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

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If Q is an odd number and the median of Q consecutive [#permalink] New post 07 Dec 2012, 03:47
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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
[Reveal] Spoiler: OA
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 07 Dec 2012, 03:52
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Walkabout 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.

Answer: A.
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 18 Dec 2012, 23:28
Walkabout 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


Let Q = 3
Set = {119,120,121} which makes 121 the largest integer

(A) (3-1)/2 + 120 = 121
(B) and (C) yields a decimal. ELIMATE!
(D) 122/2 = 61 ELIMINATE!
(E) yields a decimal. ELIMINATE!

Answer: A
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 29 Dec 2012, 19:08
Really nice method Bunuel!
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 25 Jun 2013, 07:09
Bunuel wrote:
Walkabout 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.

Answer: A.


Sorry, if this is a really stupid question. I am probably missing something, but I do not understand the logic of this approach:

If 120 is the median (i.e. in my mind the middle number of the set) how can 121 then be the largest number? I am asking, since this does not make sense to me, yet and thus I would have never come up with such a good shortcut.

Many thanks
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 25 Jun 2013, 09:18
Expert's post
Revenge2013 wrote:
Bunuel wrote:
Walkabout 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.

Answer: A.


Sorry, if this is a really stupid question. I am probably missing something, but I do not understand the logic of this approach:

If 120 is the median (i.e. in my mind the middle number of the set) how can 121 then be the largest number? I am asking, since this does not make sense to me, yet and thus I would have never come up with such a good shortcut.

Many thanks


We are told that there are Q consecutive integers in a set and Q is odd. We are also told that the median of the set is 120.

Now, say Q=3=odd. So, we have that the median of 3 consecutive integers is 120.
Question: what is the largest of these 3 integers? The set in this case must be {119, 120, 121} (3 consecutive integers with median of 120), so the largest of these 3 integers is 121.

Hope it's clear.
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 25 Jun 2013, 10:22
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] New post 08 Jan 2014, 08:57
I came across an alternate method.
Since Q is odd, therefore Q/2 is a fraction this options B and C are eliminated.( questions talks about integers only).E option is nullified since Q+120 is odd and the result will be a fraction on division with respect to 2. Left A and D just put Q =1,3 or any odd number D gives a value less than 120 therefore it cannot be the largest.

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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 08 Jan 2014, 09:19
If 120 is the middle number,then there will be Q-1/2 numbers both before and after 120.Therefore,largest number will be Q-1/2+120.
Smallest number will be 120-(Q-1/2).

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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 13 Jan 2014, 03:41
Walkabout 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



Pick numbers:

Q = 5, thus we have the numbers 118, 119, 120, 121, 122..

We need to pick an answer that yields 122... A: \frac{(5-1)}{2} + 120 = 122, so A is correct
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 28 Jan 2014, 11:23
Walkabout 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


Average of Q consecutive ints in a list = average of first and the last ints in the list
also for consecutive int mean = median
F = First Number
l = Last Number

avg = \frac{(F + L)}{2}

now L = F + (Q-1)

\frac{(F + F +(Q-1))}{2} = 120

F = 120 - \frac{(Q-1)}{2}

L = 120 - \frac{(Q-1)}{2} + (Q-1) = 120 + \frac{(Q-1)}{2}
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 04 Feb 2014, 12:15
I understand the question if you put it in parenthesis but how would you know which answers need parenthesis and which ones dont
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 05 Feb 2014, 00:55
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kedusei wrote:
I understand the question if you put it in parenthesis but how would you know which answers need parenthesis and which ones dont


Not sure I follow... The answer choices are given, you don't need to put/add anything there...
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 08 Feb 2014, 10:14
Bunuel wrote:
kedusei wrote:
I understand the question if you put it in parenthesis but how would you know which answers need parenthesis and which ones dont


Not sure I follow... The answer choices are given, you don't need to put/add anything there...


These choices have parenthesis but the choices in the book dont
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 08 Feb 2014, 10:20
Expert's post
kedusei wrote:
Bunuel wrote:
kedusei wrote:
I understand the question if you put it in parenthesis but how would you know which answers need parenthesis and which ones dont


Not sure I follow... The answer choices are given, you don't need to put/add anything there...


These choices have parenthesis but the choices in the book dont


Below is a screenshot of this question:
Attachment:
Untitled.png
Untitled.png [ 14.82 KiB | Viewed 2356 times ]
Which is the same as the options in original post:
(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

Can you please tell me what is confusing?
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 27 Feb 2014, 20:27
Bunuel wrote:
Walkabout 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.

Answer: A.


Little eager....might be stupid too but can you assume q=1. This brings me to an important question can you have a median in a set that has only one element. I know this might sound stupid but is this possible. Further if that being so my largest number through option 1 becomes 120. But that is wrong. So am I missing something or the question has been set up assuming odd number starts with 3.

Bunuel request you to please clarify this.
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 27 Feb 2014, 23:48
Walkabout 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


Let us say that the numbers are {119, 120, 121}
Q = 3

(A) (3 - 1)/2 + 120 = 121
(B) 119 + 1.5
(C) 1.5 + 120
(D) (122)/2
(E) (123)/2

Hence option A is the answer
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Re: If Q is an odd number and the median of Q consecutive [#permalink] New post 28 Feb 2014, 02:35
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davidfrank wrote:
Bunuel wrote:
Walkabout 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.

Answer: A.


Little eager....might be stupid too but can you assume q=1. This brings me to an important question can you have a median in a set that has only one element. I know this might sound stupid but is this possible. Further if that being so my largest number through option 1 becomes 120. But that is wrong. So am I missing something or the question has been set up assuming odd number starts with 3.

Bunuel request you to please clarify this.


The median of a single element set is that number itself. For example, the median of {-11} is -11.

Next, you can consider Q to be 1, in this case the set is {120} and the largest integer is 120. Substituting Q=1 into the options gives A as the answer.

Hope it's clear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If Q is an odd number and the median of Q consecutive   [#permalink] 28 Feb 2014, 02:35
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