A1 through A9

[logitech]

Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

OA TBA

[jimmiejaz]

Hi Logitech,
considering A1<A2<....<A9
As we have got odd numbers, ie. A1 to A9,
the mean is A5
range is A9-A1

For B1 to B9
the mean is B5=A5+5
range is B9-B1=A9+9-A1-1=A9-A1+8
Difference in sum of mean and range

=(A9-A1+8+A5+5)-(A9-A1+A5)
=13

[mals24]

I'm getting weird answers.

I tried plugging in numbers.

A = -1, 2, -8, 10, 12, -5, 7, 3, -4
B = 0, 4, -5, 14, 17, 1, 14, 11, 5

A's mean = 1.7
A's range = 12-(-8 ) = 20

B's mean = 6.7
B's range = 17 - (-5) = 22

Difference = 28.7 - 21.7 = 7

But when I saw jimmiejaz's method and changed the order A1<A9, I got the answer as 13.

I doubled check both the methods and you still get 7 and 13, two different answers.

If this was a DS question I would have marked E but this is PS

[rohangupta83]

considering A1<A2<....<A9
=13

But this is an assumption we are making. It's not stated explicitly in the question.

[mals24]

But this is an assumption we are making. It's not stated explicitly in the question

.

Good catch Rohan, I missed that point and was still thinking why is 7 or 13 incorrect. So that means both the options 7 and 13 can be true.

Logitech whats the OA? and if possible can you post the explanation of this question Im lost : (plus i need a shorter way to do this question, it took 15 mins!!)

[jimmiejaz]

But this is an assumption we are making. It's not stated explicitly in the question

.

Good catch Rohan, I missed that point and was still thinking why is 7 or 13 incorrect. So that means both the options 7 and 13 can be true.

Logitech whats the OA? and if possible can you post the explanation of this question Im lost : (plus i need a shorter way to do this question, it took 15 mins!!)

yes, i took that just to simplify the question. Anyways, answer will still be 13.

Mean for first set = (A1+A2+....+A9)/9 = Z
Range = A9-A1

Mean for second set = (A1+A2+....+A9+45)/9 = Z+5
Range for second set = A9+9 - A1-1 = A9-A1+8

Difference is still 13.
The key to this question is dont pick numbers coz if you do, it will consume time and will have to chk multiple options.
Hope it helps.

[mals24]

But then try plugging in values you will not get 13. You will get different values. I think rohan sort of got the catch in the question. The main trap here is people will assume that A1<A9.

You are right in your approach jimmiejaz that the mean will be the same, but then how do you determine the range? Like when I plugged in numbers I got two different ranges and the mean of B was exactly 5 more than mean of A (something which you have proved).

But when I did the general way which you did later on jimmiejaz, even I got 13.

Hence Im still confused

[jimmiejaz]

Hmm, i get your point but since it is a P.S question, this is the only thing we can assume else as u plugged in numbers, we will get diff answers.
Now, we shall look upto Logitech as to what trick he pulls out of his bag to solve this question.

[tnis0612]

Like you guys have said already I don't see how this problem can be solved based on the information given. I don't see any reason why you can't use 1,2,3,4,5,6,7,8,9 or 5,4,6,7,2,1,9,8,3 or 9,8,7,6,5,4,3,2,1 as your sets. Doing it that way you get a different answer for each one. I vote for E

[rohangupta83]

But then try plugging in values you will not get 13. You will get different values. I think rohan sort of got the catch in the question. The main trap here is people will assume that A1<A9.

You are right in your approach jimmiejaz that the mean will be the same, but then how do you determine the range? Like when I plugged in numbers I got two different ranges and the mean of B was exactly 5 more than mean of A (something which you have proved).

But when I did the general way which you did later on jimmiejaz, even I got 13.

Hence Im still confused

The difference in solutions is because jimmiejaz has again assumed something

Assumption is - the lowest number is the one which is being incremented by 1 and the largest number is the one being incremented by 9. Again its not explicitly stated that the lowest number is A1 and the largest is A9.

In hindsight, jimmiejaz has subconsciously assumed again that A1<.......<A9.

Mean will not be impacted whether we assume this or not but range does get impacted.

Hence, the difference.

I'm as confused as all you guys but I don't see a specific solution to this problem the way its put.

imo E

[jimmiejaz]

But then try plugging in values you will not get 13. You will get different values. I think rohan sort of got the catch in the question. The main trap here is people will assume that A1<A9.

You are right in your approach jimmiejaz that the mean will be the same, but then how do you determine the range? Like when I plugged in numbers I got two different ranges and the mean of B was exactly 5 more than mean of A (something which you have proved).

But when I did the general way which you did later on jimmiejaz, even I got 13.

Hence Im still confused

The difference in solutions is because jimmiejaz has again assumed something

Assumption is - the lowest number is the one which is being incremented by 1 and the largest number is the one being incremented by 9. Again its not explicitly stated that the lowest number is A1 and the largest is A9.

In hindsight, jimmiejaz has subconsciously assumed again that A1<.......<A9.

Mean will not be impacted whether we assume this or not but range does get impacted.

Hence, the difference.

I'm as confused as all you guys but I don't see a specific solution to this problem the way its put.

imo E

Rohan,
Now you have assumed that this is a DS question and hence gave the ans as E whereas its a PS question.

[uttara]

Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

OA TBA

There are two points to consider:

relative position of the numbers
&
values of the numbers
ie the first number in a set will be represented by A1 and the value of the number which is represented by A1 might be 2 or might be 10

now
Mean:
For both sets, mean is independent of relative position of the numbers

Range
Set A's Range depends only on the values of the numbers
Set B's Range depends on both relative position of the numbers & values of the numbers

The question is asking for an absolute value, which cant be found by using the given information in the question.

This cant be a PS question.

[logitech]

Good work people.

This problem can not be solved with the given information.

[cramya]

It's a PS question and the choices were

4
9
13
17
cannot be determined


Please post atleast the choices as it gives some hint to the users to solve

As someone said before (I think its Logitech) we are not taking a math midterm or final exam here..

Its GMAT and they give choices why cant we?? Just a thought!

Nice question by the way...