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# Both {14 zeros and 60} and {13 zeros and 30, 30} have sum of

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Kudos [?]: 2143 [0], given: 359

Both {14 zeros and 60} and {13 zeros and 30, 30} have sum of [#permalink]  19 Apr 2010, 17:39
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Difficulty:

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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
OG12 DS#133 page:284
Alternative solution/shortcut:

1) Both {14 zeros and 60} and {13 zeros and 30, 30} have sum of 60. Insufficient.
2) Let's pick any 3 numbers. Now, let's replace any number X out of 3 picked numbers by any number Y out of rest 12 numbers. The sum of new 3 numbers will be the same, 12. So, our operation doesn't change the sum and X=Y. Because we choose X and Y randomly, all numbers in the list are equal. Sufficient.

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Both {14 zeros and 60} and {13 zeros and 30, 30} have sum of   [#permalink] 19 Apr 2010, 17:39
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