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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

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.

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.

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.

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

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12 Mar 2015, 06:07

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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

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.

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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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.

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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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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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.

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...
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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.

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, Please help me!

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.

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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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.

Answer: A
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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.