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# A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase

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A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

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10 Dec 2018, 00:11
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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?

A. 6
B. 7
C. 8
D. 9
E. 10

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

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10 Dec 2018, 00:27
This requires a little bit of number sense.

If we write down the numbers in ascending order and assume x to be somewhere. It is clear that x cannot be at the ends as we need to be able to influence the median. Since we have an odd number of numbers, the median will be the central number.

2, 3, 5, 7, x, 11, 12

Now, if x was 7, increasing it by one still maintains the median as 7. However, on decreasing it by 1, the new median is 6 which is 1 less than before. We are done.

x = 7.

Hence Option (B) does it.

Best,

Bunuel 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?

A. 6
B. 7
C. 8
D. 9
E. 10

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

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03 Dec 2019, 06:14
any other explanation ?
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

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03 Dec 2019, 07:56
hudacse6 wrote:
any other explanation ?

Trying my bit

Median of the set of numbers - { 2, 3, 5, 7, 11, 12, and x. } must be 7

Now, try using the options -

(A) 2, 3, 5, 6 , 7, 11, 12 - Median = 6 ; If increased by 1 median increases by 1 , if decreased by 1 median decreases to 5
(B) 2, 3, 5, 7 , 7, 11, 12 - Median = 7 ; If increased by 1 median remains the same , if decreased by 1 median decreases to 6

Check with other options, only (B) works perfectly !!!
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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

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05 Dec 2019, 20:19
2
Bunuel 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?

A. 6
B. 7
C. 8
D. 9
E. 10

Since, when x increases by 1, the median of the set stays unchanged and when x decreases by 1, the median of the set also decreases by 1, it must be true that x is the median or is very close to the median. So let’s say x is the median, and we have:

2, 3, 5, x, 7, 11, 12

We see that, in this case, x could be 5, 6, or 7. Since 5 is not in the choices, let’s start with x = 6.

If x = 6 (i.e., the original median is 6), then x + 1 = 7, and the list becomes:

2, 3, 5, 7, 7, 11, 12

However, the median is now 7. Therefore, x can’t be 6 since the median is supposed to stay unchanged.

If x = 7 (i.e., the original median is 7), then x + 1 = 8, and the list becomes:

2, 3, 5, 7, 8, 11, 12

We see that the median is still 7. Furthermore, x - 1 = 6, and the list becomes:

2, 3, 5, 6, 7, 11, 12

We see that the median is 6, which is 1 less than the original median. Therefore, x must be 7.

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Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase   [#permalink] 05 Dec 2019, 20:19
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# A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase

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