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GMAT 1: 760 Q51 V42
Posts: 10,057
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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
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
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
Posts: 899
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy)
Products:
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.
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.
Posts: 6,727
Updated on: 07 Aug 2020, 06:40
Originally posted by BrentGMATPrepNow on 24 Aug 2018, 05:28.
Last edited by BrentGMATPrepNow on 07 Aug 2020, 06:40, edited 1 time in total.
Last edited by BrentGMATPrepNow on 07 Aug 2020, 06:40, edited 1 time in total.
MathRevolution
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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MathRevolution
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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MathRevolution
\(72*5 = 98*3 + 2*x\)
Or, \(360 = 294 + 2x\)
Or, \(x = 33\), Answer must be (C)
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GMAT 1: 760 Q51 V42
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=>
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
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
Theory
The average (arithmetic mean) of the five numbers in a data set is 72
Sum of 5 numbers = Average * 5 = 72*5 = 360
The average (arithmetic mean) of the first three numbers is 98
Sum of first 3 numbers = Average * 3 = 98 * 3 = 294
What is the average (arithmetic mean) of the last two numbers
Sum of last 2 numbers = Sum of 5 numbers - Sum of first 3 numbers = 360 - 294 = 66
=> Average of last 2 numbers = \(\frac{66}{2}\) = 33
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
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- ➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of all the Values = Average * Total Number of Values
The average (arithmetic mean) of the five numbers in a data set is 72
Sum of 5 numbers = Average * 5 = 72*5 = 360
The average (arithmetic mean) of the first three numbers is 98
Sum of first 3 numbers = Average * 3 = 98 * 3 = 294
What is the average (arithmetic mean) of the last two numbers
Sum of last 2 numbers = Sum of 5 numbers - Sum of first 3 numbers = 360 - 294 = 66
=> Average of last 2 numbers = \(\frac{66}{2}\) = 33
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
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All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
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