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# A collection of 36 cards consists of 4 sets of 9 cards each.

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A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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07 Jan 2014, 04:13
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Difficulty:

25% (medium)

Question Stats:

75% (01:35) correct 25% (01:46) wrong based on 612 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 21
Category: Arithmetic Properties of numbers
Page: 154
Difficulty: 600

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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07 Jan 2014, 04:14
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SOLUTION

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one cadrd 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 --> we can get the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get which card should be removed so that the new sum to have the units digit of 6 (as cards are from 1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here. Sufficient.

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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07 Jan 2014, 08:08
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Total sum of numbers on 4 decks is [(9X10)/2]X4=180

1. only 180- 4 will be get you a units digit of 6. Hence 4 is the withdrawn card. --> Sufficient
2. 180 -4 =176 . Hence again 4 is the withdrawn card. --> Sufficient

Hence D

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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07 Jan 2014, 23:03
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45 is the sum of each set (n(n+1)/2, n=9).Thus total sum would be 45*4 = 180.

Statement 1: subtracting x (x<=9) from 180 should give a units digit of 6, i.e. x=4 ---> Sufficient
Statement 2 : sum of remaining cards: 176, only 4 is left out. Sufficient

So D it is

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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08 Jan 2014, 07:57
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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 value of the card can be 1 to 9.
Statement 1) Sum of all the cards of one set = 1+2+..+9 = 9*10/2 = 45
So all the 4 sets = 4*45 = 180
last digit is 6 so card has to have a value of 4 because no other card number will satisfy the condition.

Statement 2) The sum is even more explicit. So definitely we can determine.

Hence option D)
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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11 Jan 2014, 06:10
SOLUTION

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one cadrd 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 --> we can get the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get which card should be removed so that the new sum to have the units digit of 6 (as cards are from 1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here. Sufficient.

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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17 May 2015, 23:19
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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20 Jun 2016, 09:08
Hello from the GMAT Club BumpBot!

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink]

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12 Feb 2017, 07:37
romitsn wrote:
Total sum of numbers on 4 decks is [(9X10)/2]X4=180

1. only 180- 4 will be get you a units digit of 6. Hence 4 is the withdrawn card. --> Sufficient
2. 180 -4 =176 . Hence again 4 is the withdrawn card. --> Sufficient

Hence D

Best explanation hands down

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Re: A collection of 36 cards consists of 4 sets of 9 cards each.   [#permalink] 12 Feb 2017, 07:37
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