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Quantitative Reasoning – Practice – Weighted average of the IQs!

PSA_PRACTICE_QNR22. Two classes took an IQ test. Class A averaged 80 and class B averaged 90. The two classes together averaged 83. What is the ratio of students in class B to A?

A) 8:7
B) 1:1
C) 4:3
D) 3:7
E) Cannot be determined

Ans: Let number of students in Class A and B be ‘a’ and ‘b’ respectively.
Average of class A = 80; sum of the all the scores in Class A = 80*a
Average of class B = 90; sum of the all the scores in Class B = 90*b

Sum of the all the scores in Class A & B = 80*a + 90*b

Also, it is given that the two classes together averaged 83; Sum of the all the scores in Class A & B = 83*(a+b)

80a + 90b= 83a + 83b

=>7b=3a
=>b:a= 3:7. Option d.

We could also approach the question by visualizing that ’80’ and ’90’ are two points at the end of a balance. Had there been equal number of students in both the classes, the average would have been 85 (fulcrum would be in the exact middle of ’80’ & ’90’). But, the fulcrum position is shifted towards class A (average is given as 83) suggesting that number of students in class A is more than that in B. Hence, option A,B,C,E can be ruled out.

PSA_PRACTICE_QNR22_1

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