Last visit was: 19 Jul 2024, 16:32 It is currently 19 Jul 2024, 16:32
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [90]
Given Kudos: 86332
Intern
Joined: 23 Sep 2012
Posts: 20
Own Kudos [?]: 113 [18]
Given Kudos: 5
Concentration: Technology, Operations
GMAT 1: 740 Q50 V40
GPA: 4
WE:Information Technology (Computer Software)
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [10]
Given Kudos: 86332
General Discussion
Intern
Joined: 10 Oct 2013
Posts: 31
Own Kudos [?]: 21 [4]
Given Kudos: 44
Concentration: Marketing, Entrepreneurship
GMAT 1: 730 Q50 V38
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
3
Kudos
1
Bookmarks
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
Director
Joined: 03 Feb 2013
Posts: 793
Own Kudos [?]: 2604 [2]
Given Kudos: 567
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE:Engineering (Computer Software)
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
1
Kudos
1
Bookmarks
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)
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11787 [5]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
3
Kudos
2
Bookmarks
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.

GMAT assassins aren't born, they're made,
Rich
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 393 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
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
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3650 [0]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
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.

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30837 [1]
Given Kudos: 799
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
1
Kudos
Top Contributor
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

Cheers,
Brent
Intern
Joined: 29 May 2020
Posts: 15
Own Kudos [?]: 7 [0]
Given Kudos: 94
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
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22679 [1]
Given Kudos: 286
Location: United States (CA)
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
1
Kudos
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.

Director
Joined: 29 Apr 2019
Status:Learning
Posts: 729
Own Kudos [?]: 588 [0]
Given Kudos: 49
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
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
Non-Human User
Joined: 09 Sep 2013
Posts: 34030
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car [#permalink]
Moderator:
Math Expert
94421 posts