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If x, y, and k are positive and x is less than y, then (x+k)/(y+k) is

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Re: If x, y, and k are positive and x is less than y, then (x+k)/(y+k) is

by swerve » Tue Mar 03, 2020 9:55 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:43 am
 If x, y, and k are positive and x is less than y, then (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

Answer: B
Source: Official Guide
\(x<y\)

So, \(\dfrac{x}{y} < 1\)

If \(x=1\) and \(y=2\)

\(\dfrac{x}{y}=\dfrac{1}{2}=0.5\)

Now, if we increase both the numerator and denominator by the same number then the result must be increased.
\(\dfrac{1+1}{2+1}=\dfrac{2}{3}=0.67\)

Therefore, the correct answer is B
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Re: If x, y, and k are positive and x is less than y, then (x+k)/(y+k) is

by Brent@GMATPrepNow » Tue Mar 03, 2020 10:31 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:43 am
 If x, y, and k are positive and x is less than y, then (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

Answer: B
Source: Official Guide
Key concept:
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Since x < y, we know that x/y is less than 1

So, (x + k)/(y + k) will be closer to 1 than x/y is.

In other words, (x + k)/y + k must be greater than x/y

Answer: B

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Re: If x, y, and k are positive and x is less than y, then (x+k)/(y+k) is

by Scott@TargetTestPrep » Wed Mar 11, 2020 9:37 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:43 am
 If x, y, and k are positive and x is less than y, then (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

Answer: B
Source: Official Guide
Solution:

Since x is less than y and x and y are both positive, x/y is between 0 and 1. Since k is also positive, then (x + k)/(y + k) will still be between 0 and 1 but it’s closer to 1 than x/y. Therefore, (x + k)/(y + k) is greater than x/y.

Alternate Solution:

Let’s use numbers to make the problem more understandable. Let’s let x = 3, y = 4, and k = 10. We see that

x/y = 3/4

and

(x + k) / (y + k) = (3 + 10) / (4 + 10) = 13/14

We see that 13/14 is greater than 3/4, so choice B is correct.

The rule is that if a positive constant is added to both the numerator and the denominator of a positive proper fraction, the value of the fraction increases (i.e., gets closer to 1).

Answer: B

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