The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?

12

14

15

16

17

OAB

## The average (arithmetic mean) of four distinct positive inte

##### This topic has expert replies

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**15003**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1265 members**GMAT Score:**770

Let the 4 different positive integers be A, B, C, and D such that A < B < C < Dguerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?

12

14

15

16

17

OAB

*The average (arithmetic mean) of four distinct positive integers is 10*

So, (A+B+C+D)/4 = 10

This means A+B+C+D = 40

*The average of the smaller two of these four integers is 8*

So, the average of A and B is 8

In other words, (A+B)/2 = 8

So, A+B = 16

Since we already know that A+B+C+D = 40, we can replace A+B with 16 to get:

16+C+D = 40

So, C + D = 24

We want to maximize the value of D. To do this, we need to minimize the value of C.

Also, since B < C, we want to minimize the value of B.

Since A+B = 16, the smallest possible value of B is 9.

So, we get

**A = 7**

**B = 9**

So,

**C = 10**is the smallest we can make C

This means that

**D =**[spoiler]

**14**[/spoiler]

Answer = B

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

Watch these

And check out these

**If you enjoy my solutions, I think you'll like my GMAT prep course**Watch these

**video reviews**of my courseAnd check out these

**free resources**- GMATGuruNY
- GMAT Instructor
**Posts:**15521**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1894 members**GMAT Score:**790

Sum = number * average.guerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?

12

14

15

16

17

OAB

Since the average of the 4 integers is 10, their sum = 4*10 = 40.

In ascending order, let the 4 integers = A+B+C+D.

Since A+B+C+D = 40, we get:

D = 40 - (A+B+C).

To MAXIMIZE the value of D, we must MINIMIZE the value of A+B+C.

To minimize the value of C, we must minimize the value of B.

Since the average of A and B is 8, their sum = 2*8 = 16.

Thus, the least option B is 9:

A+B = 7+9.

Thus, the least option for C is 10.

Thus:

Greatest possible value for D = 40 - (A+B+C) = 40 - (7+9+10) = 14.

The correct answer is B.

Mitch Hunt

Private Tutor for the GMAT and GRE

GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at GMATGuruNY@gmail.com.

Student Review #1

Student Review #2

Student Review #3

Private Tutor for the GMAT and GRE

GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at GMATGuruNY@gmail.com.

Student Review #1

Student Review #2

Student Review #3

- faraz_jeddah
- Master | Next Rank: 500 Posts
**Posts:**358**Joined:**18 Apr 2013**Location:**Jeddah, Saudi Arabia**Thanked**: 42 times**Followed by:**7 members**GMAT Score:**730

Brent how can we assume A < B < C < DBrent@GMATPrepNow wrote:Let the 4 different positive integers be A, B, C, and D such that A < B < C < Dguerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?

12

14

15

16

17

OAB

The average (arithmetic mean) of four distinct positive integers is 10

So, (A+B+C+D)/4 = 10

This means A+B+C+D = 40

The average of the smaller two of these four integers is 8

So, the average of A and B is 8

In other words, (A+B)/2 = 8

So, A+B = 16

Since we already know that A+B+C+D = 40, we can replace A+B with 16 to get:

16+C+D = 40

So, C + D = 24

We want to maximize the value of D. To do this, we need to minimize the value of C.

Also, since B < C, we want to minimize the value of B.

Since A+B = 16, the smallest possible value of B is 9.

So, we getA = 7

B = 9

So,C = 10is the smallest we can make C

This means thatD =[spoiler]14[/spoiler]

Answer = B

Cheers,

Brent

The question does not tell us that they are arranged in ascending order.

The 4 numbers could be - 1 15 7 17 which would make 17 the max value.

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**15003**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1265 members**GMAT Score:**770

We're told that the 4 integers are distinct, which means no two values are the same.faraz_jeddah wrote: Brent how can we assume A < B < C < D

The question does not tell us that they are arranged in ascending order.

The 4 numbers could be - 1 15 7 17 which would make 17 the max value.

So, one of them will be the smallest, one of them will be the second smallest, one of them will be the second biggest, one of them will be the biggest. To make things easier to discuss, I named these values A, B, C and D.

The example you give, {1 15 7 17} does not meet the condition that "If the average of the smaller two of these four integers is 8." In your example, the two smallest integers are 1 and 7, so their average is 4.

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

Watch these

And check out these

**If you enjoy my solutions, I think you'll like my GMAT prep course**Watch these

**video reviews**of my courseAnd check out these

**free resources**- faraz_jeddah
- Master | Next Rank: 500 Posts
**Posts:**358**Joined:**18 Apr 2013**Location:**Jeddah, Saudi Arabia**Thanked**: 42 times**Followed by:**7 members**GMAT Score:**730

### GMAT/MBA Expert

- Scott@TargetTestPrep
- GMAT Instructor
**Posts:**5549**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**24 members

**Solution:**

Since the sum of the four distinct integers is 10 x 4 = 40 and the sum of the two smallest integers is 8 x 2 = 16, the sum of the largest two integers is 40 - 16 = 24. Since we want the maximum possible value of the largest integer, we can let the second largest integer be as small as possible. The second integer can’t be 9; otherwise, the sum of the two smallest integers would be at most 7 + 8 = 15 (recall that all the integers are distinct). However, if the second smallest integer is 10 (and the two smallest integers are 7 and 9), the largest integer will then be 24 - 10 = 14.

**Answer: B**

**Scott Woodbury-Stewart**

Founder and CEO

scott@targettestprep.com

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews