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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

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

by BTGModeratorVI » Tue Mar 03, 2020 6:43 am

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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

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Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2020 6:43 am

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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:

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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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