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The average of seven numbers is 20. The average of the first four numb
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24 Oct 2023, 02:20
24 Oct 2023, 02:20
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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
(A) 23
(B) 25
(C) 32
(D) 43
(E) 63
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: The average of seven numbers is 20. The average of the first four numb
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24 Oct 2023, 09:03
24 Oct 2023, 09:03
1
Let the numbers be A,B,C,D,E,F,G. and their average is 20 so the total sum of these numbers would be 20*7=140 (averaging them would mean 140/7=20)
Now for the first four numbers A,B,C,D the average is 19 so their total sum would be 19*4=76
For the last four numbers D,E,F,G the average is 24 so their total sum would be 24*4=96
Now If we sum these two quantities we would get the sum of (A,B,C,D)+(D,E,F,G)=76+96=172
That is A+B+C+2D+E+F+G=172
But we know from the first line that the sum of all numbers is A+B+C+D+E+F+G=140
Subtracting this from the previous equation would mean (A+B+C+2D+E+F+G)-(A+B+C+D+E+F+G)=172-140 = D=32
Now for the first four numbers A,B,C,D the average is 19 so their total sum would be 19*4=76
For the last four numbers D,E,F,G the average is 24 so their total sum would be 24*4=96
Now If we sum these two quantities we would get the sum of (A,B,C,D)+(D,E,F,G)=76+96=172
That is A+B+C+2D+E+F+G=172
But we know from the first line that the sum of all numbers is A+B+C+D+E+F+G=140
Subtracting this from the previous equation would mean (A+B+C+2D+E+F+G)-(A+B+C+D+E+F+G)=172-140 = D=32
gmatclubot
Re: The average of seven numbers is 20. The average of the first four numb [#permalink]
24 Oct 2023, 09:03
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