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# If there are 5 positive integers in Set B and the mean is

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Senior Manager
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If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 06:43
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If there are 5 positive integers in Set B and the mean is equal to 7, what is median?

1. The integers in Set B are consecutive and odd

2. The mode is also equal to 7
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Kudos [?]: 418 [0], given: 47

Manager
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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 08:13
My guess is here is D.

Whats the OA?
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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 11:41
using (a) for sure if the 5 integers are w,x,y,z,r
(w+x+y+z+r)/5 = 7
w+x+y+z+r=30
using (a) consecutive odd integers, the numbers will be 3,5,7,9,11

using (b) mode=7
with same numbers w+x+y+z+r=30...r-w is satisfied by many numbers.

IMO: A

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 11:49
hmm...I also went with (D).
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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 14:38
jeeteshsingh wrote:
If there are 5 positive integers in Set B and the mean is equal to 7, what is median?

1. The integers in Set B are consecutive and odd

2. The mode is also equal to 7

st 1 ) for consequetive integers, mean and median are same.
Sufficient
st 2) mode is 7. We know the total of the number is 7 * 5 = 35 and number 7 occurs more than once. let the other 3 numbers be a,b,c - these number can be equal to 7 or more than 7 or less than 7.
- All the 3 numbers cannot be more than 7(in this case mean will be > 7) and all the numbers cannot be less than 7( in this case mean in < 7). So one or two number are more than 7 and the other numbers are less than 7 or some of the numbers could even be 7 .. in any case the median will be 7 as 7 will be the middle number
Sufficient

D

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 16:08
jeeteshsingh wrote:
If there are 5 positive integers in Set B

Does it mean Set B has only 5 integers ?

it might include also zeros and -ve numbers and the mode and mean will still be 7 but we cant get the median from St 2.

In St. one for any evenly spaced set Mean = Median

so A for me

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 16:19
Doesn't B contradict A? How can 5 consecutive odd integers also have a mode of 7? Am I wrong to assume this?

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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11 Mar 2010, 19:25
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just my interpretation, the mode is the # that appears the most, it does not say that is the only mode. There could in fact be 5 numbers that each appear once and as such are each the mode.

Statement I = Sufficient - Consecutive odd intergers of a 5 # set: mean = median so 7

Statement II = Insufficient

One example 7 7 7 7 7 mean and median are 7 mode is 7
Another example 1 2 3 7 22 mean is 7 mode is 1,2,3,7,22 and median is 3

So A

Just my thoughts

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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12 Mar 2010, 11:38
run4run wrote:
just my interpretation, the mode is the # that appears the most, it does not say that is the only mode. There could in fact be 5 numbers that each appear once and as such are each the mode.

I think if a set has 5 different numbers then it has no mode.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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12 Mar 2010, 12:53
what's the OA and the source? I think you guys brought up a good point that B kind of contradicts A...and I've never really seen any other question that has this type of contradiction.
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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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13 Mar 2010, 18:41
Pedros wrote:
run4run wrote:
just my interpretation, the mode is the # that appears the most, it does not say that is the only mode. There could in fact be 5 numbers that each appear once and as such are each the mode.

I think if a set has 5 different numbers then it has no mode.

If a set has 5 different numbers then the mode is those 5 numbers. For example (1,2,3,4,5); the mode is 1, 2, 3, 4 and 5.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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14 Mar 2010, 13:38
Yeah I remember reading that in DS all the statements MUST be true. I'm no statistician, but it seems that statement B contradicts statement A as others have mentioned.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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14 Mar 2010, 13:42
hmm take a look at this question:
gmatclub-test-m-05-question-91417.html#p699605

statement 1 is "X is a mode of [3, 0, 1, -1, 0, 5, 1]" which suggests that a set can have more than 1 mode

in that case statement 2 does not contradict statement 1 in this question, BUT the phrasing of statement 2 in this case (THE mode) suggests that there is only one...

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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14 Mar 2010, 22:45
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jeeteshsingh wrote:
If there are 5 positive integers in Set B and the mean is equal to 7, what is median?

1. The integers in Set B are consecutive and odd
2. The mode is also equal to 7

1: Sufficient.
Let a as first term so mean = a+a+2+a+4+a+6+a+8 = 5a +(2+4+6+8) = 35 hence we can find a and median.

2: Insufficient
Mode is 7 so it comes maximum number of times but not sure how many times it can be 2 or 3 or 4 or 5. Hence not sufficient to answer.

Answer should be A.
What is the OA.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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15 Mar 2010, 07:41
bangalorian2000 wrote:
jeeteshsingh wrote:
If there are 5 positive integers in Set B and the mean is equal to 7, what is median?

1. The integers in Set B are consecutive and odd
2. The mode is also equal to 7

1: Sufficient.
Let a as first term so mean = a+a+2+a+4+a+6+a+8 = 5a +(2+4+6+8) = 35 hence we can find a and median.

2: Insufficient
Mode is 7 so it comes maximum number of times but not sure how many times it can be 2 or 3 or 4 or 5. Hence not sufficient to answer.

Answer should be A.
What is the OA.

If the mode is stated to be 7, then it shouldn't matter how many times it happens. The total amount of the 5 numbers in this question has to be 35 and by playing around with numbers a bit, you'll find out that 7 will have to be the median, whether appears only twice, or all five times.
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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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15 Mar 2010, 08:14
bakfed wrote:
bangalorian2000 wrote:
jeeteshsingh wrote:
If there are 5 positive integers in Set B and the mean is equal to 7, what is median?

1. The integers in Set B are consecutive and odd
2. The mode is also equal to 7

1: Sufficient.
Let a as first term so mean = a+a+2+a+4+a+6+a+8 = 5a +(2+4+6+8) = 35 hence we can find a and median.

2: Insufficient
Mode is 7 so it comes maximum number of times but not sure how many times it can be 2 or 3 or 4 or 5. Hence not sufficient to answer.

Answer should be A.
What is the OA.

If the mode is stated to be 7, then it shouldn't matter how many times it happens. The total amount of the 5 numbers in this question has to be 35 and by playing around with numbers a bit, you'll find out that 7 will have to be the median, whether appears only twice, or all five times.

Point accepted. Median will be 7 if mode is 7. What is the OA?

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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15 Mar 2010, 09:26
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Should it be D?

1) is quite straight forward

2) Since 7 is the mode, there are at least two 7s.

If there are three or more 7s, the median would be 7.

If there are only two 7s, the set would be: {7 7 a b c} where a+b+c=35-14=21. If a > 7, b or c must be smaller than 7 to give a sum of 21. Hence, 7 will ranked the third (the median) in all scenarios.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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16 Mar 2010, 07:36
its a
cannot be b 777777 or 1 7 8 9 10

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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16 Mar 2010, 10:05
Correction: Answer is D.

Statement 1 is pretty clear.
From statement 2 you can derive that median is 7 if mode is 7.
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Last edited by sidhu4u on 22 Mar 2010, 12:41, edited 2 times in total.

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Re: If there are 5 positive integers in Set B and the mean is [#permalink]

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16 Mar 2010, 10:06
jatt86 wrote:
its a
cannot be b 777777 or 1 7 8 9 10

But (B) says that the mode is 7; therefore, there has to be at least two 7's in the 5 numbers.
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Re: If there are 5 positive integers in Set B and the mean is   [#permalink] 16 Mar 2010, 10:06

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