Explanation

Say that x = 2. That means that over 60 percent of the numbers are less than 2. If you consider there are an infinite number of numbers between 0 and 2 when you use decimals. So the 60 percent would look like (0.1, 0.12, 0.1579, 0.2, 0.29,etc).

Say that y = 1. That would mean 40% of the numbers are between 0 and 1, and another 20% are between 1 and 2 to satisfy both y = 1 and x = 2. So x – y = 2 – 1 = 1. In this case, Quantity B is greater.

But what if x were at the other extreme of the range, such as x = 48? If we keep y = 1, that would mean that 40% of the numbers were between 0 and 1 and the next 20% were between 1 and 48 (and the remaining 40% were between 48 and 50). Now x – y = 48 – 1 = 47. In this case, Quantity A is greater. Thus, the relationship cannot be determined.
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One can even consider x and y to be only INTEGER value and still solve it.Given list of 100 numbers, x is greater than 60% of the numbers
60% of 100 = 60 numbers. So x is greater than 60 numbers. Means x ranges from 61 - 100
y is greater than 40% of the numbers
40% 0f 100 = 40 numbers. So y is greater than 40 numbers. Means y ranges from 41 - 100
Since there is an overlap among these two values, we cannot predict whether x-y is going to be greater than or less than 20.
If x=67 and y=97, then B>A OR
If x=97 and y=67, then A>B
SO answer is D

GIVEN: T is a list of 100 different numbers

GIVEN: x is greater than 60 percent of the numbers in T
So, if we were to list all 100 numbers in ASCENDING order, x would be the 61st value in the list (so that 60 of the 100 numbers are less than x)

GIVEN: y is greater than 40 percent of the numbers in T
So, if we were to list all 100 numbers in ASCENDING order, y would be the 41st value in the list (so that 40 of the 100 numbers are less than y)

We want to compare x - y with 20

Consider these two possible cases:

case i: The numbers, when listed in ASCENDING ORDER are:
0.1, 0.2, 0.3, 0.4, . . . . 4.0, y = 4.1, 4.2, 4.3, . . . . 5.9, 6.0, x = 6.1, 6.2, . . .
In this case, we get:
QUANTITY A: x - y = 6.1 - 4.1 = 2
QUANTITY B: 20
In this case, Quantity B is greater


case ii: The numbers, when listed in ASCENDING ORDER are:
0.1, 0.2, 0.3, 0.4, . . . . 4.0, y = 4.1, 4.2, 4.3, . . . . 5.9, 6.0, x = 40, 40.1, 40.2, 40.3 . . .
In this case, we get:
QUANTITY A: x - y = 40 - 4.1 = 35.9
QUANTITY B: 20
In this case, Quantity A is greater

Answer: D

Cheers,
Brent
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T is a list of 100 different numbers that are greater than 0 and less than 50. The number x is greater than 60% of the numbers in [i]T, and the number y is greater than 40% of the numbers in T.[/i]