Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 15 Jul 2019, 23:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a randomly selected non-negative single digit integer is

Author Message
TAGS:

### Hide Tags

VP  Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1055
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
If a randomly selected non-negative single digit integer is  [#permalink]

### Show Tags

1
9 00:00

Difficulty:   65% (hard)

Question Stats: 61% (01:59) correct 39% (02:02) wrong based on 502 sessions

### HideShow timer Statistics 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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56236
Re: If a randomly selected non-negative single digit integer is  [#permalink]

### Show Tags

6
1
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}).

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.

Hope it's clear.
_________________
##### General Discussion
Retired Moderator Joined: 20 Dec 2010
Posts: 1736

### Show Tags

1
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"
_________________
VP  Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1055
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

### Show Tags

suppose if i add 4, then also the median of the set increases whereas the range remains the same.
_________________
Retired Moderator Joined: 20 Dec 2010
Posts: 1736

### Show Tags

1
1
siddharthasingh wrote:
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)
_________________
Intern  Joined: 13 Mar 2011
Posts: 6

### Show Tags

2
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
Senior Manager  Joined: 23 Oct 2010
Posts: 337
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 ### Show Tags

1
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? sorry
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Retired Moderator Joined: 20 Dec 2010
Posts: 1736

### Show Tags

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? 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.
_________________
Director  Joined: 03 May 2007
Posts: 760
Schools: University of Chicago, Wharton School

### Show Tags

1
1
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.
Manager  Joined: 16 Feb 2011
Posts: 190

### Show Tags

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??
Retired Moderator Joined: 20 Dec 2010
Posts: 1736

### Show Tags

1
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.
_________________
Intern  Joined: 12 Feb 2011
Posts: 16
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE: Information Technology (Computer Software)

### Show Tags

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 )?
Math Expert V
Joined: 02 Sep 2009
Posts: 56236

### Show Tags

1
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.
_________________
Intern  Joined: 12 Feb 2011
Posts: 16
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE: Information Technology (Computer Software)
Re: If a randomly selected non-negative single digit integer is  [#permalink]

### Show Tags

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}).

Intern  Joined: 12 Feb 2011
Posts: 16
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE: Information Technology (Computer Software)
Re: If a randomly selected non-negative single digit integer is  [#permalink]

### Show Tags

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}).

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.

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!!
Intern  Joined: 20 Dec 2018
Posts: 49
Re: If a randomly selected non-negative single digit integer is  [#permalink]

### Show Tags

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%. Re: If a randomly selected non-negative single digit integer is   [#permalink] 21 Dec 2018, 22:23
Display posts from previous: Sort by

# If a randomly selected non-negative single digit integer is  