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# If Q is an odd number and the median of Q consecutive

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Intern
Joined: 31 Jul 2014
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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13 Dec 2014, 09:37
1
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Since Q is a set of odd numbers and we know the median then to get the largest number we just need to know how many integers to add to the median and we will have the largest number.

Q - 1 will get us the total number of integers without the median. Divide this by 2 and we have how many numbers are on either side of the median. Add this number to the median and we get our largest number.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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11 Mar 2015, 16:30
Bunuel wrote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Consider the easiest case, say Q=3, then;
Set = {119, 120, 121};
The largest integer = 121.

Now, plug Q=3 into the answers to see which yields 121. Only answer choice A works. Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.

Bunuel - do you have more similar problems to this or any combinatorics problems? Or would doing these problems be sufficient practice : advanced-topic-probability-and-combinations-questions-with-solutions-101361.html?

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 45422
Re: If Q is an odd number and the median of Q consecutive [#permalink]

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12 Mar 2015, 03:36
GMAT01 wrote:
Bunuel wrote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Consider the easiest case, say Q=3, then;
Set = {119, 120, 121};
The largest integer = 121.

Now, plug Q=3 into the answers to see which yields 121. Only answer choice A works. Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.

Bunuel - do you have more similar problems to this or any combinatorics problems? Or would doing these problems be sufficient practice : advanced-topic-probability-and-combinations-questions-with-solutions-101361.html?

Thank you

In our Questions Bank under Statistics and Combinations tags you can find hundreds of questions to practice.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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12 Mar 2015, 06:07
1
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Well this question has already been solved and discussed and dissected but here is another method to solve it, its infact a generalization of the method being discussed above.
Let Q=2k+1
So k=(Q-1)/2
And the Q consecutive integers be n-k,n-k+1,...,n,...n+k-1,n+k
median of the numbers =n=120
now the largest number =n+k
=120+(Q-1)/2

(A)
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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23 May 2015, 03:55
Bunuel wrote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Consider the easiest case, say Q=3, then;
Set = {119, 120, 121};
The largest integer = 121.

Now, plug Q=3 into the answers to see which yields 121. Only answer choice A works. Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.

Dear Bunuel
Is this question properly formulated? "If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?"
Shouldn't it say "If Q is a set of consecutive numbers and Q is is odd, then wat is the largest of..."?
I find the wording a little confusing.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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23 May 2015, 08:29
reto wrote:
Bunuel wrote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Consider the easiest case, say Q=3, then;
Set = {119, 120, 121};
The largest integer = 121.

Now, plug Q=3 into the answers to see which yields 121. Only answer choice A works. Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.

Dear Bunuel
Is this question properly formulated? "If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?"
Shouldn't it say "If Q is a set of consecutive numbers and Q is is odd, then wat is the largest of..."?
I find the wording a little confusing.

No.

The set given is a set of "Q consecutive integers", where Q is an odd number. For example, if Q=5=odd, then the set can be {118, 119, 120, 121, 122} (set of 5 consecutive integers).
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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03 Jun 2015, 09:54
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Please could anyone tell me if he or she had problems with the wording of this question too? What does "If Q is an odd number and the median of Q consecutive integers is 120.." mean in reality? Is Q (the odd number) describing the numbers of numbers in the Set of Q? Is it just confusing to me?
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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04 Jun 2015, 17:37
3
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Expert's post
Hi reto,

You'll likely find it best to break Quant prompts down into 'pieces', so that you can deal with each piece one-at-a-time and simplify any complex-looking situations.

Here, the first thing we're told is "Q is an ODD number..." Now what does THAT mean? Here are some examples...

Q COULD be -5, -3, -1, 1, 3, 5, 7, etc.

Next, we're told "the median of Q consecutive integers is 120." 'Q' clearly refers to the 'Q' in the earlier part of the sentence; we're also dealing with the statistical term "median" (which means 'middle number of a group, when the numbers are ordered from least to greatest').

So let's list out some possibilities (it's worth noting that you can't have "negative consecutive integers", so the negative examples that I listed are not possible here):

IF...Q = 1....the median of 1 consecutive number is 120......so the 'group' is {120}
IF...Q = 3....the median of 3 consecutive numbers is 120....so the 'group' is {119, 120, 121}
IF...Q = 5....the median of 5 consecutive numbers is 120....so the 'group' is {118, 119, 120, 121, 122}
Etc.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Director Joined: 10 Mar 2013 Posts: 563 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: If Q is an odd number and the median of Q consecutive [#permalink] ### Show Tags 12 Jun 2015, 03:13 If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers? (A) (Q - 1)/2 + 120 (B) Q/2 + 119 (C) Q/2 + 120 (D) (Q + 119)/2 (E) (Q + 120)/2 B, C, E are out since these options do not yield an integer D is also out as the median is X..120..X --> so the largest possible number must be >120, D is clarly <120..just plug in Q=3 and you'll get 61... _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Intern Joined: 12 Apr 2013 Posts: 34 Concentration: Entrepreneurship, Strategy Re: If Q is an odd number and the median of Q consecutive [#permalink] ### Show Tags 25 Jul 2015, 12:20 Bunuel, How do i solve this by algebra. Thanks!! _________________ Commitment is about stretching your capabilities. It can take you across all obstacles!! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11663 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If Q is an odd number and the median of Q consecutive [#permalink] ### Show Tags 25 Jul 2015, 17:29 Hi ash99, Do you have the OG13, GMAT2015 or GMAT2016 books? If so, the algebra/logic explanation to this question can be found in any of them. In the OG13 and GMAT2015, it's PS question #91; in the GMAT2016, it's PS question #112. All things being equal though, solving this with Algebra would not be the easiest, nor the fastest, way to get to the correct answer. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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If Q is an odd number and the median of Q consecutive [#permalink]

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02 Aug 2015, 11:38
Thanks Rich.

