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A set of integers consists of 2, 3, 5, 7, 11, 12,

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A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 19 Aug 2017, 08:03
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95% (01:06) correct 4% (01:23) wrong based on 22 sessions


A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increases by 1, the me­dian of the set stays unchanged. However, if x decreases by 1, the median of the set also decreases by 1. What is the value of x?

enter your value

[Reveal] Spoiler: OA
7

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 25 Sep 2017, 05:32
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Given the set 2 3 5 7 11 12 x, the median is 7. Thus, if 1 is summed to x, the median does not change, thus x must be a number from 7 on. In addition, we know that when 1 is subtracted from x, then the median diminishes by 1. This must be that the median becomes 6 when 1 is subtracted from x. Now, which number from 7 on when is reduced by one make the median becoming 6? Only x = 7. Then, the set would become 2 3 4 5 7 7 11 12, thus the median is 7. When we include x+1 = 8 the median stays 7. When we include x-1=6, the median becomes 6. Here we are!
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 26 Feb 2018, 11:04
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No. The source is from Manhattan GRE. Usually, they create difficult questions above the average.

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 27 Feb 2018, 12:15
Am I the only one who finds this question objectionable? The question gives the impression that the set is 2,3,5,7,11,12,x. I thought x would have to be the very last number in the set. The median is the number in the middle of a set so in this case the median is 7. It won't matter what x is because it will not impact the median.
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 08 Jan 2019, 03:28
thanks
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 06 Sep 2019, 14:10
Don't understand why it x can't be 13....
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 07 Sep 2019, 10:04
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x+1 the mean does not change which means that it must be 7 as well

x-1 the mean shifts down of one spot and the seven must go up and the new number MUST be the new median

2 - 3 - 5 - 7 - 11 - 12 - 13+1=14; 7 is still the median. Fine

2 - 3 - 5 - 7 - 11 - 12 - 13 - 1=12; 7 is still the median. NO good

---------------------------------------------

2 - 3 - 5 - 7 - 11 - 12 - 7+1=8

2 - 3 - 5 - 7 - 8 - 11 - 12; 7 is still the median. Fine

2 - 3 - 5 - 7 - 11 - 12 - 7-1=6

2 - 3 - 5 - 6 - 7 - 11 - 12; 6 is the new median. GOOD

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, [#permalink] New post 11 Sep 2019, 06:11
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Carcass wrote:


A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increases by 1, the me­dian of the set stays unchanged. However, if x decreases by 1, the median of the set also decreases by 1. What is the value of x?

enter your value

[Reveal] Spoiler: OA
7


7. I let x be some large number, the median falls on 7, if x were smaller than the previous median but larger than 5, x becomes the the new median. Therefore x must be 7 otherwise the median wouldn't be 6 in the second case. (it's a new number and since we have an odd number of integers, it's not the average of 5 and 7)
Re: A set of integers consists of 2, 3, 5, 7, 11, 12,   [#permalink] 11 Sep 2019, 06:11
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