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The average (arithmetic mean) of the five numbers in a data set is 72.

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The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 24 Aug 2018, 00:54
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[Math Revolution GMAT math practice question]

The average (arithmetic mean) of the five numbers in a data set is 72. The average (arithmetic mean) of the first three numbers is 98. What is the average (arithmetic mean) of the last two numbers?

A. 31
B. 32
C. 33
D. 34
E. 35

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Re: The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 24 Aug 2018, 00:59
Average of 5 number = 72.
Sum of 5 = 72*5 = 360.
Average of first 3 = 98.
Sum of first 3 = 98*3 = 294.

Difference of 360 and 294 = 66.
The sum of the last two = 66. Average becomes 66/2 = 33.

C is the answer.
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Re: The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 24 Aug 2018, 06:28
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

The average (arithmetic mean) of the five numbers in a data set is 72. The average (arithmetic mean) of the first three numbers is 98. What is the average (arithmetic mean) of the last two numbers?

A. 31
B. 32
C. 33
D. 34
E. 35


Let a, b, c, d and e be the five numbers in the set.

The average (arithmetic mean) of the five numbers in a data set is 72.
So, (a + b + c + d + e)/5 = 72
Multiply both sides of the equation by 5 to get: a + b + c + d + e = 360

The average (arithmetic mean) of the first three numbers is 98.
So, (a + b + c)/3 = 98
Multiply both sides of the equation by 3 to get: a + b + c = 294

What is the average (arithmetic mean) of the last two numbers?
In other words, what is the average of d and e?

Take a + b + c + d + e = 360 and replace a + b + c with 294
We get: 294 + d + e = 360
Subtract 294 from both sides to get: d + e = 66

So, the average of d and e = (d + e)/2
= 66/2
= 33

Answer: C

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Re: The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 24 Aug 2018, 06:58
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The average (arithmetic mean) of the five numbers in a data set is 72. The average (arithmetic mean) of the first three numbers is 98. What is the average (arithmetic mean) of the last two numbers?

A. 31
B. 32
C. 33
D. 34
E. 35


Sum = (quantity)(average).

The average (arithmetic mean) of the five numbers in a data set is 72.
Sum = 5*72 = integer with a UNITS DIGIT OF 0.

The average (arithmetic mean) of the first three numbers is 98.
Sum = 3*98 = integer with a UNITS DIGIT OF 4.

For the sum of all 5 numbers to have a units digit of 0, the sum of the remaining 2 numbers must have a UNITS DIGIT OF 6, since INTEGER WITH A UNITS DIGIT OF 6 + INTEGER WITH A UNITS DIGIT OF 4 = INTEGER WITH A UNITS DIGIT OF 0.
Only C will yield for the other 2 numbers a sum with a units digit of 6:
2*33 = 66.


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Re: The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 24 Aug 2018, 07:34
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The average (arithmetic mean) of the five numbers in a data set is 72. The average (arithmetic mean) of the first three numbers is 98. What is the average (arithmetic mean) of the last two numbers?

A. 31
B. 32
C. 33
D. 34
E. 35


\(72*5 = 98*3 + 2*x\)

Or, \(360 = 294 + 2x\)

Or, \(x = 33\), Answer must be (C)
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Re: The average (arithmetic mean) of the five numbers in a data set is 72.  [#permalink]

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New post 26 Aug 2018, 18:24
=>

Let \(a, b, c, d\) and \(e\) be the five numbers.
Now, the average of these numbers is \(\frac{( a + b + c + d + e )}{5}= 72\), so \(a + b + c + d + e = 72 * 5 = 360\).
The average of the first three numbers is \(\frac{( a + b + c )}{3} = 98\), so \(a + b + c = 98 * 3 = 294.\)
Thus, the sum of the last two numbers is \(d + e = ( a + b + c + d + e ) – ( a + b + c ) = 360 - 294 = 66.\)
Their average is \(\frac{( d + e )}{2} = \frac{66}{2} = 33.\)

Therefore, the answer is C.
Answer: C
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Re: The average (arithmetic mean) of the five numbers in a data set is 72. &nbs [#permalink] 26 Aug 2018, 18:24
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