Agree.Plugging in numbers is a faster way to approach this problem.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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04 Oct 2015, 14:33
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Revenge2013 wrote:
Ah thanks - was indeed a stupid question, but got it now.

Thanks a lot!

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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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29 Nov 2015, 06:50
studentsensual wrote:
Dear GMAT club users,

I have some misunderstandings.
First of all WHY do we have to consider [color=#ed1c24]Q as a set of odd numbers
, when it is simply given that Q is an ODD NUMBER? It is said NOTHING about the set of numbers.

Next, according to question, Q consecutive integers - consecutive odd integers, for instance if Q is 111, consecutive odd integers are 113, 115, etc.

120 is the median, which is the integer in the middle & since all set numbers are odd, then there are two middle numbers and the median is the mean of these two, e.g., 1, 2, 3, 4, 5, 6 - 3 and 4 are middle numbers, the median of the set is (3+4)/2=3.5.

So, 120 (median) has been determined by finding average of two middle numbers (a+b)/2=120.

I also couldn't understand why Q - 1 is the total number of integers without the median?[/color]

Nowhere is it mentioned that Q is a set of ODD numbers. What is given is that Q is odd and that median of Q consecutive integers in 120. For such questions with variables, it is better to assume a particular value. Lets say Q=3 and that the set is {119,120,121}. This set has a median of 120.

Text in blue above is wrong as well. Median of a set with odd number of elements = middle most term and NOT the average of the 2 middle number. Example, in the set I have mentioned {119,120,121}, the median is the middle most term =120.

As for the Q-1 elements, you can look at the given set, {119,120,121}.

The terms other than the median = 2 = 3-1=Q-1. This is true for all sets having odd number of elements {117,118,119,120,121,122,123}. Again, the median = 120 and terms without the median = 6 = 7-1 = Q-1.

For all such questions it is always beneficial to assume certain sets/elements that satisfy the given conditions and see for yourself.

Hope this helps.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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16 Jan 2016, 21:24
Since Q is an odd number, WKT there will be equal no of integers before and after the median (i.e. 120)
Lets x = no of integers before 120 = no if integers after 120
total no of integers = Q = 2x + 1
x = (Q-1)/2
Largest Number will be 120+x = 120 + (Q-1)/2
Choice A
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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07 Jun 2016, 11:05
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

We are given that Q is an ODD NUMBER and that the median of Q CONSECUTIVE INTEGERS is 120. Let's choose a convenient number for Q, such as 3. We can now say:

The median of 3 consecutive integers is 120. Since 120 is the MEDIAN, or middle number of these integers, our 3 integers are the following:

119, 120, 121

The answer choices present us with formulas for the value of the largest integer in the sequence. To determine the correct formula, we therefore will plug 3 in for Q in each answer choice until we get 121, which is the largest value in our sample data set.

A) (Q-1)/2 + 120

(3-1)/2 + 120 = 1 + 120 = 121

This IS equal to 121.

B) Q/2 + 119

3/2 + 119 = 1.5 + 119 = 120.5

This IS NOT equal to 121.

C) Q/2 + 120

3/2 + 120 = 1.5 + 120 = 121.5

This IS NOT equal to 121.

D) (Q+119)/2

(3+119)/2 = 122/2 = 61

This IS NOT equal to 121.

E) (Q+120)/2

(3+120)/2 = 123/2 = 61.5

This IS NOT equal to 121.

The only answer that is equal to 121 is that given in answer choice A.

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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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06 Sep 2016, 08:57
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Bunuel wrote:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Consider the easiest case, say Q=3, then;
Set = {119, 120, 121};
The largest integer = 121.

Now, plug Q=3 into the answers to see which yields 121. Only answer choice A works. Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.

Awesome
Doesn't get simpler than that !!

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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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09 Oct 2016, 16:16
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

(120-n)-------------------(120)-----------------(120+n)
n values between (120-n) & 120
n values between 120 & (120+n).....duh!

n+1+n = Q
2n+1 = Q
$$n = \frac{(Q-1)}{2}$$

Largest value = $$(120 + n) = 120 + \frac{(Q-1)}{2}$$
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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26 Oct 2016, 20:55
Say we have 119 120 121 as our numbers

Q = 3

Therefore, when we plug Q into the choices, we find A to be the correct answer as the largest number in the set we've created in 121.
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Re: If Q is an odd number and the median of Q consecutive [#permalink]

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26 Dec 2016, 02:03
Re: If Q is an odd number and the median of Q consecutive   [#permalink] 26 Dec 2016, 02:03

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# If Q is an odd number and the median of Q consecutive

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