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Card problem

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Card problem

by mgmt_gmat » Fri Feb 12, 2010 2:06 am
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.
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Source: — Data Sufficiency |
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by ajith » Fri Feb 12, 2010 6:29 am
mgmt_gmat 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.
The initial sum of the numbers on the cards = 4* (1+2+...+9) = 4*45 = 180

1) The units digit of the sum of the numbers on the remaining 35 cards is 6; if we are sure that only 1 card is removed the possible range of numbers the sum can take is 171 to 179 and only 176 has the last digit as 6. 4 was removed from the collection - Sufficient

2) initial sum =180 ; sum after removing one card =176 ; number on the card which was removed = 180-176 = 4; sufficient

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