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OG - Question 21 - 2nd Edition

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OG - Question 21 - 2nd Edition

by shanice » Thu Jul 19, 2012 10:09 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 he collection, what is the number on that card?

(1)The unit 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.

Answer is D - Each statement alone is sufficient.

How do I approach this type of question?
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by Anurag@Gurome » Thu Jul 19, 2012 11:48 pm
shanice 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 he collection, what is the number on that card?

(1)The unit 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.
Sum of the numbers on 36 cards = 4*(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 4*45 = 180
As maximum number on a card is 9, the minimum sum of the numbers on the remaining 35 cards = (180 - 9) = 171

Hence, the sum of the numbers on the remaining 35 cards must be greater than 170 and less than 180.

Statement 1: Sum of the numbers on the remaining 35 cards ends with 6. Only number between 170 and 180 that ends with 6 is 176.
Hence, the number on the removed card = (180 - 176) = 4

Sufficient

Statement 2: Sum of the numbers on the remaining 35 cards is 176.
Hence, the number on the removed card = (180 - 176) = 4

Sufficient

The correct answer is D.
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by niketdoshi123 » Thu Jul 19, 2012 11:58 pm
shanice 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 he collection, what is the number on that card?

(1)The unit 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.
First look at both the statements. They both talk about the sum of the remaining cards. This means we have to find the sum of all 36 cards so that we can find the value of the card that is removed from the collection.

Sum of all 36 cards = Number of sets * Sum of numbers in each set (as all sets have the same numbers ,i.e from 1 to 9)
=> 4* (n(n+1)/2) here n(n+1)/2 is the sum of n natural numbers. n= 9 in this question
=> 4* 9*10/2 = 180

check statement 2 first as its simple.
Statement 2:SUFFICIENT

value of the card removed = sum of 36 cards - sum of 35 cards = 180 -176 =4

statement 1:SUFFICIENT

If this statement is sufficient "4" should satisfy this statement
=>180 -4 =176 . the unit digit is 6, no other number in the set will satisfy the statement.

Hence the answer is D
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