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Difficulty: 505-555 Level,    Arithmetic,                      
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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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. The 9 car [#permalink]
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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. The 9 car [#permalink]
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Hi All,

This question can actually be solved 'conceptually' - with very little math at all. However, the math involved is fairly low-level arithmetic, so here's how that math "works":

The sum of the integers from 1 to 9, inclusive = 45

Since we have 4 sets of those, the sum of ALL of the cards is 4(45) = 180

We're told that 1 card is removed and we're asked for the number on that card.

Fact 1: The units digit on the remaining cards is a 6.

With a total sum of 180, the ONLY card that we could remove and end up with a units digit of 6 is "a 4"

180 - 4 = 176.

Since the cards are numbered 1 through 9, there's no other card that can generate that same result.
Fact 1 is SUFFICIENT.

Fact 2: The sum on the remaining cards is 176.

Here, all of our prior work creates a 'shortcut' - we don't have to do any new work to deduce that the missing card was "a 4"
Fact 2 is SUFFICIENT.

Final Answer:

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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
I visualised this one.

These are our cards:
A: 1-2-3-4-5-6-7-8-9
B: 1-2-3-4-5-6-7-8-9
C: 1-2-3-4-5-6-7-8-9
D: 1-2-3-4-5-6-7-8-9

[1] The units digit of the sum of the numbers on the remaining 35 cards is 6.
As seen from above, the sum of all of the cards is 45*4=180.
Now, if the units digit is 6, and only one card was removed, then card number 4 was removed, leading to a sum of 176.

[2] The sum of the numbers on the remaining 35 cards is 176.
Having found [1], we realise that this is the same.

So, ANS D
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
pacifist85 wrote:
I visualised this one.

These are our cards:
A: 1-2-3-4-5-6-7-8-9
B: 1-2-3-4-5-6-7-8-9
C: 1-2-3-4-5-6-7-8-9
D: 1-2-3-4-5-6-7-8-9

[1] The units digit of the sum of the numbers on the remaining 35 cards is 6.
As seen from above, the sum of all of the cards is 45*4=180.
Now, if the units digit is 6, and only one card was removed, then card number 4 was removed, leading to a sum of 176.

[2] The sum of the numbers on the remaining 35 cards is 176.
Having found [1], we realise that this is the same.

So, ANS D


Good method.

Easier way to look at it is:

Once you have the pattern figured:

A: 1-2-3-4-5-6-7-8-9
B: 1-2-3-4-5-6-7-8-9
C: 1-2-3-4-5-6-7-8-9
D: 1-2-3-4-5-6-7-8-9

Statement 1, You see that the units digit of each of the 4 sets is a 5. Thus adding all 5s from all 4 sets we get a 0 as the units digit. This will give you a unit's digit of 6 if a card with unit's digit of 4 is removed. Thus sufficient. 4 is the card removed.

Statement 2, Total of all the cards = 45*4 = 180 . Total remaining = 176. A card with value 4 was clearly removed. Thus this statement is sufficient as well.

D is the correct answer.
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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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,
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
I hope I can clarify for those that are having difficulty visualizing: Albert Einstein once said, “If I can't picture it, I can't understand it.”


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.



solution:

recall: ONLY 10 digits exist.... the passage says there 4 sets of 9 cards... numbered 1 through 9....

so we have
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9

notice each set is evenly spaced out... so we can apply the following rule S = A n... where the average = median... each set = 5 x 9 = 45

total sum 45 x 4 = 160 + 20 = 180

statement 1)

only 176 is possible this implies that we subtracted 4...… so we know a card with 4 was chosen (SUFFICIENT)

statement 2)

now this statement says we have 176 after subtracting the following means we chose 4 (SUFFICIENT)


NOTE: you do not need to know that the total sum of all the cards is 180..... I wrote that only for those that needed full comprehension of the problem

if you have a good understanding of number sense you can infer knowing the resulting units digit you have all the sufficient info to find what card was removed.... SINCE we have nine units digits all different from each other


for instance: say we have an integer that is 20

each of the following produces a result with a UNIQUE units digit.... test it

20 - 1
20 - 2
20 -3
20 -4
20 -5
20 - 6
20 - 7
20 - 8
20 - 9
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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Bunuel 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.

Solution:

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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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
Correct Answer : D
Total sum of numbers on 4 decks is : 180 [4 *(1+2+3+4+5+6+7+8+9)]
1. 180 - 4 = 176 Unit Number 6 - Sufficient
2. 180 - 4 = 176 - Sufficient
Hence D
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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