### 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?**

**A 50% of persons of the group read newspaper X.**

**B 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.**

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

**A Average of all the phones sold by shopkeeper is 225.**

**B 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.**

**3. How many maximum milliliters of water can a tank hold?**

**A The tank currently holds 200 milliliters of water**

**B 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.**

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

**A Y/12 is an integer.**

**B 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**

**5. ls xy > 5?**

**A 1 ≤ x ≤ 3 and 2 ≤ y ≤ 4.**

**B 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.**

**6. For integers x and y, x2 + xy +24x = 81 , what is the value of x?**

**A x+y=3**

**B x2+y=5**

**Answer Option: 1**

**From statement A,**

**We have x+y = 3. When we substitute back into the main equation,**

**x2 + 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,**

**x2 = 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.**