Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 03:52

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56306
A collection of 36 cards consists of 4 sets of 9 cards each.  [#permalink]

### Show Tags

07 Jan 2014, 05:13
25
00:00

Difficulty:

25% (medium)

Question Stats:

76% (02:05) correct 24% (02:02) wrong based on 800 sessions

### HideShow timer Statistics

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Intern
Joined: 23 Sep 2012
Posts: 20
Concentration: Technology, Operations
GMAT 1: 740 Q50 V40
GPA: 4
WE: Information Technology (Computer Software)
Re: A collection of 36 cards consists of 4 sets of 9 cards each.  [#permalink]

### Show Tags

07 Jan 2014, 09:08
4
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
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56306
Re: A collection of 36 cards consists of 4 sets of 9 cards each.  [#permalink]

### Show Tags

07 Jan 2014, 05:14
1
1
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.

_________________
Intern
Joined: 10 Oct 2013
Posts: 33
Concentration: Marketing, Entrepreneurship
GMAT 1: 730 Q50 V38
Re: A collection of 36 cards consists of 4 sets of 9 cards each.  [#permalink]

### Show Tags

08 Jan 2014, 00:03
2
1
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: 836
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.  [#permalink]

### Show Tags

08 Jan 2014, 08:57
1
1
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)
_________________
Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

CEO
Joined: 12 Sep 2015
Posts: 3853
Re: A collection of 36 cards consists of 4 sets of 9 cards each.  [#permalink]

### Show Tags

01 Apr 2019, 07:19
1
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
_________________
Test confidently with gmatprepnow.com
Re: A collection of 36 cards consists of 4 sets of 9 cards each.   [#permalink] 01 Apr 2019, 07:19
Display posts from previous: Sort by