Problem Solving

If y is 4 greater than one-fourth of x, and x ≠ 0, what is the ratio of y to x in terms of x?

A) (x² + 16x)/4
B) (4x + 16)/x
C) (x + 16)/4x
D) (4x + 1)/x
E) (x + 16)/x

Answer: C
Difficulty level: 550-600
Source: www.gmatprepnow.com

*I'll post a solution in 2 days

Brent@GMATPrepNow wrote:If y is 4 greater than one-fourth of x, and x ≠ 0, what is the ratio of y to x in terms of x?

A) (x² + 16x)/4
B) (4x + 16)/x
C) (x + 16)/4x
D) (4x + 1)/x
E) (x + 16)/x

We see that y = (1/4)x + 4 = x/4 + 16/4 = (x + 16)/4, so

y/x = [(x + 16)/4]/x = (x + 16)/4x

Answer: C

Brent@GMATPrepNow wrote:If y is 4 greater than one-fourth of x, and x ≠ 0, what is the ratio of y to x in terms of x?

A) (x² + 16x)/4
B) (4x + 16)/x
C) (x + 16)/4x
D) (4x + 1)/x
E) (x + 16)/x

Answer: C
Difficulty level: 550-600
Source: www.gmatprepnow.com

*I'll post a solution in 2 days

The solutions above demonstrate an algebraic approach.
We can also solve the question using the INPUT-OUTPUT approach.

Let's find values for x and y that satisfy the given information (y is 4 greater than one-fourth of x)
A nice pair of values is x = 4 and y = 5
When we use these values, the answer to our question ("what is the ratio of y to x in terms of x? ") is 5/4

In other words, when we INPUT x = 4, the OUTPUT is 4/5
So, now take each answer choice, replace x with 4 and see which one yields an OUTPUT of 5/4

A) [4² + 16(4)]/4 = 20. No good. We want an output of 5/4. ELIMINATE.
B) [4(4) + 16]/4 = 8. No good. We want an output of 5/4. ELIMINATE.
C) (4 + 16)/4(4) = 20/16 = 5/4. Great! KEEP
D) [4(4) + 1]/4 = 17/4. No good. We want an output of 5/4. ELIMINATE.
E) (4 + 16)/4 = 5. No good. We want an output of 5/4. ELIMINATE.

Answer: C

Cheers,
Brent