DIRECTIONS for following questions 1 to 10: 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.
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.

Answer Option: 3
Statement (A) alone can be translated as
X^{2}+5X+6=0
X^{2}+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
Y^{2}+16Y+63=0
Y^{2}+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.

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.

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.

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.

What is the value of the sum of a list of n odd integers?

n = 8

Square of the number of integers on the list is 64.

Answer Option: 5
Statement (A) and (B) give only the number of integers in the list.
Since additional information is needed to determine the sum of the integers (for example, their average), the best answer is option 5.

Train A crosses a platform of length 120m in 20 sec.

Length of train A is 100 m

Answer Option: 3
Let the speed of Train A is 'X',
Thus, (Length of train A + 120) / 20,
Thus, Statement A is insufficient, because we can't conclude anything.
Statement B is also insufficient as it gives only the length of the train.
But both statements together tell us that speed = (100 + 120) / 20 = 11 m/s
Therefore, both statements are necessary to determine the right answer. So, the answer is option 3.

If a commercial fertilizer called Green Grow is a mixture of compounds M and N, what % of one bag of Green Grow, by weight, is nitrogen?

By weight, Green Grow consists of 7 parts M and 5 parts N.

By weight, 18 percent of compound N is nitrogen.

Answer Option: 5
The only thing to remember in these types of problems is that we don't know the composition of every compound.
Statement A only tells us the proportion of ingredients.
And it says nothing about nitrogen.
Statement B is a little trickier.
Nitrogen present in compound M is not known still. So, the answer is 5.

How many of the boys in a group of 100 children have brown hair?

Of the children in the group, 60 percent have brown hair.

Of the children in the group, 40 are boys.

Answer Option: 5
From statement (A), only the total number of children who have brown hair can be determined, so (A) alone is not sufficient.
Therefore, the answer must be 2, 3, or 5.
Clearly (B) alone is not sufficient because nothing is said about brown hair.
Therefore, the answer must be 3 or 5.
From statements (A) and (B) together, only the total number of children who have brown hair and the number of boys in the group are known.
Thus, (A) and (B) together are not sufficient, and the answer is 5.

What is the mileage of a diesel truck from city A to B?

The total cost of the Diesel used by the truck for the 1250 km distance between A & B was Rs. 2500.

The cost of the Diesel used by the truck for the journey was Rs.20 per Litre.

Answer Option: 3
Statement (A) gives the number of km the truck traveled. However, the number of litres of diesel used cannot be determined, since only the total cost of the Diesel is given. Thus, (A) alone is not sufficient, and the answer is 2, 3, or 5.
Statement (B) alone is obviously not sufficient alone; it gives the additional information needed in (A) about the number of litres of diesel used.
By combining both the statements, we can say diesel used = 2500/20 = 125 litres. So, mileage = Number of kms. / Diesel used = 1250/125 = 10 km/lit.
Therefore, (A) and (B) together are sufficient, and the answer is option 3.

Does x^{2} - y^{2} = x + y, (given x & y are non-zero real numbers)?

xy = y^{2}

x^{2} = y^{2}

Answer Option: 1
Statement A: xy = y^{2} implies that either y = 0 or x = y but y is given to be non-zero.
Thus, the question can be answered as 'no'. So, statement A alone is sufficient.
Statement B: x^{2} = y^{2} implies that x = y or x = – y. Putting in the equation, it still does not give a concrete answer. So, the answer is 1.