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03 Aug 2022, 09:41
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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63% (03:19) correct
37%
(03:45)
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Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
04 Aug 2022, 05:12
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Suraj0184
Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
A 30 second answer:-
The average score in class X is 83. The average score in class Y is 76. The average score of all students in classes X and Y together is 79.
The combined average is closer to average of Y, so the strength of Y>that of X.
The average score of all students in classes Y and Z together is 81. The average of X is 83. So surely Average lies between 81 and 83.
It will be exact 82 when strength of Y+Z is equal to X. But we know that Y>X, so Average would be closer to the average of Y+Z.
Thus, the combined average will be less than 82.
Only A left.
Algebraic
(I) 83X+76Y = 79(Y+X)
4X=3Y…
(II) 76Y+85Z = 81(Y+Z)
4Z=5Y
From above
\(Y=\frac{4X}{3}=\frac{4Z}{5}\) or Z=5X/3
Average = \(\frac{(76Y+83X+85Z)}{(X+Y+Z)}=\frac{(76*\frac{4X}{3} +83x +85*\frac{5X}{3})}{(\frac{4X}{3} +X+\frac{5X}{3})}=\frac{978}{12}=81.5\)
Calculations unlike what you would generally see on GMAT.
You can also do it through ‘Weighted average method.’ But the answer choices will help you get an answer the earliest.
04 Aug 2022, 09:03
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Suraj0184
Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
A. 81.5
B. 82.0
C. 82.5
D. 83.0
E. 83.5
Source : Wizako
I'm certainly a fan of the 30-second version posted by chetan2u and would definitely go that route!!
But if you can't wrap your head around the conceptual method and need more NUMBERS, here's another way to think through the algebraic approach.
Looking at X and Y:
The spread between 83 and 76 is 7 and the average of both combined ends up at 79. That's 4 away from X and 3 away from Y. Y has a heavier weight, so there are more Y's than there are X's and the ratio is 4:3.
X:Y = 3:4
Looking at Y and Z:
The spread between 76 and 85 is 9 and the average of both combined ends up at 81. That's 5 away from Y and 4 away from Z. Z has a heavier weight, so there are more Z's than there are Y's and the ratio is 5:4.
Y:Z = 4:5
3X:4Y:5Z
\(\frac{3(83)+4(76)+5(85)}{3+4+5} = \frac{249+304+425}{12} = \frac{978}{12} = 81.5\)
