A collection of 36 cards consists of 4 sets of 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.
[spoiler]OA=D[/spoiler]
Source: Official Guide
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A collection of 36 cards consists of 4 sets of 9 cards
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Target question: What is the number on the card?VJesus12 wrote:A collection of 36 cards consists of 4 sets of 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.
Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9.
Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6.
1+2+3+4+5+6+7+8+9=45
Since there are 4 sets of cards numbered 1 to 9, the SUM of all 36 cards = 4(45) = 180
When we remove one card, the sum of the REMAINING 35 cards = --6 (units digit 6)
In other words, 180 - (value of chosen card) = --6
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The sum of the numbers on the remaining 35 cards is 176.
In other words, 180 - (value of chosen card) = 176
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
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Solution:VJesus12 wrote: ↑Mon Apr 01, 2019 3:59 amA collection of 36 cards consists of 4 sets of 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.
[spoiler]OA=D[/spoiler]
Source: Official Guide
Question Stem Analysis:
We need to determine the number on the card that is removed from the collection of 36 cards.
Statement One Alone:
Since the sum of all the numbers on the cards is (1 + 2 + 3 + … + 9) x 4 = 45 x 4 = 180, the units digit of this sum is 0. Therefore, if one card is removed and the units digit of the sum of the numbers on the remaining 35 cards is 6, the card that is removed must have the number 4. Statement one alone is sufficient.
Statement Two Alone:
From statement one, we see that the sum of the sum of all the numbers on the cards is 180. Therefore, if the sum of the numbers on the remaining 35 cards is 176, the card that is removed must have the number 4. Statement two alone is sufficient.
Answer: D
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