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Difficulty:
5%
(low)
Question Stats:
92% (01:08) correct
8%
(01:29)
wrong
based on 2066
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The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?
(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0
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(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0
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SOLUTION
The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?
(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0
The average of 6 numbers is 8.5 --> the sum of 6 numbers = (mean)*(number of terms) = 8.5*6 = 51.
The average of 5 numbers is 7.2 --> the sum of 5 numbers = (mean)*(number of terms) = 7.2*5 = 36.
The discarded number = 51 - 36 = 15.
Answer: E.
_________________
The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?
(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0
The average of 6 numbers is 8.5 --> the sum of 6 numbers = (mean)*(number of terms) = 8.5*6 = 51.
The average of 5 numbers is 7.2 --> the sum of 5 numbers = (mean)*(number of terms) = 7.2*5 = 36.
The discarded number = 51 - 36 = 15.
Answer: E.
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Posts: 6,727
Bunuel
Average of 6 numbers = (sum of all 6 numbers)/6
We get: 8.5 = (sum of all 6 numbers)/6
So, sum of the 6 numbers = (6)(8.5)
= 51
When one number is discarded, the average of the remaining numbers becomes 7.2
Sum of remaining 5 numbers = (5)(7.2)
= 36
Discarded number = (sum of original 6 numbers) - (sum of remaining 5 numbers)
= 51 - 36
= 15
= E
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General Discussion
WoundedTiger
Joined: 25 Apr 2012
Last visit: 03 Jan 2026
Posts: 520
Location: India
GPA: 3.21
WE:Business Development (Other)
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Posts: 520
The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2 .What is the discarded number?
Sol: Since avg is given for 6 nos, we can find the sum total which is 8.5*6= 51
New average after removal of one number is 7.2 so sum total of 5 nos is 36
Discarded number is 51-36=15
Ans E
Posted from my mobile device
Sol: Since avg is given for 6 nos, we can find the sum total which is 8.5*6= 51
New average after removal of one number is 7.2 so sum total of 5 nos is 36
Discarded number is 51-36=15
Ans E
Posted from my mobile device
Given that the average of 6 numbers is 8.5, then the sum of these numbers is 6*8.5= 51.
Let 'x' be the number removed, (51-x)/5 = 7.2. Solving for x, we get x = 15, so (E).
Let 'x' be the number removed, (51-x)/5 = 7.2. Solving for x, we get x = 15, so (E).
Let's assume every number was 8.5 in the original set, now in order to reduce average to 7.2 by removing just one number, 1.3 \((8.5-7.2=1.3)\) needs to be subtracted from remaining 5 numbers \((1.3*5=6.5)\) along with removing one of the original numbers, i.e. \(6.5+8.5=15.0\)
Answer: E
Answer: E
Here is my solution to this one-->
Sum(1)=6*8.5=>51
Sum(2)=5*7.2=>36
Hence the discarded number must be 51-36=15
Hence E
Sum(1)=6*8.5=>51
Sum(2)=5*7.2=>36
Hence the discarded number must be 51-36=15
Hence E
Abhishek009
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Last visit: 17 Dec 2025
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Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,880
Bunuel
\(8.5*6 - x = 7.2*5\)
Or, \(51 - x = 36\)
Or, \(x = 15\)
Hence, answer will be (E) 15
_________________
this can be solved very easily from the following method
N-7.2/6 +7.2=8.5 so the new no. will be after solving for N=15
so the answer is E
after knowing the S.D. very precisely we gonna solve these questions within 30 sec.
N-7.2/6 +7.2=8.5 so the new no. will be after solving for N=15
so the answer is E
after knowing the S.D. very precisely we gonna solve these questions within 30 sec.
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,880
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,880
Bunuel
\(8.5*6 - X = 7.2*5\)
\(51 - x = 36\)
Or, \(x = 15\)
Thus, the discarded number will be (E) 15.00
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TheNightKing
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,119
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,119
Quote:
(8.5*6)-(7.2*5)=51-36=15. Option E.
8.5*6= 51
7.2*5= 36
51-36=15
Answer is E.
7.2*5= 36
51-36=15
Answer is E.
Theory
The average (arithmetic mean) of 6 numbers is 8.5
Sum of 6 numbers = Average * 6 = 8.5 * 6 = 51
When one number is discarded, the average of the remaining numbers becomes 7.2
Sum of remaining 5 numbers = Average * 5 = 7.2 * 5 = 36
Discarded number = Sum of 6 numbers - Sum of remaining 5 numbers = 51 - 36 = 15
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
_________________
- ➡ 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 6 numbers is 8.5
Sum of 6 numbers = Average * 6 = 8.5 * 6 = 51
When one number is discarded, the average of the remaining numbers becomes 7.2
Sum of remaining 5 numbers = Average * 5 = 7.2 * 5 = 36
Discarded number = Sum of 6 numbers - Sum of remaining 5 numbers = 51 - 36 = 15
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
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GMAT Club Topic Wise Problems
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
GMAT Club Topic Wise Problems
Let's denote the discarded number as x.
The average of 6 numbers is given as 8.5, so the sum of these 6 numbers is 6 * 8.5 = 51.
When the number x is discarded, the average of the remaining 5 numbers becomes 7.2. So, the sum of the remaining 5 numbers is 5 * 7.2 = 36.
To find the discarded number x, we can subtract the sum of the remaining 5 numbers from the sum of the original 6 numbers:
51 - 36 = 15
Therefore, the discarded number is 15.
The average of 6 numbers is given as 8.5, so the sum of these 6 numbers is 6 * 8.5 = 51.
When the number x is discarded, the average of the remaining 5 numbers becomes 7.2. So, the sum of the remaining 5 numbers is 5 * 7.2 = 36.
To find the discarded number x, we can subtract the sum of the remaining 5 numbers from the sum of the original 6 numbers:
51 - 36 = 15
Therefore, the discarded number is 15.
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