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If a randomly selected non-negative single digit integer is

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If a randomly selected non-negative single digit integer is [#permalink] New post   08 Aug 2011, 06:38
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If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   09 Mar 2014, 12:17
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reddevils wrote:
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.


If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

"A randomly selected non-negative single digit integer is added to {2, 3, 7, 8}":
We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

Hence, the total number of outcomes is 10.

We need to find the probability that the median of the set will increase but the range still remains the same.

The median of {2, 3, 7, 8} is (3 + 7)/2 = 5 --> the number selected must be greater than 5
The range of {2, 3, 7, 8} is 8 - 2 = 6 --> the number selected must be from 2 to 8, inclusive.

To satisfy both condition the number selected must be 6, 7, or 8.

Hence, the number of favorable outcomes is 3.

P = (favorable)/(total) = 3/10.

Answer: B.

Hope it's clear.
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Re: Range [#permalink] New post   08 Aug 2011, 23:36
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siddharthasingh wrote:
what about 4 and 5?
suppose if i add 4, then also the median of the set increases whereas the range remains the same.


Median is the average of two middle terms if there are even number of elements arranged in ascending order.
Median is the the middle terms if there are odd number of elements arranged in ascending order.

Here, there are even number of elements.
{2, 3, 7, 8}
Middle terms are 3 and 7.
Their average: (3+7)/2=10/2=5
So, median is presently 5.

If you add 4 and 5, medians will be 4 and 5 respectively.
{2, 3, 4, 7, 8}: Middle term=4(odd number of elements)->Ignore
{2, 3, 5, 7, 8}: Middle term=5(odd number of elements)->Ignore
{2, 3, 6, 7, 8}: Middle term=6(odd number of elements)
{2, 3, 7, 7, 8}: Middle term=7(odd number of elements)
{2, 3, 8, 7, 8}={2, 3, 7, 8, 8}: Middle term=7(odd number of elements)
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Re: Range [#permalink] New post   09 Aug 2011, 05:27
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Call X - new number
Let's consider the 2 conditions:

* median increase:
Old median : 2+3+7+8/4 =5
New median: 2+3+7+8+x/5 = 20+x/5
New median increase: 20 + x/5 > 5 --> x >5
* Range unchanged:
with the same smallest number is 2, x>5 then new x must <= 8
---> 5<x<=8 then x can be (6,7,8)
* Probability = 3/10 = 0.3
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Re: Range [#permalink] New post   15 Aug 2011, 18:37
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fluke wrote:
siddharthasingh wrote:
If a randomly selected non-negtive single digit integer is added to {2, 3, 7,8}. What is the probability that the median of the set will increase but the range still remains the same?

a)0.2
b)0.3
c)0.4
d)0.5
e)0.6


Non-negative digit adds to the confusion.

A digit is always non-negative.

Condition will be satisfied if the digit is one of: {6, 7, 8}

Total digits=10

P=3/10=0.3

Ans: "B"


Good job...

+1.


Remember => A digit is always a non-negative integer e.g 0-9.
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Re: Range [#permalink] New post   08 Aug 2011, 07:13
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siddharthasingh wrote:
If a randomly selected non-negtive single digit integer is added to {2, 3, 7,8}. What is the probability that the median of the set will increase but the range still remains the same?

a)0.2
b)0.3
c)0.4
d)0.5
e)0.6


Non-negative digit adds to the confusion.

A digit is always non-negative.

Condition will be satisfied if the digit is one of: {6, 7, 8}

Total digits=10

P=3/10=0.3

Ans: "B"
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Re: Range [#permalink] New post   15 Aug 2011, 12:28
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fluke wrote:
siddharthasingh wrote:

Total digits=10

P=3/10=0.3

Ans: "B"


sorry for a stupid question )) but how did u get 10? :oops: sorry
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Re: Range [#permalink] New post   16 Aug 2011, 01:18
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DeeptiM wrote:
Isn't "0" neither negative nor positive??

Shouldn't it then be 3/9??


