NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 11:55 It is currently 25 Apr 2024, 11:55
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

D01-20

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [103]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
D01-20 [#permalink] New post   16 Sep 2014, 00:12
12
Kudos
91
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

47% (01:44) correct 53% (01:56) wrong based on 389 sessions
Hide Show timer Statistics
If \(a\), \(b\), and \(c\) are integers and \(a < b < c\), are \(a\), \(b\), and \(c\) consecutive integers?


(1) The median of \((a!, \ b!, \ c!)\) is an odd number.

(2) \(c!\) is a prime number.
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [24]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re D01-20 [#permalink] New post   16 Sep 2014, 00:12
12
Kudos
12
Bookmarks
Expert Reply
Official Solution:


If \(a\), \(b\), and \(c\) are integers and \(a < b < c\), are \(a\), \(b\), and \(c\) consecutive integers?

Note that:

1. The factorial of a negative number is undefined.

2. \(0!=1\).

3. Only two factorials are odd: \(0!=1\) and \(1!=1\).

4. If \(x!\) is a prime number, then \(x = 2\) is the only solution.

(1) The median of \((a!, \ b!, \ c!)\) is an odd number.

This implies that \(b!\) is odd. Therefore, \(b\) must be either 0 or 1. However, if \(b = 0\), then \(a\) would be a negative number (since \(a < b\)), making \(a!\) undefined, which is not possible. Therefore, \(a = 0\) and \(b = 1\) (yielding \((a!, \ b!, \ c!)=(1, 1, c!)\)). If \(c = 2\), the answer is YES, but if \(c\) is any other number, the answer is NO. Not sufficient.

(2) \(c!\) is a prime number.

This implies that \(c=2\). Not sufficient.

(1) + (2) From the previous analysis, we know that \(a = 0\), \(b = 1\), and \(c = 2\). Thus, the answer to the question is YES. Sufficient.


Answer: C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [7]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   11 Jan 2015, 11:18
6
Kudos
1
Bookmarks
Expert Reply
GMAT888 wrote:
I think this question is poor and helpful.
I believe the given answer is incorrect and the correct one is B -> statement 2 by itself is sufficient. Indeed, if c! is prime then it must be 2 and since a < b < c and a,b,c are INTEGERS AND factorial is not defined for negative numbers then a and b have no other choice but to be 0 and 1 respectively! Thus, statement 2 is enough by itself. I would like to hear your comments. Thanks.


That's NOT correct. For (2) we don't know whether a and b are positive integers. WE cannot use the info from (1) when considering the second statement.
General Discussion
User avatar
GMAT888
Manager
Manager
Joined: 01 Jul 2009
Posts: 136
Own Kudos [?]: 98 [12]
Given Kudos: 39
Send PM
GMAT ToolKit User
Re: D01-20 [#permalink] New post   11 Jan 2015, 10:49
11
Kudos
1
Bookmarks
I think this question is poor and helpful.
I believe the given answer is incorrect and the correct one is B -> statement 2 by itself is sufficient. Indeed, if c! is prime then it must be 2 and since a < b < c and a,b,c are INTEGERS AND factorial is not defined for negative numbers then a and b have no other choice but to be 0 and 1 respectively! Thus, statement 2 is enough by itself. I would like to hear your comments. Thanks.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   21 Jul 2016, 22:27
3
Kudos
Expert Reply
JarvisR wrote:
Bunuel and others:
I have similar doubt like others. I appreciate your inputs.

Lets ignore Stmt A for now.
Question says, If a, b, and c are integers and a<b<c, are a, b, and c consecutive integers?
Stmt(1): ignore.
Stmt(2): c! is a prime number.
only possible number is 2. !2 =2 a prime number.
Now, a<b<c and they are integers. The only possible combination i see here is 0,1,2. I ignored combination with negative numbers such as -1,1,2 because !negative is undefined.
Where am i going wrong here?


You do not have factorial of a or b in stem or in (2) so you cannot ignore negative numbers.
User avatar
Thoughtosphere
Manager
Manager
Joined: 02 Jul 2012
Posts: 151
Own Kudos [?]: 711 [2]
Given Kudos: 84
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
GPA: 2.6
WE:Information Technology (Consulting)
Send PM
Reviews Badge
Re: D01-20 [#permalink] New post   23 Oct 2014, 04:22
1
Kudos
1
Bookmarks
Bunuel wrote:
If a, b, and c are integers and \(a \lt b \lt c\), are a, b, and c consecutive integers?


(1) The median of {a!, b!, c!} is an odd number.

(2) c! is a prime number.


I got this question wrong in the test, because I didn't pay special attention to every detail given in the question.

Here's the right solution :

1. The median of a! b! c! is an odd number, it means that b is either 0 or 1. Since we can have a!, it means that a is greater than or equal to 0. We also know that a < b < c, so a = 0, b = 1, but we have no information about c. SO, this is insufficient.

2. c! is a prime number, this means that c = 2. Here we have no information about a and b, so Insufficient.

Combining 1 & 2, we get that a = 0, b = 1, c=2.

So, C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   10 May 2017, 11:53
1
Kudos
Expert Reply
Albert__ wrote:
How can we determine that c must be 2 (not any other prime number) from the :

2) c! is a prime number.


n! = 1*2*3*...*n

Now, if c is any other number than 2, c! will have at least 2 and 3 as its factor and we know that a prime number has only two factors 1 and itself, thus for c! to be prime c must be 2. For example, if c = 4, then c! = 4! = 1*2*3*4, which is not a prime.

