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If Q is an odd number and the median of Q consecutive
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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
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Re: If Q is an odd number and the median of Q consecutive
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07 Dec 2012, 03:52
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
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08 Jan 2014, 09:19
If 120 is the middle number,then there will be Q1/2 numbers both before and after 120.Therefore,largest number will be Q1/2+120. Smallest number will be 120(Q1/2).
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Re: If Q is an odd number and the median of Q consecutive
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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) (31)/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
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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
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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
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25 Jun 2013, 09:18
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
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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
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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
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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: \(\frac{(51)}{2} + 120 = 122\), so A is correct



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Re: If Q is an odd number and the median of Q consecutive
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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 + (Q1) \frac{(F + F +(Q1))}{2} = 120 F = 120  \frac{(Q1)}{2} L = 120  \frac{(Q1)}{2} + (Q1) = 120 + \frac{(Q1)}{2}



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Re: If Q is an odd number and the median of Q consecutive
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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
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05 Feb 2014, 00:55
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
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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
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08 Feb 2014, 10:20
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 [ 14.82 KiB  Viewed 65145 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
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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
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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
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28 Feb 2014, 02:35
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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Re: If Q is an odd number and the median of Q consecutive
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01 Sep 2014, 12:30
[quote="AKG1593"]If 120 is the middle number,then there will be Q1/2 numbers both before and after 120.Therefore,largest number will be Q1/2+120. Smallest number will be 120(Q1/2).
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Can you please elaborate on this? How did you get Q1/2? Versus Q*1/2?



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Re: If Q is an odd number and the median of Q consecutive
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03 Sep 2014, 01:38
Chin926926 wrote: AKG1593 wrote: If 120 is the middle number,then there will be Q1/2 numbers both before and after 120.Therefore,largest number will be Q1/2+120. Smallest number will be 120(Q1/2).
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Can you please elaborate on this? How did you get Q1/2? Versus Q*1/2? Just refer to Bunuel's method at the top. Plugging in the numbers of example 119, 120, 121 should give the perfect result




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