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A very interesting question testing concepts in absolute values, number line, and the meaning of arithmetic mean of a set of numbers. A good question to understand the meaning of the absolute values of the difference between two numbers.
p, q, and r are three points on the real number line where q = .
Quantity A:
Quantity B:
Choice A – Quantity A is greater
Given: q =
Let’s make sense of this information.
Cross multiplying, we get q(p + r) = 2pr
i.e., qp + qr = 2pr
Divide the equation by pqr
+ =
Divide the equation by 2
=
The same inference that we can draw if someone told us that z =
The inference we will draw is that z is the arithmetic mean (average) of x and y.
Using the same logic, we can infer that is the arithmetic mean (average) of and .
If z is the average of x and y, it is evident that z will lie between x and y on the number line.
By the same logic, will lie between and on the number line.
and
If x and y are two points on the number line, what does |x – y| measure?
|x – y| measures the distance between the two points x and y.
Extending that logic, measures the distance between points and
Similarly, quantity B measures the distance between points and
We deduced that lies between and .
Therefore, the distance between and (quantity A) will be greater than the distance between and
Hence, Quantity A is greater than Quantity B
There’s more where this question came from