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

Question

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

BrentGMATPrepNow · Answer

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

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

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

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    
e + f + g +  d  = 96

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

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

Answer: C

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

gracie · Answer

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

ScottTargetTestPrep · Answer

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

btrg · Answer

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

AyushCrackVerbal · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards