GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Nov 2018, 07:48

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### \$450 Tuition Credit & Official CAT Packs FREE

November 15, 2018

November 15, 2018

10:00 PM MST

11:00 PM MST

EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth \$100 with the 3 Month Pack (\$299)
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# A bag contains six tokens, each labeled with one of the inte

Author Message
Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 496
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

27 Nov 2013, 21:15
8
00:00

Difficulty:

95% (hard)

Question Stats:

21% (01:47) correct 79% (01:36) wrong based on 203 sessions

### HideShow timer Statistics

A bag contains six tokens, each labeled with one of the integers from 1 to 6, inclusive. Each integer appears on one token. When three tokens are removed at random, without replacement, what is the probability that the sum of numbers on those three tokens is equal to the positive integer N?

(1) There is only one combination of three tokens in the bag that sums to N
(2) N is a multiple of 7

Attachment:

632444379.png [ 23.68 KiB | Viewed 2972 times ]

No explanation provided - Need help in solving.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
VP
Joined: 02 Jul 2012
Posts: 1181
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A bag contains 6 tokens.  [#permalink]

### Show Tags

27 Nov 2013, 22:12
Actually, I think A is a better answer than D.

Reasons:
Statement 1) Whatever N is, there is only one combination to give it. N cannot be all 6,7,14 and 15. So probability has to be 1/20. Sufficient.

Statement 2) What if N = 7000. In that case answer is 0. Insufficient.

Edit: Tough one.. I thought the answer was an easyD
A...
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Intern
Joined: 19 Sep 2012
Posts: 23
Re: A bag contains 6 tokens.  [#permalink]

### Show Tags

27 Nov 2013, 22:24
Probability of getting sum of N from 3 tokens= no. of combinations from 3 tokens which leads to N/ total sum of combination from 3 token
1)---> only 1 combnination of exists which leads to N... Hence, total outcomes =20.. using 6C3... 1/20..
2) N is a multiple of 7.. Two such combinations exist.. 1,2,4 = 7 and 3,6,5 = 14... Probabilty = 2/20

Both the statements seem to contradict each other

What is OA ???

Dont know what am I missing here
Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 496
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: A bag contains 6 tokens.  [#permalink]

### Show Tags

27 Nov 2013, 22:38
1
perseverance84 wrote:
Probability of getting sum of N from 3 tokens= no. of combinations from 3 tokens which leads to N/ total sum of combination from 3 token
1)---> only 1 combnination of exists which leads to N... Hence, total outcomes =20.. using 6C3... 1/20..
2) N is a multiple of 7.. Two such combinations exist.. 1,2,4 = 7 and 3,6,5 = 14... Probabilty = 2/20

Both the statements seem to contradict each other

What is OA ???

Dont know what am I missing here

The OA is B. I just did an excel workpaper to solve this problem and it appears there are four combinations that result in one number. It is 1,2,3 (sum=6), 1, 2, 4 (sum=7), 3,5,6 (sum= 14) and 4,5,6 (sum= 15). Here is the whole chart of the 20 combinations.

1 2 3 6 One combination
1 2 4 7 One combination
1 2 5 8
1 2 6 9
1 3 4 8
1 3 5 9
1 3 6 10
1 4 5 10
1 4 6 11
1 5 6 12
2 3 4 9
2 3 5 10
2 3 6 11
2 4 5 11
2 4 6 12
2 5 6 13
3 4 5 12
3 4 6 13
3 5 6 14 One combination
4 5 6 15 One combination
VP
Joined: 02 Jul 2012
Posts: 1181
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A bag contains 6 tokens.  [#permalink]

### Show Tags

27 Nov 2013, 22:50
Edited my previous answer. I go with A. Still don't agree with the OA though..
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 295
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

28 Aug 2017, 22:44
Does it not mean we just have 6 tokens with 1-6 written on it without duplicates?
Math Expert
Joined: 02 Sep 2009
Posts: 50583
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

28 Aug 2017, 23:20
1
RMD007 wrote:
Does it not mean we just have 6 tokens with 1-6 written on it without duplicates?

Yes, it means that there are 6 tokens numbered from 1 to 6, inclusive: [1]; [2]; [3]; [4]; [5]; [6].

