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 the statements A and B are needed
Mark 4 if each of statement A or statement B alone is sufficient.
Mark 5 if both of them together are not sufficient

What could be the maximum number of people in a group reading both newspapers X & Y?

50% of persons of the group read newspaper X.

30% of persons of the group read newspaper Y.

Answer Option: 3
Statement (A) "50% of persons read newspaper X", is not sufficient since we can't conclude anything.
Statement (B) "30% of persons read newspaper Y", is not sufficient since we can't conclude anything.
But using both together,
We can say maximum 30% of persons could read both newspaper X & Y.
So it is seen that (A) and (B) together are sufficient to answer the question.

A shopkeeper sells a phone X on 20% profit. What is the Cost Price of phone X?

Average of all the phones sold by shopkeeper is 225.

Selling Price of Phone X is Rs. 14400.

Answer Option: 2
Given that, Profit = 20%
SP= 120% of CP
Statement (A) is not sufficient since it implies only that average of all the phones sold by shopkeeper is 225. Therefore, we can't conclude the answer.
From the second statement, SP=Rs. 14400
SP= 120% of CP
14400= 120% of CP
CP= Rs. 12000
Hence, Statement B alone is sufficient to answer the question.

How many maximum milliliters of water can a tank hold?

The tank currently holds 200 milliliters of water

If 150 milliliters of water is added to the tank then tank is half filled.

Answer Option: 3
Statement A alone is not sufficient since it implies only that tank holds at least 200 milliliters. Therefore, we can't conclude the answer.
Statement B alone is not sufficient because it does not mention the current status of water in the tank.
By combining both the statements,we can say
if t is the capacity of the tank and on adding 150 mls of water, then the volume of water will be 350 milliliters which is equal to 1/2 of capacity of tank
i.e t/2= 350 milliliters.
t=700 milliliters.
So, we can find out capacity of the tank. Hence, option 3.

Product of X and Y is 48 where X & Y are positive integers. Find X.

Y/12 is an integer.

X/4 is an integer.

Answer Option: 3
From the first statement, Y can be 12, 24 or 48.
From the second statement, X can be 4, 8,12,16,20,....,48.
But if we combine both the statements, we can say Y = 12,X = 4
So,both the statements A and B are needed. Hence, answer is option 3

ls xy > 5?

1 ≤ x ≤ 3 and 2 ≤ y ≤ 4.

x + y = 5

Answer Option: 5
Statement A alone is not sufficient, since the product could be as small as (1)(2) = 2 or as large as (3)(4) = 12 Therefore, the answer must be 2, 3, or 5.
Statement B alone is not sufficient since if x were 1, y would be 4 and xy = 4; but if x were 2, y would be 3 and xy = 6. Hence, the answer must be 3 or 5.
Both statements together are not sufficient since both of the examples x = 1, y = 4 and x = 2, y = 3 are consistent with both statements. Therefore, the best answer is 5.

For integers x and y, x^{2} + xy +24x = 81 , what is the value of x?

x+y=3

x^{2}+y=5

Answer Option: 1
From statement A,
We have x+y = 3. When we substitute back into the main equation,
x^{2} + xy +24x = 81
x( x + y ) + 24x = 81
3x + 24x = 81
27x=81; we get x =3 which is integer. Statement A alone is sufficient to get the answer.
From statement B,
x^{2} = 5-y
So, equation becomes, 5 - y + xy + 24 x = 81
xy - y + 24x = 76
y ( x - 1 ) + 24 ( x - 1 ) = 76 - 24 = 52
( y + 24 ) (x - 1 ) = 52 = 1 x 52, 2 x 26, so on.
Hence Statement B alone is not sufficient to answer the question.
Statement A alone is sufficient to get the answer. Hence, answer is option 1.

Chaaya, the wife of Bharat's only brother Chauhan does not have any siblings

Bhavna is Chaaya's brother in law's wife.

Answer Option: 3
From statement A, we know that Chaaya has no siblings and she is the wife of Bharat's only brother Chauhan. However, this statement does not give any information about Bhavna. From statement B, we know that Bhavna is Chaaya's brother in law's wife. This statement establishes a relation between Chaaya and Bhavna. However, this statement does not give any information about Bharat. Hence, statement B alone is not sufficient to answer the question.
Now, if we combine both statements, we know that Bharat and Chaaya are related to each other through Chauhan, who is the only brother of Bharat and that Bhavna is Chaaya's brother in law's wife.
Chaaya does not have any siblings and hence her brother in law has to necessarily be her husband's sibling. As Chauhan is the only brother of Bharat, Chaaya's brother in law has to be Bharat and Bhavna is his wife. So, option 3 is the answer.

What is the distance between Ghaziabad and Karnal in Kms?

It takes 2 hours to cover whole distance from Ghaziabad to Delhi with the speed of 27 km/hr.

With the average speed of 36 km/hr, it takes 10 hours to cover ½ of the total journey from Ghaziabad to Karnal.

Answer Option: 2
Statement A alone is not sufficient; because we can only conclude the distance between Ghaziabad to Delhi.
Statement B can be expressed as (1/2 x d)= 10 x 36, which can be solved for d.
Thus, statement B alone is sufficient, But Statement A is insufficient and the best answer is option 2.

If P is an integer between 10 and 100, what is the value of P?

One of the digits of P is 3 more than the other, and the sum of its digits is 9

P < 50

Answer Option: 3
If x and y are the digits of P, statement (A) can be concluded as x = y + 3 and x + y = 9, which can be solved. It is also possible to see that only the numbers 36 and 63 are possible without actually setting up equations, but the position of digits is not known, regardless of the method used. Statement A alone is not sufficient, and the answer must be 2, 3 or 5.
Clearly, (B) alone is not sufficient because it only gives a range of possible values of P. Therefore, the answer is 3 or 5.
But if we combine both the statements we can conclude that the possible value of P is 36 only. So it is seen that (A) and (B) together are sufficient to determine the value of P, and the best answer is 3.

Find the fifth term of the sequence.

Average of the first four terms of the sequence is 53

Third term of the sequence is 72

Answer Option: 5
From Statement A, we can calculate sum of 1^{st} four terms as 212. But we can’t find 5^{th} term. So Statement A alone is not sufficient to answer the question;
From Statement B, we only have 3^{rd} term as 72. But we cannot find fifth term.Statement B alone is not sufficient to answer the question
Even by combining both the statements, fifth term cannot be found. Thus,the answer is option 5.