0 is indeed neither negative nor positive. But, non-negative means everything that's not negative AND 0 is not negative. So, we must consider 0 for all the non-negative cases. We must consider 0 for non-positive case as well because 0 is not positive.
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Re: Range [#permalink] New post   09 Mar 2014, 04:08
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reddevils wrote:
If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

As per the question, the range of numbers in the set should not change. So the possible outcomes must be between 2 and 8. Thus, so according to me the answer is 3/7. Any thoughts? Bunuel(Can't look farther than Bunuel for quant :D )?


We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

The part about the range and the median are constraints, which limit/define the favorable outcomes.

Hope it's clear.
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Re: Range [#permalink] New post   08 Aug 2011, 23:17
what about 4 and 5?
suppose if i add 4, then also the median of the set increases whereas the range remains the same.
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Re: Range [#permalink] New post   15 Aug 2011, 12:35
LalaB wrote:
fluke wrote:
siddharthasingh wrote:

Total digits=10

P=3/10=0.3

Ans: "B"


sorry for a stupid question )) but how did u get 10? :oops: sorry


non-negative digits: {0,1,2,3,4,5,6,7,8,9}. How many of these are there? 10, right.

Probability=Favorable Outcomes/Possible outcomes and "Possible outcomes"=10 because any of the 10 digits can possibly be chosen.
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Re: Range [#permalink] New post   15 Aug 2011, 20:53
fluke wrote:
siddharthasingh wrote:
If a randomly selected non-negtive single digit integer is added to {2, 3, 7,8}. What is the probability that the median of the set will increase but the range still remains the same?

a)0.2
b)0.3
c)0.4
d)0.5
e)0.6


Non-negative digit adds to the confusion.

A digit is always non-negative.

Condition will be satisfied if the digit is one of: {6, 7, 8}

Total digits=10

P=3/10=0.3

Ans: "B"


Isn't "0" neither negative nor positive??

Shouldn't it then be 3/9??
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Re: Range [#permalink] New post   09 Mar 2014, 02:47
fluke wrote:

non-negative digits: {0,1,2,3,4,5,6,7,8,9}. How many of these are there? 10, right.

Probability=Favorable Outcomes/Possible outcomes and "Possible outcomes"=10 because any of the 10 digits can possibly be chosen.


As per the question, the range of numbers in the set should not change. So the possible outcomes must be between 2 and 8. Thus, so according to me the answer is 3/7. Any thoughts? Bunuel(Can't look farther than Bunuel for quant :D )?
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   09 Mar 2014, 12:00
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   09 Mar 2014, 13:03
Bunuel wrote:
reddevils wrote:
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.


If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

"A randomly selected non-negative single digit integer is added to {2, 3, 7, 8}":
We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

Hence, the total number of outcomes is 10.

We need to find the probability that the median of the set will increase but the range still remains the same.

The median of {2, 3, 7, 8} is (3 + 7)/2 = 5 --> the number selected must be greater than 5
The range of {2, 3, 7, 8} is 8 - 2 = 6 --> the number selected must be from 2 to 8, inclusive.

To satisfy both condition the number selected must be 6, 7, or 8.

Hence, the number of favorable outcomes is 3.

P = (favorable)/(total) = 3/10.

Answer: B.

Hope it's clear.


Thank you Bunuel. I really do feel numb. Don't know what I was thinking regarding the constraint of range. Thanks again for taking the pains to clarify a dumb query.

Cheers to you!!
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   21 Dec 2018, 22:23
We have 10 single-digit non-negative integer from 0 -9.
We can’t add 0,1 and 9 because this will change the range of the set.
We can’t add 0-5 because if we add any number from 0-4 it will decrease the median and if we add 5, the median won’t change.
So, the only possible numbers that could be added are = 6, 7 and 8.
So, probability = 3/10 = 0.3 = 30%.
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   24 Feb 2020, 11:43
Hi!
How do you know that the question isn't testing probability as well?
My answer was 8/100
which is basically:
Prob of Event A happening* Prob of Event B happening
So=4/10*2/10
While I understand your approach pretty well, I'd get terribly stuck in the exam if I don't see an answer choice that matches. Taking a 180 turn and looking for another approach is time-consuming :(
Thanks!!

