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Manager  P
Joined: 10 Oct 2018
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Is the median of class A and class B combined greater than the mean of  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 40% (01:56) correct 60% (01:48) wrong based on 50 sessions

### HideShow timer Statistics  Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a + b = 69
(2) a = 37, b = 32

Attachment: 2016-01-12_2221.png [ 4.08 KiB | Viewed 591 times ]

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Originally posted by EncounterGMAT on 06 Dec 2018, 09:56.
Last edited by Bunuel on 29 Mar 2019, 06:35, edited 3 times in total.
Manager  S
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!

Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. Mean = $$\frac{(72a + 69b)}{a+b}$$
Mean cannot be found as we do not know 'a' and 'b'. Median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Mean can be found since we have 'a' and 'b'. However, median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = $$\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}$$
However, that is an incorrect approach.
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Originally posted by Darshi04 on 22 Dec 2018, 14:13.
Last edited by Darshi04 on 23 Dec 2018, 00:36, edited 1 time in total.
GMAT Tutor B
Joined: 07 Nov 2016
Posts: 56
GMAT 1: 760 Q51 V42 Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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Darshi04 wrote:
topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!

Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. By knowing the total number of students in the class, we can find mean, i.e $$\frac{Mean(a) + Mean(a)}{a + b}$$
However, median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = $$\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}$$
However I believe this can be done only in case of Mean.

I think there should be a correction in your explanation for St 1

Mean for both the classes combined = $$\frac{(72a + 69b)}{( a +b )}$$

= $$\frac{(72a + 69b)}{(69)}$$

Cannot be found
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Manager  S
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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ksrutisagar wrote:
Darshi04 wrote:
topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!

Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. By knowing the total number of students in the class, we can find mean, i.e $$\frac{Mean(a) + Mean(a)}{a + b}$$
However, median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = $$\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}$$
However I believe this can be done only in case of Mean.

I think there should be a correction in your explanation for St 1

Mean for both the classes combined = $$\frac{(72a + 69b)}{( a +b )}$$

= $$\frac{(72a + 69b)}{(69)}$$

Cannot be found

ksrutisagar
Ahh, thanks for pointing that out. Will edit the response!
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We learn permanently when we teach,
We grow infinitely when we share. Re: Is the median of class A and class B combined greater than the mean of   [#permalink] 23 Dec 2018, 00:31
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