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555-605 (Medium)|   Statistics and Sets Problems|                                 
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EMPOWERgmatRichC
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If Q is an odd number and the median of Q consecutive integers is 120 03 Apr 2021, 11:53
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Hi chayma,

How often have you actually tried TESTing VALUES and ended up facing the specific situation that you are concerned about? Keep in mind that some questions will actually require that you TEST more than one value (or set of values) based on how the prompt is worded - and since DS questions are all about whether the answer to the question is consistent or inconsistent, you HAVE to TEST multiple values to make sure that you have the correct answer.

When TESTing VALUES, as long as you are following whatever 'restrictions' the prompt describes, if only one answer matches what you are looking for, then that answer is the correct answer.

GMAT assassins aren't born, they're made,
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If Q is an odd number and the median of Q consecutive integers is 120 04 Apr 2021, 07:35
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chayma
I have a problem with plugging in numbers , i always think that it won't work if i try different values. How do i make sure that it would be the same result everytime ?
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Dear chayma,
begin you journey from that tasks, take into consideration what restrictions are ?
In our case:
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

So, you can start to put any ODD numbers, and the upshot will be the same.

3: 119, 120, 121
5: 118, 119, 120, 121, 122
etc.

Then substitute in the equations to find right one

(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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If Q is an odd number and the median of Q consecutive integers is 120 30 May 2021, 07:13
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Walkabout
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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Answer: Option A

Video solution by GMATinsight


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If Q is an odd number and the median of Q consecutive integers is 120 01 Aug 2021, 08:17
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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If Q is an odd number and the median of Q consecutive integers is 120 19 Feb 2022, 20:33
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BrentGMATPrepNow
Walkabout
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

A very fast solution is to see what happens when Q = 1.
This means that there's only ONE integer in the set.
So, if the median of the set is 120, then the set is {120}, which means the greatest value in the set is 120

So the correct answer choice should yield 120 when Q = 1.

a) (1-1)/2 + 120 = 120 PERFECT!
b) 1/2 + 119 = some non-integer
c) 1/2 + 120 = some non-integer
d) (1+119)/2 = 60
e) (1+120)/2 = some non-integer

Since only answer choice A yield the correct output, it is the correct answer.

Cheers,
Brent
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BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)
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If Q is an odd number and the median of Q consecutive integers is 120 20 Feb 2022, 06:57
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BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)
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The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.
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If Q is an odd number and the median of Q consecutive integers is 120 13 Jun 2022, 14:19
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Testing cases is the best option here, but here is the algebra for those who are interested:
S = smallest integer, L = largest integer, Q=number of terms in a set (and we're given that it's odd).

In any set of consecutive integers, the mean is equal to the median and either can be found by finding the average of the smallest and the largest integer. Since median is 120, it follows that:
\(\frac{(S+L)}{2} = 120\)
\(S+L = 240\)
\(S = 240-L\)

The number of terms (inclusive) in a set in which the difference between each term is constant is given by:
\(\frac{(L-S)}{(Difference)} + 1\)
Since we have a set of consecutive integers, the difference between each term is 1 and so:

\(Q=(L-S)+1 \)
\(L = Q-1+S \) (Plug in for S using above)
\(L=Q-1+240-L\)
\(2L=Q-1+240\)
\(L=\frac{(Q-1)}{2} + 120\)
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If Q is an odd number and the median of Q consecutive integers is 120 14 Jun 2022, 09:51
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BrentGMATPrepNow
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BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)

The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.
Show more




Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?
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If Q is an odd number and the median of Q consecutive integers is 120 14 Jun 2022, 16:29
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BrentGMATPrepNow
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BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)

The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.




Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?
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Hi woohoo921,

Yes - when TESTing VALUES, if only one of the 5 answers matches what you are looking for, then that answer is the correct answer. If more than one answer matches, then one of those answers is the correct answer (and the other(s) only sometimes match what you are looking for) - meaning that you would then have to TEST again with a different value (or values) to find the one answer that is ALWAYS a match.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]
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If Q is an odd number and the median of Q consecutive integers is 120 14 Jun 2022, 16:51
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EMPOWERgmatRichC
woohoo921




Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?

Hi woohoo921,

Yes - when TESTing VALUES, if only one of the 5 answers matches what you are looking for, then that answer is the correct answer. If more than one answer matches, then one of those answers is the correct answer (and the other(s) only sometimes match what you are looking for) - meaning that you would then have to TEST only the answer choices that are still remaining (you do not need to test anything that was already eliminated with your first set of values) again with a different value (or values) to find the one answer that is ALWAYS a match.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]
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woohoo921

Maybe more cooks in the kitchen than you need, especially since Rich and Brent have already done a great job answering...great enough that I'll simply add a few words to Rich's post (in red) juuuuuust in case it wasn't already clear.
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If Q is an odd number and the median of Q consecutive integers is 120 06 Jun 2023, 23:24
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If we were to derive it.
nth term in Arithmetic Progression is

\(t_n = a + (n-1)d\)

where a is first term, n is number of the term in the sequence, d is difference between two successive terms and \(t_n\) is the actual value of nth term

120 is the median and Q is given as odd. So it is the \(\frac{(Q+1)}{2}\) th term. Here d is 1 since numbers are consecutive.

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

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

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

We will use this value of a in the next step.

Now the Qth term which will be the largest term in the sequence

\(= a + (Q-1) 1\)

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

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

Ans: A
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If Q is an odd number and the median of Q consecutive integers is 120 19 May 2024, 06:59
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Even if it is confusing at first, we can just check the options by using 1st 5 consecutive no. i.e. 1,2,3,4,5.

3 is the median and the last no. is 5.

Place the value of Q= 5 in options A and D (as B, C and E and already eliminated).

Only A satisfies the condition. Hence, the answer.
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If Q is an odd number and the median of Q consecutive integers is 120 27 May 2025, 09:56
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Sum of N consecutive integers assuming that we are strating from zero and N=Q

(N(N+1))/2

For an oddly spaced set, mean=median, thus mean =120
120=(Q(Q+1)/2)/Q
Q=239

thus numbers are 1......119(119 numbers) 120 121..........239(119 numbers)
Largest number thus can be expressed as 120+ (Q-1)2

Also you can substitute Q in answer choices which I don't recommend since we need to conceptually solve this problem.

Revert if you have any doubts


Walkabout
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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If Q is an odd number and the median of Q consecutive integers is 120 30 May 2026, 03:20
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