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

Question

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

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

Gladiator59 · Answer

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,
Gladi

hudacse6 · Answer

any other explanation ?

Abhishek009 · Answer

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 !!!

ScottTargetTestPrep · Answer

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.

Answer: B

sanya2711 · Answer

only x=7 will fulfill the conditions mentioned in the question. as if x=7, then when x becomes 8 then also median does not change. when x becomes 6 the median becomes 6 instead of 7. Thus all conditions are fulfilled

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

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