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# x is an integer greater than 7. What is the median of the set of integ

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x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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14 Oct 2014, 06:20
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54% (01:43) correct 46% (01:56) wrong based on 215 sessions

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Tough and Tricky questions: Statistics.

x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.
(2) The range of the set of integers from 1 to x inclusive is 20.

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x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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14 Oct 2014, 08:00
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Bunuel wrote:

Tough and Tricky questions: Statistics.

x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.
(2) The range of the set of integers from 1 to x inclusive is 20.

X>7 and the set (let it be S) contains 1 to X inclusive.

I normally read both the statements and start with the easier one. In this case, it is statement 2.

Statement 2: If the range is 20. Then X must be 21. Since X is the last term. In this case, we can easily find the median. So Sufficient.

Statement 1: If we know the average of the set, we can find the sum and number of elements in the set. But this is a tedious process to jot down all the numbers and find the sum.

But we can use statement 2 as a clue to solve this easily without crushing our brain. Since two statements never contradicts each other. If we plugin X as 21. We get the sum as 231(using the sum of n numbers formula) and average as 11.

Bingo!!

We can find the median from this statement as well. So Sufficient.

Answer : D: Both statement Individually sufficient to solve.
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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14 Oct 2014, 08:43
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Gnpth wrote:
Bunuel wrote:

Tough and Tricky questions: Statistics.

x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.
(2) The range of the set of integers from 1 to x inclusive is 20.

X>7 and the set (let it be S) contains 1 to X inclusive.

I normally read both the statements and start with the easier one. In this case, it is statement 2.

Statement 2: If the range is 20. Then X must be 21. Since X is the last term. In this case, we can easily find the median. So Sufficient.

Statement 1: If we know the average of the set, we can find the sum and number of elements in the set. But this is a tedious process to jot down all the numbers and find the sum.

But we can use statement 2 as a clue to solve this easily without crushing our brain. Since two statements never contradicts each other. If we plugin X as 21. We get the sum as 231(using the sum of n numbers formula) and average as 11.

Bingo!!

We can find the median from this statement as well. So Sufficient.

Answer : D: Both statement Individually sufficient to solve.

we can solve statement 1 in the following manner

since number are consecutive integers. therefore there sum from 1 to x can be given as (x(1+x))/2; where x is the last term

now average is =11
thus (x(1+x))/2) =11x
1+x=22
or x=21
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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16 Oct 2014, 01:18
Sorry to ask stupid question,

I answered E because the question is not explicitly telling that this set is consecutive. So, I assume it's not. But how do you know that it is??
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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16 Oct 2014, 07:44
Phunnie wrote:
Sorry to ask stupid question,

I answered E because the question is not explicitly telling that this set is consecutive. So, I assume it's not. But how do you know that it is??

We are told that the set consists of integers from 1 to x inclusive, so the set consists of consecutive integers. For example, if x=8, then set is {1, 2, 3, 4, 5, 6, 7, 8}.
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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02 Nov 2014, 02:45
Bunuel wrote:

Tough and Tricky questions: Statistics.

x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?

(1) The average of the set of integers from 1 to x inclusive is 11.
(2) The range of the set of integers from 1 to x inclusive is 20.

D.

1) Avg = 11
sum of consecutive integers from 1 to x (inclusive) = x(x+1)/2
avg = {x(x+1)/2*x} = 11
or x = 21
so median can be calculated. sufficient.

2) range = 20
x = 21
again media can be calculated. sufficient.
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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04 Mar 2016, 09:52
For an evenly spaced out set, the mean == median.
here the set is space of consecutive integers.
Stmt1: Sufficient.
Stmt2: x-1= 20; x=21. Avg==mean =11. Sufficient.
Therefore D.
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x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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04 Mar 2016, 18:40
Statement 1: AM(average ) of an arithmetic progression = (a+L) /2
a ------> first term of the series
L ------> last term of the series
This gives 11= (1+x)/2 ( since 1 is the first term and x is the last term of the series)
therefore x= 21
so sufficient to find the median

Statement 2: range is 20 therfore x=21
Sufficient

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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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21 Dec 2018, 22:27
)Statement 1. If a set has equally distant elements i.e. if the set is in A.P., then the mean of the set is also the median of the set.
Here, we are given the mean of the set and we are told that the set is in A.P. So, the median would also be 11. Hence, Sufficient.
Statement 2. Range of a set = (Biggest element – smallest element)
We know that the smallest no is 1 and the range of the set is 20. So, the biggest number should be 21.
Now, We can easily find the median of the set consisting of integers from 1 to 21.
The median is 11. Hence, Sufficient.
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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21 Dec 2018, 22:29
Probability of picking 1 vowel from Set#1 = 2/5
Probability of not picking any vowel from Set#1 = 3/5
Probability of picking 1 vowel from Set#2 = 1/6
Probability of not picking any vowel from Set#2 = 5/6
Probability of picking atleast 1 vowel= P(2 vowels) + P(vowel from Set#1 & consonant from Set#2) + P(vowel from Set#2 & consonant from Set#1)
Probability of picking atleast 1 vowel = 2/5 x 1/6 + 2/5 x 5/6 + 3/5 x 1/6 = 15/30 = 1/2.
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Re: x is an integer greater than 7. What is the median of the set of integ  [#permalink]

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22 Jan 2019, 20:24
Bunuel wrote:
Phunnie wrote:
Sorry to ask stupid question,

I answered E because the question is not explicitly telling that this set is consecutive. So, I assume it's not. But how do you know that it is??

We are told that the set consists of integers from 1 to x inclusive, so the set consists of consecutive integers. For example, if x=8, then set is {1, 2, 3, 4, 5, 6, 7, 8}.

Can we always consider "the set consists of integers from 1 to x inclusive" as "a set of consecutive integers"? I really got stuck here. I thought the integers are not evenly spaced and can be repeated.

Can you suggest any material talk about this idea? Thank you.
Re: x is an integer greater than 7. What is the median of the set of integ   [#permalink] 22 Jan 2019, 20:24
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