GreenlightTestPrep wrote:
If 0 < y < x, then which of the following is a possible value of
27x+23y3x+2y?
A) I only
B) II only
C) III only
D) I and II only
E) II and III only
*Kudos for all correct solutions
I'm going to add a few extra steps to my original solution.
First notice that
27x+18y is a multiple of
3x+2y because
27x+18y=9(3x+2y)I'm going to use this fact by taking the expression
27x+23y and rewriting it as
27x+18y+5yWhen we do this we get:
27x+23y3x+2y=27x+18y+5y3x+2yUseful property: a+bc=ac+bcApply the property to split up our fraction as follows:
=27x+18y3x+2y+5y3x+2yRewrite the numerator of the first fraction:
=9(3x+2y)3x+2y+5y3x+2ySimplify the first fraction:
=9+5y3x+2ySince x and y are both POSITIVE, the numerator and denominator of
5y3x+2y will be POSITIVE, which means
5y3x+2y has a POSITIVE value.
This means
9+5y3x+2y will evaluate to be a number that's GREATER THAN 9
So, value I (8.7) is not possibleNow let's take a closer look at
5y3x+2yNotice that
5y3y+2y=5y5y=1 [since the numerator and denominator are EQUAL]However, since we're told that
y<x, we know that
3y+2y<3x+2yThis means
5y3x+2y<1 [since the numerator is LESS THAN the denominator]If
5y3x+2y<1, then we can conclude that
9+5y3x+2y<10So, value III (10.8) is not possibleThis leaves us with value II (9.2), which IS possible.
Answer: B
Cheers,
Brent