

- The product of five integers is 0.
- The sum of five integers is 0.

**Answer Option: 2**

**From statement A, if product of 5 integers is 0, it implies that one of the integers is 0.**

**But, that is still not enough to tell us whether the smallest integer is even or not.**

**From statement B, if sum of 5 integers is 0, given that this is an odd number and consecutive integers, then the sequence is**

*–*2,*–*1, 0, 1, 2. Thus, we know that the smallest integer is even. Hence, answer is option 2.**4. What is the total number of students in Class XII?**

- Average marks of students of class XII is 24.
- Number of students who passed in XII were 20.

**Answer Option: 5**

**Statement (A) is insufficient to answer the question, we can’t conclude anything from it.**

**Clearly (B) alone is not sufficient because of same reason. Even by combining both the statements, we cannot calculate total number of students because there is no information about failed candidates.**

**Thus, (A) and (B) together are not sufficient, and the answer is option 5.**