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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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New post 07 Jan 2014, 05:13
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A
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Question Stats:

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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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New post 07 Jan 2014, 09:08
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1
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 Hence 4 is the withdrawn card.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 Hence again 4 is the withdrawn card.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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New post 07 Jan 2014, 05:14
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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.

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

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New post 08 Jan 2014, 00:03
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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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New post 08 Jan 2014, 08:57
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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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New post 01 Apr 2019, 07:19
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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.


Target question: What is the number on the card?

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

Cheers,
Brent
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Re: A collection of 36 cards consists of 4 sets of 9 cards each.   [#permalink] 01 Apr 2019, 07:19
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