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­The sum of x numbers is what percent greater than the average 09 Mar 2024, 01:28
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­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?
  
A. \(\frac{x}{100}\)%
   
B.\(\frac{x - 1}{100}\)%
   
C. \((x - 1)\)%
   
D. \(100x\)%
  
E. \(100( x - 1)\)%


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­The sum of x numbers is what percent greater than the average 09 Mar 2024, 07:33
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gmatophobia
­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?
  
A. \(\frac{x}{100}\)%
   
B.\(\frac{x - 1}{100}\)%
   
C. \((x - 1)\)%
   
D. \(100x\)%
  
E. \(100( x - 1)\)%


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Assuming the sum of x numbers is s, the question asks to find what percent greater is s than s/x:

\(\frac{s - \frac{s}{x}}{(\frac{s}{x})}*100 = \)

\(=\frac{1 - \frac{1}{x}}{(\frac{1}{x})}*100 = \)

\(=(1 - \frac{1}{x})x*100 = \)

\(=(x - 1)*100\)

Answer: E.

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­The sum of x numbers is what percent greater than the average 09 Mar 2024, 01:40
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­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?
  
    A. \(\frac{x}{100}\)%
       
    B.\(\frac{x - 1}{100}\)%
       
    C. \((x - 1)\)%
       
    D. \(100x\)%
      
    E. \(100( x - 1)\)%
­
  
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Let's assume 3 numbers, 10, 20, and 30. Hence, \(x = 3\)
  
The sum of three numbers = 60
  
The average of three numbers = 20
  
Let's assume that the sum is g% greater. 
 
\(20(1+\frac{g}{100}) = 60\)
 
\(1 + \frac{g}{100} = 3\)
 
\(\frac{g}{100} = 2\)
 
\(g = 200\)%
  
Answer Choice Elimination 
 
A. \(\frac{3}{100}\)% 
 
The value is not equal to 200%. Eliminate. 
 
B.\(\frac{3 - 1}{100}\)%
 
The value is not equal to 200%. Eliminate. 
 
C. \((2 - 1)\)%
 
The value is not equal to 200%. Eliminate. 
 
D. \(100*3\)%
 
The value is not equal to 200%. Eliminate. 
 
E. \(100( 3 - 1)\)%
 
The value of option E is 200%. This matches the value we are looking for.
 
Option E­
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­The sum of x numbers is what percent greater than the average 09 Mar 2024, 05:03
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gmatophobia
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­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?
  
    A. \(\frac{x}{100}\)%
       
    B.\(\frac{x - 1}{100}\)%
       
    C. \((x - 1)\)%
       
    D. \(100x\)%
      
    E. \(100( x - 1)\)%
­
  
Show Spoiler
Attachment:
Screenshot 2024-03-09 135754.png
­
Let's assume 3 numbers, 10, 20, and 30. Hence, \(x = 3\)
  
The sum of three numbers = 60
  
The average of three numbers = 20
  
Let's assume that the sum is g% greater. 
 
\(20(1+\frac{g}{100}) = 60\)
 
\(1 + \frac{g}{100} = 3\)
 
\(\frac{g}{100} = 2\)
 
\(g = 200\)%
  
Answer Choice Elimination 
 
A. \(\frac{3}{100}\)% 
 
The value is not equal to 200%. Eliminate. 
 
B.\(\frac{3 - 1}{100}\)%
 
The value is not equal to 200%. Eliminate. 
 
C. \((2 - 1)\)%
 
The value is not equal to 200%. Eliminate. 
 
D. \(100*3\)%
 
The value is not equal to 200%. Eliminate. 
 
E. \(100( 3 - 1)\)%
 
The value of option E is 200%. This matches the value we are looking for.
 
Option E­
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Isn't x/100 % = (x/100)/100 = 100x/100?
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­The sum of x numbers is what percent greater than the average 09 Mar 2024, 07:26
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gmatophobia
gmatophobia
­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?
  
    A. \(\frac{x}{100}\)%
       
    B.\(\frac{x - 1}{100}\)%
       
    C. \((x - 1)\)%
       
    D. \(100x\)%
      
    E. \(100( x - 1)\)%
­
  
Show Spoiler
Attachment:
Screenshot 2024-03-09 135754.png
­
Let's assume 3 numbers, 10, 20, and 30. Hence, \(x = 3\)
  
The sum of three numbers = 60
  
The average of three numbers = 20
  
Let's assume that the sum is g% greater. 
 
\(20(1+\frac{g}{100}) = 60\)
 
\(1 + \frac{g}{100} = 3\)
 
\(\frac{g}{100} = 2\)
 
\(g = 200\)%
  
Answer Choice Elimination 
 
A. \(\frac{3}{100}\)% 
 
The value is not equal to 200%. Eliminate. 
 
B.\(\frac{3 - 1}{100}\)%
 
The value is not equal to 200%. Eliminate. 
 
C. \((2 - 1)\)%
 
The value is not equal to 200%. Eliminate. 
 
