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Math Expert V
Joined: 02 Sep 2009
Posts: 55729
If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:29) correct 32% (01:27) wrong based on 249 sessions

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If x, y, and k are positive and x is less than y, then $$\frac{x + k}{y + k}$$ is

A. 1
B. greater than x/y
C. equal to x/y
D. less than x/y
E. less than x/y or greater than x/y, depending on the value of k

PS87502.01
Quantitative Review 2020 NEW QUESTION

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CEO  V
Joined: 12 Sep 2015
Posts: 3786
Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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1
Top Contributor
Bunuel wrote:
If x, y, and k are positive and x is less than y, then $$\frac{x + k}{y + k}$$ is

A. 1
B. greater than x/y
C. equal to x/y
D. less than x/y
E. less than x/y or greater than x/y, depending on the value of k

PS87502.01
Quantitative Review 2020 NEW QUESTION

Key concept (also covered in video below): Since x < y, we know that x/y is less than 1

So, $$\frac{x + k}{y + k}$$ will be closer to 1 than x/y is.

In other words, $$\frac{x + k}{y + k}$$ must be greater than x/y

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

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CEO  P
Joined: 18 Aug 2017
Posts: 3897
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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Bunuel wrote:
If x, y, and k are positive and x is less than y, then $$\frac{x + k}{y + k}$$ is

A. 1
B. greater than x/y
C. equal to x/y
D. less than x/y
E. less than x/y or greater than x/y, depending on the value of k

PS87502.01
Quantitative Review 2020 NEW QUESTION

let x=5 ,y=6 and k =1
solve
$$\frac{x + k}{y + k}$$ = 6/7
and x/y=5/6
we see that 6/7>5/6
IMO B
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Manager  B
Joined: 25 Sep 2018
Posts: 60
Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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Bunuel wrote:
If x, y, and k are positive and x is less than y, then $$\frac{x + k}{y + k}$$ is

A. 1
B. greater than x/y
C. equal to x/y
D. less than x/y
E. less than x/y or greater than x/y, depending on the value of k

PS87502.01
Quantitative Review 2020 NEW QUESTION

x<y
So, x/y= less than 1
If x=1
y=2
x/y=1/2=.5

Now, if we increase both numerator and denominator by same number then result must be increased.
1+1/2+1=2/3=.67

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Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6589
Location: United States (CA)
Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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Bunuel wrote:
If x, y, and k are positive and x is less than y, then $$\frac{x + k}{y + k}$$ is

A. 1
B. greater than x/y
C. equal to x/y
D. less than x/y
E. less than x/y or greater than x/y, depending on the value of k

PS87502.01
Quantitative Review 2020 NEW QUESTION

When a positive constant is added to the numerator and denominator of a positive fraction, the resulting value of the fraction increases. For example, to the fraction 1/6, add 4 to both the numerator and denominator, obtaining 5/10, which is greater than 1/6.

Thus, (x + k)/(y + k) is greater than x/y.

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Scott@TargetTestPrep.com

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CrackVerbal Quant Expert B
Joined: 23 Apr 2019
Posts: 15
Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)  [#permalink]

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One way to solve this question is to know that if you add the same constant to the numerator and denominator of a positive fraction, then the value of the fraction increases and will always tend to 1. But even if we did not know this, we can easily solve the question by using the answer choices. Remember this is a PS question, so there have to be only ONE possible answer.

We have x, y and k to be positive and x < y. The question asks us for (x + k)/(y + k)

A. If (x + k)/(y + k) = 1, then x = y. This is not possible since x < y
B. If (x + k)/(y + k) > x/y, cross multiplying (since x and y are positive), we get xy + yk > xy + xk. Cancelling xy on both sides, we get y > x or x < y. So B works.

Hope this helps!

CrackVerbal Quant Expert Re: If x, y, and k are positive and x is less than y, then (x + k)/(y + k)   [#permalink] 23 May 2019, 21:49
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