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# In the above sequence, x and y are integers, and the numbers are arran

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Math Expert
Joined: 02 Sep 2009
Posts: 60484
In the above sequence, x and y are integers, and the numbers are arran  [#permalink]

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02 Dec 2019, 00:42
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Difficulty:

45% (medium)

Question Stats:

68% (01:48) correct 33% (01:15) wrong based on 40 sessions

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10, x, 30, y, 50

In the above sequence, x and y are integers, and the numbers are arranged in increasing order. What is the value of y - x ?

(1) The median of the sequence is equal to the mean.

(2) $$\frac{y+x}{2}=30$$

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Re: In the above sequence, x and y are integers, and the numbers are arran  [#permalink]

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02 Dec 2019, 02:32
Clearly E ;
as both 1 &2 give same info

Bunuel wrote:
10, x, 30, y, 50

In the above sequence, x and y are integers, and the numbers are arranged in increasing order. What is the value of y - x ?

(1) The median of the sequence is equal to the mean.

(2) $$\frac{y+x}{2}=30$$

Are You Up For the Challenge: 700 Level Questions
Intern
Joined: 16 Nov 2019
Posts: 1
Re: In the above sequence, x and y are integers, and the numbers are arran  [#permalink]

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02 Dec 2019, 05:09
Statement 1 tells us that Mean = Median ie 30 = 10+X+30+Y+50/5 as they are arranged in increasing order

150 = 10+X+30+Y+50

150 = X+Y+90

X+Y = 60 but does not give any value of Y-X.

Statement 2 tells us the half of X+Y = 30 but does not give any value of Y-X either.

So, ans is E.
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Re: In the above sequence, x and y are integers, and the numbers are arran  [#permalink]

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02 Dec 2019, 05:44
1
The answer is A.
Quote:
(1) The median of the sequence is equal to the mean.

The fact that med = mean implies that we have an arithmetic progression.
As we have a couple of known terms, so we can easily deduct "d" - difference of arithmetic progression:
a3= a1 + 2d = 10 + 2d = 30
a5=a1 + 4d = 10 + 4d = 50

d=10.
So x(a2)=a1+d=10+10=20; y(a4)=a1+3d=10+30=40

y-x=40-20=20.
Sufficient.

(2) (y+x)/2=30
From this statement we only know that x+y = 60. There are can be more than one pair of x and y that satisfies the statetment:
x=11 and y = 49 > y-x=38
x=12 and y=48 > y-x=36
Not sufficient.
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Joined: 08 Jul 2017
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Re: In the above sequence, x and y are integers, and the numbers are arran  [#permalink]

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06 Dec 2019, 03:37
Bunuel wrote:
10, x, 30, y, 50

In the above sequence, x and y are integers, and the numbers are arranged in increasing order. What is the value of y - x ?

(1) The median of the sequence is equal to the mean.

(2) $$\frac{y+x}{2}=30$$

Are You Up For the Challenge: 700 Level Questions

when mean =median, then series is in AP. that is why we can determine X & Y . kindly correct me
Re: In the above sequence, x and y are integers, and the numbers are arran   [#permalink] 06 Dec 2019, 03:37
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# In the above sequence, x and y are integers, and the numbers are arran

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