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# Set X consists of seven consecutive integers, and set Y

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Manager
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Set X consists of seven consecutive integers, and set Y [#permalink]

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11 May 2011, 18:17
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55% (hard)

Question Stats:

48% (01:13) correct 52% (01:52) wrong based on 33 sessions

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Set X consists of seven consecutive integers, and set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y.
(2) The median of the numbers in set Y is 0.

OPEN DISCUSSION OF THIS QUESTION IS HERE: set-x-consists-of-seven-consecutive-integers-and-set-y-128503.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Jul 2016, 02:32, edited 1 time in total.
Renamed the topic and edited the question.

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Director
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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11 May 2011, 19:18
Evaluating 2) First. The mean of the set Y is known but the median of set X is unknown.

S2 also tells us that there are equal number of +ve and -ve numbers in set Y. But it is insufficient.

S1 Gives no information about the median of Y. Insufficient

1) + 2)

Sufficient. The only way to get the sum equal when X and Y have consecutive integers is to "symmetric" about the zero. Hence we are sure that median is zero for both sets. Sufficient

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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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11 May 2011, 21:03
(1)

The sum of the numbers in set X is equal to the sum of the numbers in set Y when the following is true:

X = {-2,-1,0,1,2}

Y = {-4,-3,-2,-1,0,1,2,3,4}

X = {6,7,8,9,10,11,12} => Sum = 63, median = 9

Y = {3,4,5,6,7,8,9,10,11} => Sum = 63, median = 7

Not Sufficient

(2)

Insufficient as we don't know about X

(1) + (2)

Sufficient.

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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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11 May 2011, 22:26
taking LCM of 9 and 7 = 63
Sum = 63 | 0

a. Sum = 63 for positive sets X|Y medians of X|Y = 7 and 9
for negative sets X|y medians of X|Y = -7 and -9

Sum = 0 both sets X|Y have medians = 0 as 7* (median)= 9*(median) = 0

Not sufficient.

b Set Y has median = 0 doesn't mean Set X will have the same median for different sets of consecutive integers. Not sufficient.

a+b Sum = 0, and median of set Y = 0 gives the same median for set X too.

Hence C.
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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11 May 2011, 23:48
fanatico wrote:
Set X consists of seven consecutive integers, and set Y consists
of nine consecutive integers. Is the median of the numbers in
set X equal to the median of the numbers in set Y ?
(1) The sum of the numbers in set X is equal to the sum of
the numbers in set Y.
(2) The median of the numbers in set Y is 0.

For set of consecutive integers Median=Mean.
Mean of 7 consecutive integer = M7= Sum of 7 consecutive integers (S7) / 7
Mean of 9 consecutive integer = M9= Sum of 9 consecutive integers (S9) / 9
Question: M7=M9?

1) S7=S9. M7=S7/7 and M9=S9/9 IS M7=M9? Cannot say even if S7=S9. Take S7=S9=63. Different values of M7 and M9. Insufficient.

2) M9 = 0. We don't know M7. Insufficient.

Together, M9=0. Also, M9=S9/9. Hence S9=0. As S7=S9, S7=0. Hence M7=0/7 and M9=0/9. M7=M9.
Sufficient.

OA C.
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Manager
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 08:29
Set X consists of seven consecutive integers, and set Y consists
of nine consecutive integers. Is the median of the numbers in
set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of
the numbers in set Y.
(2) The median of the numbers in set Y is 0.

Kudos [?]: 94 [0], given: 7

Senior Manager
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 09:05
Statement 2: Does not talk about Set X: Not Sufficient
Statement 1: I see only one possibility for set X and Y
X= {-3,-2,-1,0,1,2,3}
Y={-4,-3,-2,-1,0,1,2,3, 4}
0 being the median for both. Sufficient

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Senior Manager
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 10:07
dreambeliever wrote:
Set X consists of seven consecutive integers, and set Y consists
of nine consecutive integers. Is the median of the numbers in
set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of
the numbers in set Y.
(2) The median of the numbers in set Y is 0.

1- Insufficient

There are 7 consecutive integers in X. Lets say the smallest x. The others will be x+1...x+6
There are 9 consecutive integers in Y. Lets say the smallest y. The others will be y+1...y+8

Sum of X = 7x+21= 7.(x+3)
Sum of Y = 9y+36 =9.(y+4)

if Sum of X = Sum of Y then makes 7(x+3)=9(y+4)..................(1)
median of X = x+3
median of Y = y+4

if median of X = median of Y then 7(x+3) must be equal to 9 (x+3) it is possible in only one case that is x=-3.

So we do not infer from this statement that median of x is equal to median of y.

2) we do not know anything about X

getting them together
we see that y+4= 0, so y = -4
and total of them are 0
and if total of X = 0 and X consists of 7 consequtive integers, X must be -3,..0,..3
So medians are equal

D

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Manager
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 10:35
thanks guys!
Ans = b

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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 11:09
dreambeliever wrote:
thanks guys!
Ans = b

Let set X be (a-3,a-2,......a+3) and set Y be (b-4,b-3,....b+4)
S1:The sum of the numbers in set X is equal to the sum of
the numbers in set Y.

So we have 7a = 9b. Now this is possible if
a=b=0 or if a=9 and b=7. Insufficient. Median may be same or different.

S2: The median of the numbers in set Y is 0. i.e b=0. We do not have any data on the set X. Hence Median may be same or different.

S1 and S2: Sufficient. a=b=0 Median are same sufficient.

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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 13:03
I think C is the answer

Posted from my mobile device

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Senior Manager
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 16:52
I was freaking out while scrolling down this thread....B, B and than OA was C..I was relieved.

Cheers!
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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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04 Dec 2011, 23:31
Is using Algebra is the best way to deal with SET problem? i was using picking number and had tough to find sets for which the sum is equal (for this problem).
Experts: any specific guidelines for this sort of set problem?

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Re: Set X consists of seven consecutive integers, and set Y [#permalink]

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24 Jul 2016, 02:33
Expert's post
1
This post was
BOOKMARKED
fanatico wrote:
Set X consists of seven consecutive integers, and set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y.
(2) The median of the numbers in set Y is 0.

Set X consists of seven consecutive integers, and set Y consists of nine consecutive integers. Is the median of the numbers in set X equal to the median of the numbers in set Y?

Sets X and Y are evenly spaced. In any evenly spaced set (aka arithmetic progression):
(mean) = (median) = (the average of the first and the last terms) and (the sum of the elements) = (the mean) * (# of elements).

So the question asks whether (mean of X) = (mean of Y)?

(1) The sum of the numbers in set X is equal to the sum of the numbers in set Y --> 7*(mean of X) = 9* (mean of Y) --> answer to the question will be YES in case (mean of X) = (mean of Y) = 0 and will be NO in all other cases (for example (mean of X) =9 and (mean of Y) = 7). Not sufficient.
For example consider following two sets:
Set X: {6, 7, 8, 9, 10, 11, 12} --> sum 63;
Set Y: {3, 4, 5, 6, 7, 8, 9, 10, 11} --> sum 63.

(2) The median of the numbers in set Y is 0 --> (mean of Y) = 0, insufficient as we know nothing about the mean of X, which may or may not be zero.

(1)+(2) Since from (2) (mean of Y) = 0 and from (2) 7*(mean of X) = 9* (mean of Y) then (mean of X) = 0. Sufficient.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: set-x-consists-of-seven-consecutive-integers-and-set-y-128503.html
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Re: Set X consists of seven consecutive integers, and set Y   [#permalink] 24 Jul 2016, 02:33
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