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Intern  Joined: 14 May 2014
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Concentration: General Management, Operations
GPA: 3.15
List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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20 00:00

Difficulty:   65% (hard)

Question Stats: 53% (01:53) correct 47% (01:51) wrong based on 226 sessions

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List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?

(1) The smallest number in list Q is greater than the largest number in list P.

(2) m = n

Need some help; see spoiler below.
I got this questions wrong since it was not defined that the any of the numbers are positive, i.e. if the set of n number are negative, then m+n < m, therefore the median of list R is less than the median of list P. However, it if is positive, then median of list R is greater than the median of list P.

Is the word number stating that it is the set of natural numbers?

I picked E

Source MGMAT CAT.
Intern  Joined: 22 Mar 2014
Posts: 25
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16
1
wunsun wrote:
List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?

(1) The smallest number in list Q is greater than the largest number in list P.

(2) m = n

Need some help; see spoiler below.
I got this questions wrong since it was not defined that the any of the numbers are positive, i.e. if the set of n number are negative, then m+n < m, therefore the median of list R is less than the median of list P. However, it if is positive, then median of list R is greater than the median of list P.

Is the word number stating that it is the set of natural numbers?

I picked E

Source MGMAT CAT.

First, median is the middle number of the set of numbers.

Now, statement (1) says that the smallest number of Q is greater than the largest of P.

There are three possibilities here:
(i) - if m>n then the median will come from the list P as all the n numbers will be greater than the median. It seems that the median would be greater than the median of P but there is the trick (which got me too). What if P consist of all equal numbers? then the median is equal to the median of P.

(ii)- if m>n then the median will come from the list Q and would be greater than the median of P.

(iii) - if m = n then the median will be the average of P's largest number and Q's smallest number. Which would be greater than the median of P (even if P has all equal numbers).

So from statement (1) we can get median equal to P or greater than P. Insuff.

statement (2) tells us m=n. doesn't tell us what numbers P and Q holds. Insuff.

Combining the two: m=n is third scenario discussed in statement (1). i.e. we know that the average of P's largest number and Q's smallest number. Which is greater than the median of P. Suff.

Pressing +1 costs nothing _________________
-Sameer
Press Kudos if the post helped

Originally posted by sameer_kalra on 13 Jul 2014, 06:41.
Last edited by sameer_kalra on 13 Jul 2014, 07:38, edited 3 times in total.
General Discussion
Intern  Joined: 02 Jun 2014
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Location: India
Concentration: Strategy, Operations
Schools: LBS '16, ISB '15
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Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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I got 1 example for C...

1 and 2 are both insufficient on its own.

4>3 (as per point 1)
lets assume m=n=3
P(1,2,3) and Q(4,5,6)

Then median of R (1,2,3,4,5,6) = 3.5 > median of P which is 2.
Now expanding that to a larger subset, if smallest digit of Q is always > largest digit of P

This means First digit of Q is > Last digit of P (arrange in ascending order for getting your median).
I think it holds true, with random numbers...

Hope this helps.

_______________
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Intern  Joined: 24 Jan 2013
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Intern  Joined: 24 Jan 2013
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Quote:
statement (2) tells us m>n. doesn't tell us what numbers P and Q holds. Insuff.

statement 2 is m=n.
Great catch on the numbers being equal.
Intern  Joined: 22 Mar 2014
Posts: 25
Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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peacewarriors wrote:
Quote:
statement (2) tells us m>n. doesn't tell us what numbers P and Q holds. Insuff.

statement 2 is m=n.
Great catch on the numbers being equal.

sorry for missing that. post edited.

Hope i helped.
_________________
-Sameer
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Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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1
Quote:
List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?

(1) The smallest number in list Q is greater than the largest number in list P.

(2) m = n

Need some help. How do we know whether to take positive number or negative number or odd or even. Because if m/n is odd/even, then the median can change between integer and non integer.
Manager  Joined: 24 Nov 2013
Posts: 56
Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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sameer_kalra wrote:

First, median is the middle number of the set of numbers.

Now, statement (1) says that the smallest number of Q is greater than the largest of P.

There are three possibilities here:
(i) - if m>n then the median will come from the list P as all the n numbers will be greater than the median. It seems that the median would be greater than the median of P but there is the trick (which got me too). What if P consist of all equal numbers? then the median is equal to the median of P.

(ii)- if m>n then the median will come from the list Q and would be greater than the median of P.

For (i) - if m>n, from Sameer's post

we can also have P =(1,2,3,4,5,6,7) and Q = (9,10)..even in this case the median is from P.
In this case the elements of P are all not the same.

(ii) from from Sameer's post must be m < n... in case Q has more number of terms such that "The smallest number in list Q is greater than the largest number in list P", then
the median will be from Q.
Manager  Joined: 24 Nov 2013
Posts: 56
Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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Mechmeera wrote:
Quote:
List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?

(1) The smallest number in list Q is greater than the largest number in list P.

(2) m = n

Need some help. How do we know whether to take positive number or negative number or odd or even. Because if m/n is odd/even, then the median can change between integer and non integer.

m and n can be anything - odd/even...

if m is odd, but the terms are 0.5, 0.5, 0.5 -> the median would be a non-integer
if m is odd, but the terms are 1, 1, 1 -> the median would be an integer

if m is even and the terms are 1,2,2,4.. the median can still be an integer.
if m is even and the terms are 1,2,3,4.. the median will be a non-integer.

the value of median would depend on the value of elements and not the number of elements
Manager  Joined: 24 Nov 2013
Posts: 56
Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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we have a takeaway from this question...

we can use the options presented in the DS question to our advantage. In this question, statement 2 says number of terms are same.

We should take this as a hint while examining statement 1. We have to ask ourselves whether we have considered the scenario where m = n, m > n etc

I did not follow this...got the wrong answer!
Senior Manager  Joined: 15 Oct 2015
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Concentration: Finance, Strategy
GPA: 3.93
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Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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Success2015 wrote:
we have a takeaway from this question...

we can use the options presented in the DS question to our advantage. In this question, statement 2 says number of terms are same.

We should take this as a hint while examining statement 1. We have to ask ourselves whether we have considered the scenario where m = n, m > n etc

I did not follow this...got the wrong answer!

Experts posts will be appreciated in this
CEO  S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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1
2
Nez wrote:
]

Experts posts will be appreciated in this

This is a great question to understand how you can play around with the information given in the DS question. You are given 2 sets with m and n elements each. nowhere it is mentioned whether m=n or whether you can have same elements in any given set. You can thus use these things to your advantage. Additionally, statement 2 should give you that bit of clue.

The question wants to know whether the median of R is > median of P. Start by analyzing the 2 statements.

Per statement 1, P={1}, Q = {2,3}, R={1,2,3} will give you a "yes" for the question asked but with P={1,1,1}, Q = {2,3}, R={1,1,1,2,3} will give you a "no" for the question asked. This statement is thus not sufficient.

Per statement 2, m=n, again P={1,1}, Q = {2,3}, R={1,1,2,3} will give you a "yes" for the question asked but with P={10,10}, Q = {2,3}, R={2,3,10,10} will give you a "no" for the question asked. This statement is thus not sufficient.

Combining, you get that the min element of Q > max. element of P and m=n, giving you in all possibilities that the median of R > median of P. C is thus the correct answer.

Hope this helps.
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Re: List P contains m numbers; list Q contains n numbers. If th  [#permalink]

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_________________ Re: List P contains m numbers; list Q contains n numbers. If th   [#permalink] 03 Jul 2019, 05:36
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