Hope it's clear.
User avatar
JarvisR
Senior Manager
Senior Manager
Joined: 05 Nov 2012
Posts: 343
Own Kudos [?]: 4586 [0]
Given Kudos: 606
Concentration: Technology, Other
Schools: IIMA Simon '17 (D) Carlson '18 (D) Katz '17 (A$) IIML'17 (A) UConn FT "18 (A$) IIMB
Send PM
GMAT ToolKit User Reviews Badge
Re: D01-20 [#permalink] New post   21 Jul 2016, 22:22
Top Contributor
Bunuel and others:
I have similar doubt like others. I appreciate your inputs.

Lets ignore Stmt A for now.
Question says, If a, b, and c are integers and a<b<c, are a, b, and c consecutive integers?
Stmt(1): ignore.
Stmt(2): c! is a prime number.
only possible number is 2. !2 =2 a prime number.
Now, a<b<c and they are integers. The only possible combination i see here is 0,1,2. I ignored combination with negative numbers such as -1,1,2 because !negative is undefined.
Where am i going wrong here?
User avatar
B
Darkhorse12
Intern
Intern
Joined: 08 Feb 2017
Posts: 7
Own Kudos [?]: 15 [0]
Given Kudos: 22
Send PM
Re: D01-20 [#permalink] New post   17 Feb 2017, 06:34
Bunuel
As per the solution given:
(1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient.

it says b is 0 or 1. Is 0 an odd number?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   17 Feb 2017, 09:05
Expert Reply
Darkhorse12 wrote:
Bunuel
As per the solution given:
(1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient.

it says b is 0 or 1. Is 0 an odd number?


0 is an even integer. But 0! = 1 = odd.
avatar
S
praneet87
Intern
Intern
Joined: 27 Aug 2014
Posts: 45
Own Kudos [?]: 16 [0]
Given Kudos: 6
Location: Canada
Concentration: Strategy, Technology
Schools: Tepper '20 Johnson '20 Ross '20 Ivey '19
GMAT 1: 660 Q45 V35
GPA: 3.66
WE:Consulting (Consulting)
Send PM
Re: D01-20 [#permalink] New post   22 Apr 2017, 21:29
How is 0 factorial 1?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   23 Apr 2017, 03:41
Expert Reply
praneet87 wrote:
How is 0 factorial 1?


0! = 1.

It's a math property you need not know why it's so but if still interested check this video:

avatar
B
Albert__
Intern
Intern
Joined: 03 Apr 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 11
Send PM
Re: D01-20 [#permalink] New post   10 May 2017, 11:41
How can we determine that c must be 2 (not any other prime number) from the :

2) c! is a prime number.
avatar
Sk18
Intern
Intern
Joined: 06 Dec 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 16
Send PM
Re: D01-20 [#permalink] New post   21 Sep 2019, 00:06
I think this is a high-quality question and I agree with explanation. Great question! Tests a mix of multiple basic facts on numbers.
User avatar
B
dc2880
Intern
Intern
Joined: 22 Jan 2021
Posts: 15
Own Kudos [?]: 10 [0]
Given Kudos: 41
Send PM
Re: D01-20 [#permalink] New post   02 Feb 2021, 19:07
Bunuel Would you be able to help me with this?

How do we know that "The median of {a!, b!, c!} is an odd number" means that b is odd?
User avatar
L
akadiyan
Retired Moderator
Joined: 31 May 2017
Posts: 749
Own Kudos [?]: 670 [0]
Given Kudos: 53
Concentration: Technology, Strategy
Schools: IIMA PGPX'23 Bayes Said '23
Send PM
GMAT ToolKit User Reviews Badge
Re: D01-20 [#permalink] New post   02 Feb 2021, 19:59
dc2880 wrote:
Bunuel Would you be able to help me with this?

How do we know that "The median of {a!, b!, c!} is an odd number" means that b is odd?


The important point to remember is that factorial of negative number is undefined. Option A says "The median of {a!, b!, c!} is an odd number" , which means b! is odd.

Only 2 options results in odd numbers either 0! or 1!. But since a < b, b cannot be 0 (which means a < b , and a is negative and a! is undefined) , so b is 1 (odd number).

I hope i answered your question.
avatar
B
BrunoAlbrecht
Intern
Intern
Joined: 07 Nov 2020
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 14
GMAT 1: 670 Q42 V41
Send PM
Re: D01-20 [#permalink] New post   19 Feb 2021, 12:58
I think this is a high-quality question and I agree with explanation.
avatar
B
SimpleSimon123
Intern
Intern
Joined: 25 Jun 2017
Posts: 6
Own Kudos [?]: 0 [0]
Given Kudos: 12
Send PM
Re: D01-20 [#permalink] New post   08 Jun 2021, 10:46
I think this is a high-quality question and I agree with explanation.
User avatar
B
meghnajeendgar
Intern
Intern
Joined: 24 Jun 2015
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: D01-20 [#permalink] New post   12 Oct 2022, 05:14
I don't agree with the explanation. What if C=3. It is a prime number and it is greater than 1. The answer to the question will be no in this case. Would not option E make more sense?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618997 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-20 [#permalink] New post   12 Oct 2022, 08:00
Expert Reply
meghnajeendgar wrote:
I don't agree with the explanation. What if C=3. It is a prime number and it is greater than 1. The answer to the question will be no in this case. Would not option E make more sense?


(2) says that c! is prime. If c = 3, then c! = 6, which is not a prime. So, c cannot be 3.

Does this make sense?
GMAT Club Bot
gmatclubot
Re: D01-20 [#permalink]
12 Oct 2022, 08:00
 1   2   
Moderator:
Bunuel
Math Expert
92914 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions