GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 11:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The mean of three numbers is 10 more than the least of the numbers and

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59587
The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

18 Mar 2019, 02:19
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

65% (03:05) correct 35% (02:52) wrong based on 31 sessions

### HideShow timer Statistics

The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

(A) 5
(B) 20
(C) 25
(D) 30
(E) 36

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

18 Mar 2019, 03:04
Bunuel wrote:
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

(A) 5
(B) 20
(C) 25
(D) 30
(E) 36

a+b+c/3 = 10+a = c-15
b=5
a= m-10
c=m+15
so
m-10+5+m+15 = 3m
10=m
sum
30
IMO D
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4125
The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

Updated on: 18 Mar 2019, 19:57
Top Contributor
Bunuel wrote:
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

(A) 5
(B) 20
(C) 25
(D) 30
(E) 36

Let x, y and z be the 3 numbers such that x ≤ y ≤ z

The median of the three numbers is 5.
So, y = 5

The mean of three numbers is 10 more than the least of the numbers
We can write: (x + 5 + z)/3 = x + 10
Multiply both sides by 3 to get: x + 5 + z = 3x + 30
Subtract 5 from both sides to get: x + z = 3x + 25
Subtract x from both sides to get: z = 2x + 25

The mean of three numbers is 15 less than the greatest.
We can write: (x + 5 + z)/3 = z - 15
Multiply both sides by 3 to get: x + 5 + z = 3z - 45
Subtract 5 from both sides to get: x + z = 3z - 50
Subtract z from both sides to get: x = 2z - 50

What is the value of x + y + z?
We get: x + y + z = (2z - 50) + 5 + 2x + 25
Simplify to get: x + y + z = 2z + 2x - 20
Subtract y and z from both sides to get: y = z + x - 20
Since y = 5, we get: 5 = z + x - 20
Add 20 to both sides: 25 = z + x
Since y = 5, we get: 30 = x + y + z

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 18 Mar 2019, 08:28.
Last edited by GMATPrepNow on 18 Mar 2019, 19:57, edited 1 time in total.
Intern
Joined: 29 May 2018
Posts: 1
Re: The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

18 Mar 2019, 17:17
1
GMATPrepNow wrote:

Multiply both sides by 3 to get: x + 5 + z = 3x + 10

Multiply both sides by 3 to get: x + 5 + z = 3z - 15

Hi, why are you not multiplying the 10 and the -15 by 3 when you are multiplying both sides by 3?
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4125
Re: The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

18 Mar 2019, 19:58
Top Contributor
gmgmgm wrote:
GMATPrepNow wrote:

Multiply both sides by 3 to get: x + 5 + z = 3x + 10

Multiply both sides by 3 to get: x + 5 + z = 3z - 15

Hi, why are you not multiplying the 10 and the -15 by 3 when you are multiplying both sides by 3?

Ugh!
Silly mistakes!
I've edited my response accordingly.

Cheers and thanks,
Brent
_________________
Test confidently with gmatprepnow.com
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

19 Mar 2019, 01:50
1
Bunuel wrote:
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

(A) 5
(B) 20
(C) 25
(D) 30
(E) 36

Simply use the concept of deviation from mean discussed on our blog here:
https://www.veritasprep.com/blog/2012/0 ... eviations/

The least number is 10 less than mean while the greatest is 15 more. To balance out the shortfall with the excess, the third number should be 5 less than mean too.
Since median is 5, it is the middle number. The middle number must be 5 less than mean so mean must be 10.

Hence the other two numbers must be 0 and 25.

Sum of all numbers = 0 + 5 + 25 = 30

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8620
Location: United States (CA)
Re: The mean of three numbers is 10 more than the least of the numbers and  [#permalink]

### Show Tags

19 Mar 2019, 19:06
Bunuel wrote:
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

(A) 5
(B) 20
(C) 25
(D) 30
(E) 36

We can let the least value = a, the middle value = 5, and the greatest value = c, thus:

(a + 5 + c)/3 = 10 + a

a + 5 + c = 30 + 3a

c = 25 + 2a

and

(a + 5 + c)/3 = c - 15

a + 5 + c = 3c - 45

a = 2c - 50

Substituting c = 25 + 2a into a = 2c - 50, we have:

a = 2(25 + 2a) - 50

a = 50 + 4a - 50

-3a = 0

a = 0

So c = 25 + 2(0) = 25, and their sum is 0 + 5 + 25 = 30.

Alternate Solution:

Let m denote the mean. Then, the smallest number is m -10 and the greatest number is m + 15. We are also given that the middle (median) number is 5; thus we can create the equation:

(m - 10 + 5 + m + 15)/3 = m

2m + 10 = 3m

m = 10

Since the mean of the three numbers is 10, the sum is 3 x 10 = 30.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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

Re: The mean of three numbers is 10 more than the least of the numbers and   [#permalink] 19 Mar 2019, 19:06
Display posts from previous: Sort by