swerve wrote:If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?

1) None of the four numbers is greater than 60.
2) Two of the four numbers are 9 and 10, respectively.

The OA is C.

Please, can anyone explain this DS question? I tried to solve it but I don't understand why C is the correct answer. I need help. Thanks.

Given, that the average (arithmetic mean) of four different numbers is 30, the sum of the four numbers = 30*4 = 120.

We have to find out the count of the numbers that are greater than 30.

Let's take each statement one by one.

1) None of the four numbers is greater than 60.

Say, one of the numbers is 60, thus, the sum of other three = 120 - 60 = 60.

Case 1: One of the possibilities: Other three are: 10, 20, 30. Only one number (60) is greater than 30.
Case 2: Another possibility: Other three are: 5, 15, 40. Two numbers (40 & 60) are greater than 30.

No unique answer. Insufficient.

2) Two of the four numbers are 9 and 10, respectively.

=> Sum of the other two numbers = 120 - 9 - 10 = 101.

Case 1: Say a number is 60; thus, the other number = 101 - 60 = 41. Two numbers (41 & 60) are greater than 30.
Case 2: Say a number is 30; thus, the other number = 101 - 30 = 71. Only one number (71) is greater than 30.

No unique answer. Insufficient.

(1) and (2) together

From Statement (1), we have the sum of the other two numbers = 101.

Since the average of the numbers is 30, and two numbers are less than 30 (9 and 10), at least one number must be greater than 30. Say, the number is 31; thus, the 4th number is 101 - 31 = 70 (No possible since the maximum value of a number can be 60). Say, the number is 51; thus, the 4th number is 101 - 51 = 50. Two numbers (51 & 50) are greater than 30.

Now, let's make use of the Statement (1). Say a number is 60 (maximum possible); thus, the 4th number is 101 - 60 = 41. Two numbers (41 & 60) are greater than 30.

Unique answer. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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swerve wrote:If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?

1) None of the four numbers is greater than 60.
2) Two of the four numbers are 9 and 10, respectively.

We are given that the average (arithmetic mean) of four different numbers is 30, so the sum of the four numbers is 120. We need to determine how many of the numbers are greater than 30.

Statement One Alone:

None of the four numbers is greater than 60.

Let's say one of the four numbers is 60; then the sum of the other three numbers is 60. The other three numbers can be 19, 20, and 21 or they can be 9, 10, and 41. In the former case, there is only 1 number greater than 30; however, in the latter case, there are two numbers greater than 30. Statement one alone is not sufficient to answer the question.


Statement Two Alone:

Two of the four numbers are 9 and 10, respectively.

That means the sum of the other two numbers is 101. The other two numbers can be 1 and 100,or they can be 50 and 51. In the former case, there is only 1 number greater than 30; however, in the latter case, there are two numbers greater than 30. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since two of the numbers are 9 and 10, the sum of the other two numbers is 101. On average, the other two numbers have to be about 50 each. Since no number is greater than 60, we see that if one of the remaining two numbers is 60, the other must be 41. 41 is the minimum value of one of the remaining two numbers, since if it's any smaller, the very last number will be more than 60 (but we can't have that). So there must be two numbers that are greater than 30.

Answer: C