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A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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02 Jul 2013, 22:30
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A set S = {x, 8, 5, 4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy? (A) 1 (B) 0 (C) 1 (D) 2 (E) Cannot be determined.
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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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02 Jul 2013, 22:39
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A set S = {x, 8, 5, 4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy?
(A) 1 (B) 0 (C) 1 (D) 2 (E) Cannot be determinedThe median of a set with even (8) terms is the average of two middle terms, thus \(median = \frac{4+4}{2} = 0\). \(mean = \frac{x  8  5  4 + 4 + 6 + 9 + y}{8} = 0 = median\) > \(2 + x + y = 0\) > \(x + y = 2\). Now, since the elements in the set are arranged in increasing order, then \(x<0\) and \(y>0\), so \(xy=xy=(x+y)=(2)=2\). Answer: D.
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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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02 Jul 2013, 22:42
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A set S = {x, 8, 5, 4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy? (A) 1 (B) 0 (C) 1 (D) 2 (E) Cannot be determined. Median of the set = (4+4)/2 = 0 As per statement, Mean of the set = 0 Mean of the set y x +1917 = 0 (where x is negative n y is positive) y x = 2 So the absolute difference between two numbers is 2 Answer D
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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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02 Jul 2013, 22:51
vtran wrote: A set S = {x, 8, 5, 4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy?
(A) 1 (B) 0 (C) 1 (D) 2 (E) Cannot be determined. Alternatively, you can use the concept of deviation from mean to solve it. Median is average of middle two terms = (4 + 4)/2 = 0 So mean = 0 too. Now notice the terms on either side of mean. 4 is 4 less than 0 but 4 is 4 more so they balance out. 5 is 5 less but 6 is 6 more so there is an extra positive 1. 8 and 9 have an extra positive 1 too. To get a mean of 0, x should have negative 2 more than y i.e. x = 12, y = 10 or x = 13, y = 11 etc. In any case, xy = 2 Check this post for more on this method: http://www.veritasprep.com/blog/2012/05 ... eviations/
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A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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12 Sep 2015, 15:13
Hi, This question is built around a number of statistics concepts and you have to pay careful attention to how you organize your work. The prompt gives us a number of Facts to work with: 1) We're given the following set of values: {X, 8, 5, 4, 4, 6, 9, Y} 2) We're told that they are in INCREASING order 3) We're told the Median and the Mean are the SAME We're asked for the value of X  Y Since there are 8 terms, the Median will equal the average of the 'middle two' terms. Those 'middle two' terms are 4 and 4, so the Median is 0 (and since the Median = the Mean, the overall average is 0). Since the overall average is 0, the sum of the 8 terms MUST be 0... Adding up the terms, we have... X + Y + 2 So, since X+Y+2 = 0.... X+Y = 2 At this point, since X and Y have an established relationship, we can use any pair of values that fits all of the facts...We can TEST VALUES to prove the answer.... IF.... X = 12 Y = 10 12  10 = +2 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged in incr [#permalink]
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12 Sep 2015, 15:33
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This is what I did, we know Median which is 0 ( 4+ 4/2),. since Mean is same, it has to be 0. ( x, 8, 5, 4, 4, 6, 9, y ) so how will it be 0. if x, 8, 5, 4 = 4, 6, 9, y .
hence the number is x 12 and and y 10. D is the answer.



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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arrang [#permalink]
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13 Sep 2015, 08:54
shasadou wrote: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy?
A. 1 B. 0 C. 1 D. 2 E. Cannot be determined. S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged in increasing order This means x < 0 and y > 0. The median of a series with even numbers is the average of the middle two numbersHence the median here is (4 + 4)/2 = 0 Mean = sum of all the terms/ no. of terms (x  8 5 5 +4 +6 +9 + y)/8 = 0 (Given that median = mean) Hence, x + y = 2 We need to find x  y and we know that x < 0 and y > 0 Opening the modulus with appropriate signs: Modulus of any number is the absolute value of the number, or simply the positive value Always remember that the modulus of a negative number opens with a negative sign and of a positive number opens with a positive signWe have , x  y = x  y = (x + y) = (2) = 2 Hence Option D



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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged in incr [#permalink]
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02 Apr 2016, 06:51
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shasadou wrote: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of xy?
A. 1 B. 0 C. 1 D. 2 E. Cannot be determined. Hi, the set is { x, 8, 5, 4, 4, 6, 9, y } median is the center of middle 2 numbers as number of elements in set is EVEN..median= (4+4)/2=0.. it is given MEAN = MEDIAN.. so MEDIAN= MEAN = { x +(8)+( 5)+( 4)+ 4+ 6+ 9+ y }/8 = 0\(\frac{(x+y+2)}{8}=0\).. or x+y+2=0.. x= (y+2) x=(y+2).. so xy= y+2y= y+2y=2 D
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Re: A set S = { x, 8, 5, 4, 4, 6, 9, y } with elements arranged [#permalink]
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13 Oct 2016, 23:13
We know that the median in this set is 0 If the mean of this set must be equal to 0, the sum of elements in the set must always be zero Adding the terms, we get x17+19+y = 0 This is only possible when x = 2+y eg, if y = 10, x=12 Since x will always bme greater than y & we will have a difference of 2. mod(x)  mod(y) = 2 always(Option B)
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