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

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11 May 2011, 17:17

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A

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C

D

E

Difficulty:

65% (hard)

Question Stats:

48% (02:10) correct
52% (01:44) wrong based on 31 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.

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

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11 May 2011, 18:18

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

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

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11 May 2011, 22:48

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.
_________________

My dad once said to me: Son, nothing succeeds like success.

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

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04 Dec 2011, 07:29

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.

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

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04 Dec 2011, 08:05

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

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

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04 Dec 2011, 09:07

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

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

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04 Dec 2011, 15:52

My answer is C. 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, 22:31

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?

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.

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