The terms of each set above are given in ascending order

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

The terms of each set above are given in ascending order

by BTGModeratorVI » Tue Feb 18, 2020 10:51 am

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Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Manhattan Prep
Answer: B

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Source: Beat The GMAT — Problem Solving | Tue Feb 18, 2020 10:51 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

Re: The terms of each set above are given in ascending order

by Jay@ManhattanReview » Fri Feb 21, 2020 12:20 am

BTGModeratorVI wrote: ↑
Tue Feb 18, 2020 10:51 am
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Manhattan Prep
Answer: B

Median of Set A = (x + 8)/2;
Median of Set B = (y + 9)/2;

=> (x + 8)/2 = (y + 9)/2

x + 8 = y + 9 => y – x = –1

The correct answer: B

Hope this helps!

-Jay
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Manhattan Review

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Re: The terms of each set above are given in ascending order

by Brent@GMATPrepNow » Fri Feb 21, 2020 7:00 am

BTGModeratorVI wrote: ↑
Tue Feb 18, 2020 10:51 am
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Manhattan Prep
Answer: B

Key property: When we have an EVEN number of terms, the median of those terms will be the AVERAGE of the two middlemost terms, when those terms are listed in ascending order

So the median of Set A = (x + 8)/2
And the median of Set B = (y + 9)/2

Since we're told that the two medians are equal, we can write: (x + 8)/2 = (y + 9)/2
Multiply both sides of the equation by 2 to get: x + 8 = y + 9
Subtract x from what sides to get: 8 = y - x + 9
Subtract 9 from both sides to get: -1 = y - x

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Re: The terms of each set above are given in ascending order

by Scott@TargetTestPrep » Tue Sep 08, 2020 9:31 am

BTGModeratorVI wrote: ↑
Tue Feb 18, 2020 10:51 am
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2

Answer: B

Solution:

The median of set A is (x + 8)/2 and the median of set B is (y + 9)/2. Since they two medians are equal, we can create the equation:

(x + 8)/2 = (y + 9)/2

x + 8 = y + 9

-1 = y - x

Answer: B

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