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collection of tough problems from G PREP - 32

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collection of tough problems from G PREP - 32

by abhasjha » Mon Feb 08, 2010 3:25 am
Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

1) The median of the numbers in Set S is 0.

2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
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by shashank.ism » Mon Feb 08, 2010 4:10 am
abhasjha wrote:Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

1) The median of the numbers in Set S is 0.

2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
Ans is B

S= n, n+1, ....n+4.
T= m, m+1,.....m+6

S1: if median = 0 so we can easily say S=-2,-1,0,1,2 , T = -3,-2,-1,0,1,2,3 ------sufficient.
S2: sum of no. in set S = set T .. It exactly give soln

e.g. S=-2,-1,0,1,2 , T = -3,-2,-1,0,1,2,3----sufficient


so ans is

D
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by sanju09 » Mon Feb 08, 2010 4:53 am
abhasjha wrote:Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

1) The median of the numbers in Set S is 0.

2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
If S is m, m + 1, m + 2, m + 3, and m + 4 then its median is m + 2, and if T is n, n + 1, n + 2, n + 3, n + 4, n + 5 and n + 6 then its median is n + 3. The question is: Is m + 2 = n + 3 or is m - n = 1? Let's find

(1) It means that, m + 2 = 0, but we don't have n to answer whether m - n = 1. Insufficient

(2) It means that, 5 m + 10 = 7 n + 21 or 5 m - 7 n = 11, this cannot determine m - n uniquely. Insufficient

taken together

with m + 2 = 0 and (I'm editing it to correct "5 m - 7 n = 21" only) 5 m - 7 n = 11, m - n can be determined uniquely. Sufficient

[spoiler]C[/spoiler]
Last edited by sanju09 on Mon Feb 08, 2010 10:46 pm, edited 1 time in total.
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by stufigol » Mon Feb 08, 2010 3:14 pm
so what s wrong ith shakan explanation? did he forget a detail...
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by sanju09 » Mon Feb 08, 2010 10:42 pm
stufigol wrote:so what s wrong ith shakan explanation? did he forget a detail...
I'm sorry for having that not seen before.

shashank.ism wrote:
Ans is B

S= n, n+1, ....n+4.
T= m, m+1,.....m+6

S1: if median = 0 so we can easily say S=-2,-1,0,1,2 , T = -3,-2,-1,0,1,2,3 ------sufficient.
S2: sum of no. in set S = set T .. It exactly give soln

e.g. S=-2,-1,0,1,2 , T = -3,-2,-1,0,1,2,3----sufficient


so ans is

D
I can see that shashank.ism must have misconstrued the statement (1) here, which is utterly for set S.
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by ajith » Tue Feb 09, 2010 2:56 am
abhasjha wrote:Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

1) The median of the numbers in Set S is 0.

2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
1. Is insufficient - It does not say anything about the set T
2. The sum of integers are the same
It is possible only when 5 members are the same and the next two members are on the either side
In which case the median are the same.
Sufficient

[spoiler]B
[/spoiler]
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by sanju09 » Tue Feb 09, 2010 3:13 am
ajith wrote:
abhasjha wrote:Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

1) The median of the numbers in Set S is 0.

2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
1. Is insufficient - It does not say anything about the set T
2. The sum of integers are the same
It is possible only when 5 members are the same and the next two members are on the either side
In which case the median are the same.
Sufficient

[spoiler]B
[/spoiler]
What if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}?

If set S is {-2, -1, 0, 1, 2} and set T is {-3, -2, -1, 0, 1, 2, 3}, then in my terminology, YES, m - n = 1; and if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}, then in my terminology, NO, m - n ≠ 1. Insecurity reigns.
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by ajith » Tue Feb 09, 2010 4:31 am
sanju09 wrote:
What if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}?

If set S is {-2, -1, 0, 1, 2} and set T is {-3, -2, -1, 0, 1, 2, 3}, then in my terminology, YES, m - n = 1; and if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}, then in my terminology, NO, m - n ≠ 1. Insecurity reigns.
I agree, Mistake again... Little too hasty I suppose.... I am not writing GMAT with this hit rate
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by sanju09 » Tue Feb 09, 2010 4:55 am
ajith wrote:
sanju09 wrote:
What if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}?

If set S is {-2, -1, 0, 1, 2} and set T is {-3, -2, -1, 0, 1, 2, 3}, then in my terminology, YES, m - n = 1; and if set S is {5, 6, 7, 8, 9} and set T is {2, 3, 4, 5, 6, 7, 8}, then in my terminology, NO, m - n ≠ 1. Insecurity reigns.
I agree, Mistake again... Little too hasty I suppose.... I am not writing GMAT with this hit rate
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