D. \(100*3\)%
 
The value is not equal to 200%. Eliminate. 
 
E. \(100( 3 - 1)\)%
 
The value of option E is 200%. This matches the value we are looking for.
 
Option E­
­
Isn't x/100 % = (x/100)/100 = 100x/100?
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x/100% = (x/100)/100 = x/100*1/00 = x/10,000
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­The sum of x numbers is what percent greater than the average 13 Jul 2024, 02:10
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Sum = AVG * Number of Items

Percent change formula: 100* (Final value - Initial value) / Initial value

100*(X*AVG - AVG) / AVG = 100*(X - 1)
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­The sum of x numbers is what percent greater than the average 21 Oct 2024, 15:32
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Any similar such questions? Is the best way to approach these kinds of problems to set up the formula?
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­The sum of x numbers is what percent greater than the average 22 Oct 2024, 00:41
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Any similar such questions? Is the best way to approach these kinds of problems to set up the formula?
Show more

There are a couple of different approaches shown above, so pick the one that suits you best. That being said, to score high, it's important to master both the algebraic and number-plugging approaches.

For similar or any other questions, head to the PS forum and use the dropdowns to select the category you want to practice:





Hope this helps!
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­The sum of x numbers is what percent greater than the average 05 Dec 2024, 21:55
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­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?

ex) x = 5 = {1, 2, 3, 4, 5}

Sum of 5 numbers = 15
Average of the 5 numbers = 3

Question: 15 is what percent greater than 3?
= percentage increase from 3 to 15
= 15 - 3 / 3 * 100%
= 12 / 3 * 100%
= 400%

Therefore, (E) 100(x−1)%
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­The sum of x numbers is what percent greater than the average 11 Jan 2025, 00:29
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­The sum of x numbers is what percent greater than the average (arithmetic mean) of the x numbers?

A. \(\frac{x}{100}\)%

B.\(\frac{x - 1}{100}\)%

C. \((x - 1)\)%

D. \(100x\)%

E. \(100( x - 1)\)%


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When we have variables in the options, we plug in a value. Say x = 2
.
Average of 2 numbers = Sum/2

Sum = 2 * Average

Since sum is twice the average, it means it is 100% greater than the average.

If we had 3 numbers, we would get Sum = 3 * Average
So here sum would be 200% greater than Average.

Hence Sum is 100(x-1)% greater than Average.

Answer (E)
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­The sum of x numbers is what percent greater than the average 08 Oct 2025, 06:12
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Let's think about what this question is really asking: You have x numbers, and you want to know: by what percent is their SUM greater than their AVERAGE?

Here's the key insight you need to see: there's a fundamental relationship between sum and average that makes this problem work beautifully.

Step 1: Establish the Sum-Average Relationship

Let's call the average of your x numbers "A". Now, remember how averages work:
Average = Sum ÷ Number of values

So if we flip this around:
Sum = Average × Number of values
Sum = \(A \times x\)

Notice that we now have both the sum and average expressed in terms of A.

Step 2: Find the Difference

How much greater is the sum than the average?
Difference = Sum - Average
Difference = \((A \times x) - A\)
Difference = \(A(x - 1)\)

Let's test this with real numbers to make sure it makes sense. Say you have 3 test scores: 80, 90, and 100.
  • Sum = 270
  • Average = 90
  • Difference = 270 - 90 = 180

Using our formula: \(A(x-1) = 90(3-1) = 90(2) = 180\) ✓

Step 3: Convert to Percentage

Here's where you need to be careful. The question asks "what percent GREATER THAN" - this means we need the percent increase formula:

\(Percent\ increase = \frac{Difference}{Original} \times 100\%\)

What are we comparing to? The average. So:

\(Percent\ increase = \frac{A(x-1)}{A} \times 100\%\)

Notice how the A's cancel out:
\(= (x-1) \times 100\%\)
\(= 100(x-1)\%\)

Step 4: Verify

Let's check with our example (3 test scores, sum = 270, average = 90):
Using our formula: \(100(3-1)\% = 100(2)\% = 200\%\)

Direct calculation: \(\frac{270-90}{90} \times 100\% = \frac{180}{90} \times 100\% = 200\%\) ✓

Answer: E - 100(x-1)%

The beautiful thing about this result is that it doesn't matter what the actual numbers are or what the average is - the percent increase only depends on HOW MANY numbers you have (x).

Want to master this question type?

While you've got the core solution here, there's something really valuable about understanding WHY this pattern emerges and how to recognize similar structures in other GMAT problems. The complete solution on Neuron breaks down the systematic framework for all "percent greater than" problems and shows you the exact traps to avoid (like confusing "percent greater than" with "percent of" - which trips up many students at the answer choice stage!).

You can check out the detailed step-by-step solution on Neuron to see the smart numbers alternative approach (which can be faster for some students) and learn the broader patterns that apply to similar questions. You can also practice with comprehensive explanations for other official questions on Neuron to build systematic accuracy across all question types.
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