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# If y is 4 greater than one-fourth of x, and x ≠ 0

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If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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25 Jun 2018, 12:59
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Difficulty:

35% (medium)

Question Stats:

72% (01:39) correct 28% (02:04) wrong based on 71 sessions

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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

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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25 Jun 2018, 13:13
Given
y=x/4 +4

we need y/x in term of x
so lets divide the given equation by x

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

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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25 Jun 2018, 13:14
y=(x/4)+4
So, y=(x+16)/4

Now divide by x on both sides
y/x = (x+16)/4x

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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26 Jun 2018, 01:04

Solution

Given:
• y is 4 greater than one-fourth of x
• x ≠ 0

To find:
• The ratio of y to x, in terms of x

Approach and Working:
As per the given relation, we can write:
• $$y = 4 + \frac{x}{4} = \frac{16 + x}{4}$$

Therefore, the ratio of y to x is:
• $$\frac{y}{x} = \frac{16+x}{4x} = \frac{x + 16}{4x}$$

Hence, the correct answer is option C.

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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27 Jun 2018, 07:34
Hey Guys

Might be a silly doubt but here it is

I assumed value of y=20. therefore x=64

Now, y/x = 5/16

So even I substituted the values in option C. I don't get 5/16. Where am I going wrong?
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If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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27 Jun 2018, 07:39
pikolo2510 wrote:
Hey Guys

Might be a silly doubt but here it is

I assumed value of y=20. therefore x=64

Now, y/x = 5/16

So even I substituted the values in option C. I don't get 5/16. Where am I going wrong?

Hey pikolo2510

Option C is $$\frac{x + 16}{4x} = \frac{64 + 16}{4*64} = \frac{80}{4*64} = \frac{5}{16}$$

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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27 Jun 2018, 07:48
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

Take value of X but keep it simple, so X =4..
Y =4+4*1/4=5
So y/X = 5/4

Check the values of choices by substituting X=4..
A,B and E can be eliminated as they will clearly not leave any denominator..
C =(4+16)/(4*4)=20/16=5/4
D=(4*4+1)/4

So Ans C
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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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27 Jun 2018, 07:51
pushpitkc wrote:
pikolo2510 wrote:
Hey Guys

Might be a silly doubt but here it is

I assumed value of y=20. therefore x=64

Now, y/x = 5/16

So even I substituted the values in option C. I don't get 5/16. Where am I going wrong?

Hey pikolo2510

Option C is $$\frac{x + 16}{4x} = \frac{64 + 16}{4*64} = \frac{80}{4*64} = \frac{5}{16}$$

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0  [#permalink]

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30 Jun 2018, 07:13
Top Contributor
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

I typically prefer an algebraic approach, but 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.

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Re: If y is 4 greater than one-fourth of x, and x ≠ 0 &nbs [#permalink] 30 Jun 2018, 07:13
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