GreenlightTestPrep wrote:

If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?

A) I only

B) II only

C) III only

D) I and II only

E) II and III only

*Kudos for all correct solutions

One approach is to simplify the expression.

(27x + 23y)/(

3x + 2y) = (

27x + 18y +

5y)/(

3x + 2y)

= (

27x + 18y)/(

3x + 2y) + (

5y)/(

3x + 2y)

=

9 + (

5y)/(

3x + 2y)

First recognize that, since x and y are both POSITIVE, the numerator and denominator of (

5y)/(

3x + 2y) will be POSITIVE, which means (

5y)/(

3x + 2y) is equal to a POSITIVE value.

This means that

9 + (

5y)/(

3x + 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 (

5y)/(

3x + 2y)

Notice that (

5y)/(

3y + 2y) = 5y/5y = 1

[since the numerator and denominator are EQUAL]However, since we're told that y < x, we know that

3y + 2y <

3y + 2xThis means that (

5y)/(

3x + 2y) < 1,

[since the numerator is LESS THAN the denominator]If (

5y)/(

3x + 2y) < 1, then we can conclude that

9 + (

5y)/(

3x + 2y) < 10

So, value III (10.8) is not possibleThis leaves us with value II (9.2), which IS possible.

Answer:

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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