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

It is currently 15 Dec 2019, 03:02

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The average of seven numbers is 20. The average of the first four numb

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59727
The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 25 Sep 2018, 04:53
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:42) correct 23% (02:02) wrong based on 71 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4155
Location: Canada
Re: The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 25 Sep 2018, 07:29
1
Top Contributor
Bunuel wrote:
The average of seven numbers is 20. The average of the first four numbers is 19 and that of the last four is 24. What is the value of the fourth number?

(A) 23
(B) 25
(C) 32
(D) 43
(E) 63


Let the 7 numbers be {a, b, c, d, e, f, g}

The average of seven numbers is 20
We can write: (a + b + c + d + e + f + g)/7 = 20
Multiply both sides by 7 to get: a + b + c + d + e + f + g = 140 [equation #1]

The average of the first four numbers is 19
So, (a + b + c + d)/4 = 19
Multiply both sides by 4 to get: a + b + c + d = 76 [equation #2]

The average of the last four numbers is 24
So, (e + f + g + d)/4 = 24
Multiply both sides by 4 to get: e + f + g + d = 96 [equation #3]

What is the value of the fourth number?
We want to find the value of d

Take the following two equations:
a + b + c + d = 76 [equation #2]
e + f + g + d = 96 [equation #3]

Add them to get: a + b + c + 2d + e + f + g = 172 [equation #4]
Notice that this equation looks A LOT like the first equation.

In fact, we have:
a + b + c + 2d + e + f + g = 172 [equation #4]
a + b + c + d + e + f + g = 140 [equation #1]
Subtract the bottom equation from the top equation to get: d = 32

Answer: C

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1217
The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 25 Sep 2018, 17:09
Bunuel wrote:
The average of seven numbers is 20. The average of the first four numbers is 19 and that of the last four is 24. What is the value of the fourth number?

(A) 23
(B) 25
(C) 32
(D) 43
(E) 63


sum of first four numbers=19*4=76
sum of last four numbers=24*4=96
sum of seven numbers=20*7=140
76+96-140=32
C
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 27 Sep 2018, 17:32
Bunuel wrote:
The average of seven numbers is 20. The average of the first four numbers is 19 and that of the last four is 24. What is the value of the fourth number?

(A) 23
(B) 25
(C) 32
(D) 43
(E) 63


The sum of all 7 numbers is 20 x 7 = 140.

The sum of the first 4 numbers is 4 x 19 = 76.

The sum of the last 4 numbers is 4 x 24 = 96.

Note that when the sum of the first 4 numbers and the sum of the last 4 numbers are added together, the result will be the sum of the 7 numbers plus the 4th number, which has been added twice since it belongs to both the sums.

So the 4th number is 96 + 76 - 140 = 32.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
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.

Manager
Manager
avatar
S
Joined: 31 Oct 2018
Posts: 77
Location: India
Re: The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 28 May 2019, 20:47
Lets consider 7 no.s to be a b c d e f g


Now a b c d should have a value of 19 each, and d e f g should have a value of 24 each

Point 1 --Now, we can see that there is a loss of 3 because of a b c. (19 - 20) * 3 = -3
Also we can see the surplus of 12 because of e f g . (24 - 20) * 3 = 12

Point 2 -- Finally, D has both a loss of 1 and surplus of 4.

Hence the value of D = Avg Value of D - (loss of -1(from point 2)) + (surplus of 4 (from point 2)) - 3 (point 1)+ 12 (point 1)

therefore d = 20 - 1 + 4 -3 + 12 = 32

Bunuel wrote:
The average of seven numbers is 20. The average of the first four numbers is 19 and that of the last four is 24. What is the value of the fourth number?

(A) 23
(B) 25
(C) 32
(D) 43
(E) 63
CrackVerbal Representative
User avatar
B
Joined: 13 May 2019
Posts: 69
Re: The average of seven numbers is 20. The average of the first four numb  [#permalink]

Show Tags

New post 28 May 2019, 22:55
Average of the 7 numbers = 20

Sum of the 7 numbers = 20*7 = 140

Average of 1st four numbers = 19

Sum of first four numbers = 19*4 = 76

Average of last four numbers = 24

Sum of last 4 numbers = 24*4 = 96

If we sum up the first four numbers and last four numbers, then the sum will be equal to the sum of 7 numbers + the 4th number, as the 4th number will be added twice.

76 + 96 = 140 + 4th number

4th number = 172 - 140 = 32

The correct answer is C
_________________
GMAT Club Bot
Re: The average of seven numbers is 20. The average of the first four numb   [#permalink] 28 May 2019, 22:55
Display posts from previous: Sort by

The average of seven numbers is 20. The average of the first four numb

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne