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kevincan
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Jonah adds the greatest of three numbers to the average of t 24 Apr 2026, 14:24
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65% (hard)

Question Stats:

65% (02:37) correct 35% (03:12) wrong based on 79 sessions

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Jonah adds the greatest of three numbers to the average of the other two and divides the sum by two. If the result is x more than the average of the three numbers, what is the difference between the greatest of the three numbers and the average of the other two?

A. x
B. 2x
C. 3x
D. 4x
E. 6x
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E
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Jonah adds the greatest of three numbers to the average of t 26 Apr 2026, 18:02
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Jonah adds the greatest of three numbers to the average of the other two and divides the sum by two. If the result is x more than the average of the three numbers, what is the difference between the greatest of the three numbers and the average of the other two?

This is a good example of a question we can answer using smart numbers because the answer for any set of three numbers such that one of them is greater than the other two will work for all such sets of numbers.

Pick smart numbers:

6, 6, 12

These numbers are all divisible by both 2 and 3. So, the average of any two or all three of them will be an integer value.

Use the numbers to do what the stem says:

adds the greatest of three numbers to the average of the other two and divides the sum by two

(12 + 6)/2 = 9

the result is x more than the average of the three numbers

x = 9 - 24/3 = 9 - 8 = 1

Answer the question asked:

what is the difference between the greatest of the three numbers and the average of the other two?

12 - 6 = 6 = 6x

A. x
B. 2x
C. 3x
D. 4x
E. 6x

Correct answer: E
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Jonah adds the greatest of three numbers to the average of t 26 Apr 2026, 23:49
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Jonah adds the greatest of three numbers to the average of t 27 Apr 2026, 00:23
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kevincan
Jonah adds the greatest of three numbers to the average of the other two and divides the sum by two. If the result is x more than the average of the three numbers, what is the difference between the greatest of the three numbers and the average of the other two?

A. x
B. 2x
C. 3x
D. 4x
E. 6x
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Responding to a pm:

When there is a variable in the options, plugging in a value is the easiest way to proceed. Just assume values and proceed step by step.

Assume the numbers are 1, 3, 5
Average of the smaller two numbers is 2. Average of the greatest number (5) and 2 is 3.5.
Average of all three numbers is 3.
So x = 3.5 - 3 = 0.5
The difference between 5 and average of other 2 i.e. 2 is 3.
3 = 6 * 0.5 so answer will be 6x.

Answer (E)
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Jonah adds the greatest of three numbers to the average of t 06 Jun 2026, 01:25
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Let the three numbers be a, b, and c, where c is the greatest number.

Step 1: Translate Jonah's actions into a fraction

The average of the other two numbers is: (a + b) / 2

Jonah adds the greatest number (c) to that: c + (a + b) / 2

He divides everything by 2: (c + (a + b) / 2) / 2

To clean up this double fraction, we multiply the top and bottom by 2:
Jonah's Final Number = (2c + a + b) / 4

Step 2: Compare it to the true average
The true average of all three numbers is: (a + b + c) / 3

The problem says Jonah's number is "x more than" the true average:
(2c + a + b) / 4 = (a + b + c) / 3 + x

Step 3: Clear the fractions
Multiply every single term by 12 to get rid of the denominators:
3 * (2c + a + b) = 4 * (a + b + c) + 12 * x
6c + 3a + 3b = 4a + 4b + 4c + 12x

Step 4: Group the letters together
Move all the a, b, and c terms to the left side by subtracting them:
(6c - 4c) + (3a - 4a) + (3b - 4b) = 12x
2c - a - b = 12x

Step 5: Find the final answer
The question asks for the difference between the greatest number (c) and the average of the other two ((a + b) / 2):
Difference = c - (a + b) / 2

To combine these into one fraction, give c a common denominator:
Difference = (2c - a - b) / 2

Since we already discovered in Step 4 that (2c - a - b) equals 12x, we substitute it right into the formula:
Difference = 12x / 2
Difference = 6x

Correct Answer: E. 6x
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