The average (arithmetic mean) of 6 numbers is 8.5.

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

The average (arithmetic mean) of 6 numbers is 8.5.

by M7MBA » Sun Dec 17, 2017 8:46 am

Timer

00:00

Your Answer

Global Stats

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 OA is E.

How can I know the value of the discarded number without knowing the rest of the numbers? Experts, can you help me here? Thanks in advanced.

Quote

Source: Beat The GMAT — Problem Solving | Sun Dec 17, 2017 8:46 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 17, 2017 9:01 am

M7MBA wrote: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

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sun Dec 17, 2017 9:02 am

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 OA is E.

How can I know the value of the discarded number without knowing the rest of the numbers? Experts, can you help me here? Thanks in advanced.

Hi M7MBA,
Let's take a look at your question.

The average (arithmetic mean) of 6 numbers is 8.5.
We know that,
$$Average\ =\ \frac{\text{Sum of Quantities}}{\text{Number of Quantities}}$$
$$8.5=\ \frac{\text{Sum of 6 numbers}}{6}$$
$$\text{Sum of 6 numbers}=6\times8.5$$
$$\text{Sum of 6 numbers}=51 ... (i)$$

When one number is discarded, the average of the remaining numbers becomes 7.2,
$$7.2=\ \frac{\text{Sum of 5 numbers}}{5}$$
$$\text{Sum of 5 numbers}=5\times7.2$$
$$\text{Sum of 5 numbers}=36 ... (ii)$$

We can now find the discarded number by subtracting the sum of 5 numbers from the sum of 6 numbers.
$$\text{Discarded number}\ =\ \text{Sum of 6 numbers}-\text{Sum of 5 numbers}$$
$$\text{Discarded number}\ =\ 51-36=15$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 16, 2019 10:23 am

M7MBA wrote: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 OA is E.

How can I know the value of the discarded number without knowing the rest of the numbers? Experts, can you help me here? Thanks in advanced.

Since the average of 6 numbers is 8.5, the sum of those numbers is 6 x 8.5 = 51.

We can let x = the discarded number, and we can create the following equation:

(51 - x)/5 = 7.2

51 - x = 36

x = 15

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]