A bag contains six tokens, each labeled with one of the integers from 1 to 6, inclusive. Each integer appears on one token. When three tokens are removed at random, without replacement, what is the probability that the sum of numbers on those three tokens is equal to the positive integer N?

Notice several things:
1. We are picking without replacement, so if we pick [1] there won't be any more [1]'s left in the bag.
2. The least possible sum (N) is 1 + 2 + 3 = 6 and the greatest possible sum is 6 + 5 + 4 = 15.
3. The sums from 6 to 15 has different ways (combinations) to occur. For example, we can get 6 only in one way: 1 + 2 + 3 = 6 but we can get 8 in 2 ways: 1 + 2 + 5 = 1 + 3 + 4 = 8.
4.We can get the number of combinations for each sum, thus we can get the total number of combinations for all sums.

(1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient.

(2) N is a multiple of 7. The greatest sum is 6 + 5 + 4 = 15, so for N to be a multiple of 7 it must be 7 or 14. Both of these numbers can be broken into the sum of three distinct positive integers only in one way: 7 = 1 + 2 + 4 and 14 = 6 + 5 + 3. Sufficient.

Hope it helps.
_________________
Manager
Joined: 07 Jun 2017
Posts: 103
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

28 Aug 2017, 23:55
the answer should not be B
because there is more than 1 combination has a multiple of 7.
waiting someone to explain on this, thank you so much
Math Expert
Joined: 02 Sep 2009
Posts: 50583
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

29 Aug 2017, 00:44
pclawong wrote:
the answer should not be B
because there is more than 1 combination has a multiple of 7.
waiting someone to explain on this, thank you so much

The answer IS B and it's explained in the post just above yours.

For (2): it does not matter whether N is 7 or 14, the probability will still be the same for either of these values.
_________________
Manager
Joined: 14 Mar 2011
Posts: 143
GMAT 1: 760 Q50 V42
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

29 Aug 2017, 02:38
Hello Bunuel,

Can you please explain more on this,

Bunuel wrote:

(1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient.

A mentions that "there is only one combination of three tokens in the bag that sums to N", so how N=1 become one possibility.

_________________

If you find my posts/replies helpful, please take a moment to click on the "kudos" icon.

Math Expert
Joined: 02 Sep 2009
Posts: 50583
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

29 Aug 2017, 03:04
1
1
godot53 wrote:
Hello Bunuel,

Can you please explain more on this,

Bunuel wrote:

(1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient.

A mentions that "there is only one combination of three tokens in the bag that sums to N", so how N=1 become one possibility.

Yes, you can get N = 1 in only one way (in 0 ways) but the probability of getting the sum of 1 is 0, while you can get N = 6 also in only one way (in 1 way) but the probability of getting the sum of 6 is NOT 0.
_________________
Intern
Joined: 05 Feb 2014
Posts: 3
Re: A bag contains six tokens, each labeled with one of the inte  [#permalink]

### Show Tags

12 Oct 2017, 23:50
I am a little lost here.

"what is the probability that the sum of numbers on those tokens is equal to the positive integer N"
"the positive integer N". i might be mistake but "the number" should be one specific number.
the probability of getting 7= the probability of getting 14. i am perfectly fine here.
but probability of getting either 7 or 14 is twice as much.
let us imagine this is not a DS question and it is a problem solving assignment where we have the general statement + the 2th (B) statement, "what is the probability that the sum of numbers on those tokens is equal to the positive integer N"

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: A bag contains six tokens, each labeled with one of the inte &nbs [#permalink] 12 Oct 2017, 23:50
Display posts from previous: Sort by