Bunuel wrote:
reddevils wrote:
If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

As per the question, the range of numbers in the set should not change. So the possible outcomes must be between 2 and 8. Thus, so according to me the answer is 3/7. Any thoughts? Bunuel(Can't look farther than Bunuel for quant :D )?


We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

The part about the range and the median are constraints, which limit/define the favorable outcomes.

Hope it's clear.
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   02 Mar 2020, 07:18
Bunuel wrote:
reddevils wrote:
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.


If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

"A randomly selected non-negative single digit integer is added to {2, 3, 7, 8}":
We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

Hence, the total number of outcomes is 10.

We need to find the probability that the median of the set will increase but the range still remains the same.

The median of {2, 3, 7, 8} is (3 + 7)/2 = 5 --> the number selected must be greater than 5
The range of {2, 3, 7, 8} is 8 - 2 = 6 --> the number selected must be from 2 to 8, inclusive.

To satisfy both condition the number selected must be 6, 7, or 8.

Hence, the number of favorable outcomes is 3.

P = (favorable)/(total) = 3/10.

Answer: B.

Hope it's clear.


Hi Bunuel,
The solution is clear but the question. I misunderstood the question to be stating that the non-negative digit is added to each element of the set, that is 2+x, 3+x, etc and not being included in the set. Can you please let me know why my understanding of the question on that was is wrong here.
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   06 Mar 2020, 01:16
Bunuel wrote:
reddevils wrote:
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.


If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

"A randomly selected non-negative single digit integer is added to {2, 3, 7, 8}":
We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

Hence, the total number of outcomes is 10.

We need to find the probability that the median of the set will increase but the range still remains the same.

The median of {2, 3, 7, 8} is (3 + 7)/2 = 5 --> the number selected must be greater than 5
The range of {2, 3, 7, 8} is 8 - 2 = 6 --> the number selected must be from 2 to 8, inclusive.

To satisfy both condition the number selected must be 6, 7, or 8.

Hence, the number of favorable outcomes is 3.

P = (favorable)/(total) = 3/10.

Answer: B.

Hope it's clear.


I have a major doubt here.
Say if I take the number =3
My range will then be (8+3)-(2+3) which is still = 6
And the median will be (3+3)+(7+3)/2 = 16/2=8 which is increased from 5
Both my conditions suffice when I take 3, so why have we just considered 6;7;8 as the answer ...?
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Re: If a randomly selected non-negative single digit integer is [#permalink] New post   06 Mar 2020, 01:22
Tanshorey wrote:
Bunuel wrote:
reddevils wrote:
Bunuel - Ok but still I unable to get my head around the range constraint. The question talks about the range of single digit non negative numbers? I thought the question talks about the range of the set of 4 numbers given ({2, 3, 7, 8}).

Please clarify.


If a randomly selected non-negative single digit integer is added to {2, 3, 7, 8}. What is the probability that the median of the set will increase but the range still remains the same?

A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6

"A randomly selected non-negative single digit integer is added to {2, 3, 7, 8}":
We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.

Hence, the total number of outcomes is 10.

We need to find the probability that the median of the set will increase but the range still remains the same.

The median of {2, 3, 7, 8} is (3 + 7)/2 = 5 --> the number selected must be greater than 5
The range of {2, 3, 7, 8} is 8 - 2 = 6 --> the number selected must be from 2 to 8, inclusive.

To satisfy both condition the number selected must be 6, 7, or 8.

Hence, the number of favorable outcomes is 3.

P = (favorable)/(total) = 3/10.

Answer: B.

Hope it's clear.


I have a major doubt here.
Say if I take the number =3
My range will then be (8+3)-(2+3) which is still = 6
And the median will be (3+3)+(7+3)/2 = 16/2=8 which is increased from 5
Both my conditions suffice when I take 3, so why have we just considered 6;7;8 as the answer ...?


Even i misuderstood the question this same way. Just hope GMAT's language is not so confusing!!!
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Re: If a randomly selected non-negative single digit integer is [#permalink]
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