collection of tough problems from G PREP - 27

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abhasjha
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Topic: collection of tough problems from G PREP - 27

Mon Feb 08, 2010 4:14 am

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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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shashank.ism
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Mon Feb 08, 2010 4:54 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 _________________ Nothing is Impossible, even Impossible says I'm possible.

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Ian Stewart
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Mon Feb 08, 2010 2:37 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. _________________ private GMAT tutor contact me via the tutor directory at www.gmatix.com

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papgust
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Mon Feb 08, 2010 10:05 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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harsh.champ
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Tue Feb 09, 2010 12:43 am

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. _________________ Just because something is hard doesn't mean you shouldn't try,it means you should just try harder. "Keep Walking" - Johnny Walker http://www.beatthegmat.com/who-will-win-the-ipl-t54684.html#236707