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Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?
  • a)
    x - 1
  • b)
    x
  • c)
    x + 1
  • d)
    x + 2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Average of three numbers is x. Instead of the first number if we take ...
If half of the first number is removed, the average decreases by 1, that means, the total decreases by 3.We assume that the number is z.
Therefore, if we take 2z instead of z, the total will increase by 6 and the average increases by 2.
So, it will be x + 2.
 
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Average of three numbers is x. Instead of the first number if we take ...
Let the three numbers be a, b, and c.

Average of the three numbers = x

According to the given information, if we take only half of the first number instead of the first number, the average will be x - 1.

So, the new average is (x - 1).

We can write this as:

(a/2 + b + c)/3 = x - 1

Simplifying this equation, we get:

a/2 + b + c = 3x - 3

Now, let's find the average when twice the first number is taken in place of the first number.

Twice the first number = 2a

The new sum of the three numbers will be (2a + b + c).

The new average can be calculated as:

(2a + b + c)/3 = ?

We need to find the value of this expression.

Let's substitute the value of (a/2 + b + c) from the previous equation into this expression:

(2a + b + c)/3 = (2(a/2 + b + c))/3

Simplifying this expression, we get:

(2a + b + c)/3 = (2a/2 + 2b + 2c)/3

(2a + b + c)/3 = (a + 2b + 2c)/3

We know that the average of any set of numbers remains the same when the same number is added to or subtracted from all the numbers.

So, the average of (a/2 + b + c) and (2a + b + c) will be the same, which is x.

Therefore, the average when twice the first number is taken in place of the first number is x.

Hence, the correct answer is option D) x.
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There are nine boxes arranged in a 3 × 3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.(i) The minimum among the numbers of coins in the three sacks in the box is 1.(ii) The median of the numbers of coins in the three sacks is 1.(iii) The maximum among the numbers of coins in the three sacks in the box is 9.For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same? Correct answer is '4'. Can you explain this answer?

There are nine boxes arranged in a 3 × 3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.(i) The minimum among the numbers of coins in the three sacks in the box is 1.(ii) The median of the numbers of coins in the three sacks is 1.(iii) The maximum among the numbers of coins in the three sacks in the box is 9.In how many boxes do all three sacks contain different numbers of coins? Correct answer is '5'. Can you explain this answer?

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Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?a)x - 1b)xc)x + 1d)x + 2Correct answer is option 'D'. Can you explain this answer?
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Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?a)x - 1b)xc)x + 1d)x + 2Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?a)x - 1b)xc)x + 1d)x + 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?a)x - 1b)xc)x + 1d)x + 2Correct answer is option 'D'. Can you explain this answer?.
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