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collection of tough problems from G PREP - 27

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by abhasjha » Mon Feb 08, 2010 3:14 am
Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.
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Source: — Data Sufficiency |
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by shashank.ism » Mon Feb 08, 2010 3:54 am
abhasjha wrote:Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.
statement 1: 60 = 15* 4 so either all numbers are 4 but their can be other numbers like 3+5= 4+4 etc. ...insufficient
statement 2: 12 =3* 4 .. so but these 3 nos can be arranged among themselves like 2+3 +7 = 4+4+4 etc. ---- insufficient.

combined... a group of 3 can be arranged similarly among 60 numbers since 60 is divisible by 5..
so again insufficient
hence ans is E
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by Ian Stewart » Mon Feb 08, 2010 1:37 pm
abhasjha wrote:Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.
Statement 1 is clearly not sufficient.

Statement 2: Say we have the numbers a, b, c, and x in our list. We know from S2:

a + b + c = 12
x + b + c = 12

Subtract the second equation from the first and you find that a = x. Since I can prove that for any two numbers in the list in the same way (there's nothing special about a and x here), all the numbers in the list must be equal (they all must be 4), and Statement 2 is sufficient.
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by papgust » Mon Feb 08, 2010 9:05 pm
Ian Stewart wrote:Statement 2: Say we have the numbers a, b, c, and x in our list. We know from S2:

a + b + c = 12
x + b + c = 12

Subtract the second equation from the first and you find that a = x. Since I can prove that for any two numbers in the list in the same way (there's nothing special about a and x here), all the numbers in the list must be equal (they all must be 4), and Statement 2 is sufficient.
Ian,

I couldn't get your Statement II logic. Can you pls explain a bit more?
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by harsh.champ » Mon Feb 08, 2010 11:43 pm
papgust wrote:
Ian Stewart wrote:Statement 2: Say we have the numbers a, b, c, and x in our list. We know from S2:

a + b + c = 12
x + b + c = 12

Subtract the second equation from the first and you find that a = x. Since I can prove that for any two numbers in the list in the same way (there's nothing special about a and x here), all the numbers in the list must be equal (they all must be 4), and Statement 2 is sufficient.
Ian,

I couldn't get your Statement II logic. Can you pls explain a bit more?
Well,
In statement 2 it is given that the sum of 3 no.s is 12,
so a+b+c=12 as well as x+b+c =12
WHICH IS ONLY POSSIBLE WHEN A=X.
So,it can be proved that all the no.s are equal and their value = 4.

Hence,statement 2 is sufficient.
I hope you get it now.:)
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