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A collection of cards

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A collection of cards

by arorag » Sat Jul 19, 2008 5:02 pm
A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?
(1) The units digit of the sum of the numbers on the remaining 35 cards is 6. (2) The sum of the numbers on the remaining 35 cards is 176.

I know II is insuff. what abt I??
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by Mustang » Sat Jul 19, 2008 7:15 pm
I believe that the answer should be D...is it right? i will give my explaination once I know i am not just fantasizing
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by Stuart@KaplanGMAT » Sun Jul 20, 2008 12:29 am
Each statement is sufficient by itself: choose (D).

(1) There are 9 different numbers, so if you know what the units digit is when you remove 1 card, you can definitely figure out which number got removed.

We could (but lord knows we don't want to) add up all 36 cards and figure out the units digit of the sum. If we subtract the units digit of the sum of the remaining 35 cards, we get the card number that was removed.

(2) Again, we can add up all 36 cards. If we subtract 176, we know the number of the card that's missing.
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by farooq » Wed Jan 20, 2010 10:03 am
arorag wrote:A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?
(1) The units digit of the sum of the numbers on the remaining 35 cards is 6. (2) The sum of the numbers on the remaining 35 cards is 176.

I know II is insuff. what abt I??
This is really an interesting questions.

Four set can be:
A - 1,2,3.......9
B - 1,2,3.......9
C - 1,2,3.......9
D - 1,2,3.......9

Sum of 1 to 9 = 45.
Therefore sum of four sets = 4*45 = 180.

Statement A: Sum of 35 cards is _ _ 6. It can be 166, 176, 156 but lowest number is 1 and highest number is 9.

180 - (a number from 1 to 9) = 176.
It is only possible when we subtract 4. Hence the given information is sufficient.

Statement B: Sum of 36 numbers = 180
Sum of rest 35 = 176.
180-176 = 4 Sufficient.

D
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Farooq Farooqui.
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