NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 22:45 It is currently 24 Apr 2024, 22:45
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

If a, b and c are positive integers, what is the value of (a + b)(c +

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
devinawilliam83
Manager
Manager
Joined: 25 Aug 2011
Posts: 116
Own Kudos [?]: 1488 [15]
Given Kudos: 11
Location: India
GMAT 1: 730 Q49 V40
WE:Operations (Insurance)
Send PM
If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   08 Mar 2012, 22:57
4
Kudos
10
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

67% (01:20) correct 33% (01:15) wrong based on 338 sessions
Hide Show timer Statistics
If a, b and c are positive integers, what is the value of (a + b)(c + d)

(1) 4a! = b!
(2) 5c! = d!
ShowHide Answer
Official Answer
C
User avatar
B
subhashghosh
Retired Moderator
Joined: 16 Nov 2010
Posts: 909
Own Kudos [?]: 1173 [4]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Send PM
Reviews Badge
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   09 Mar 2012, 01:03
2
Kudos
2
Bookmarks
1)

a!/b! = 1/4

=> a = 3
b = 4

No information about c and d though
2)

c!/d! = 1/5

=> c = 4, d = 5

No information about a and b though

Sufficient together
Answer - C
User avatar
devinawilliam83
Manager
Manager
Joined: 25 Aug 2011
Posts: 116
Own Kudos [?]: 1488 [0]
Given Kudos: 11
Location: India
GMAT 1: 730 Q49 V40
WE:Operations (Insurance)
Send PM
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   09 Mar 2012, 09:08
subhashghosh wrote:
1)

a!/b! = 1/4

=> a = 3
b = 4

No information about c and d though
2)

c!/d! = 1/5

=> c = 4, d = 5

No information about a and b though

Sufficient together
Answer - C



How have you identified the values of here, have u tested numbers and picked up the first non fraction values. ?
User avatar
B
subhashghosh
Retired Moderator
Joined: 16 Nov 2010
Posts: 909
Own Kudos [?]: 1173 [1]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Send PM
Reviews Badge
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   09 Mar 2012, 09:53
1
Bookmarks
I thought it is pretty intuitive :

3!/4! = 1/4 , I can't imagine in any other case where the factorials would divide in such a manner that the remaining number in denominator is the highest leftover from the factorial. Think of it like this -> n! = n * (n-1)!
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   13 Oct 2016, 07:16
devinawilliam83 wrote:
If a, b and c are positive integers, what is the value of (a+b)(c+d)

(1) 4a!= b!
(2) 5c!=d!


1. b!/a! = 4. which means that b=4, and a must be 3. what about c and d?
2. d!/c! = 5. d=5 and c=4. what about a and b?

1+2
we have all the values.
avatar
B
GSBae
Manager
Manager
Joined: 23 May 2013
Posts: 170
Own Kudos [?]: 402 [0]
Given Kudos: 42
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M$)
GMAT 1: 760 Q49 V45
GPA: 3.5
Send PM
GMAT ToolKit User
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   10 Nov 2016, 08:47
Just to throw a wrench in here, we do have to consider the possibility that one of the a,b,c,d could be 1 or 0. For instance, if one of the statements read:

(1) 6c!=d!, then (c,d) could be (5,6) or it could also be (0,3) or (1,3).

However, neither 4 or 5 are factorial numbers so we're safe. Always good to think of these cases though!
User avatar
MHI
Intern
Intern
Joined: 24 Jan 2016
Posts: 16
Own Kudos [?]: 10 [0]
Given Kudos: 0
Send PM
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   10 Nov 2016, 13:22
Answer:C
If a, b and c are positive integers, what is the value of (a+b)(c+d)
(1) 4a!= b!
(2) 5c!=d!
1- 4x3!=4! ⇒ a=3 and b=4 -- c and d unknown -- NOT SUFFICIENT
2- 5x4!=5! ⇒ c=4 and d=5 -- a and b unknown -- NOT SUFFICIENT
Taking --1-- and --2-- together, we have all 4 variables -- SUFFICIENT
avatar
georgekaterji
Intern
Intern
Joined: 23 Oct 2016
Posts: 25
Own Kudos [?]: 12 [0]
Given Kudos: 17
Send PM
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   14 Nov 2016, 03:41
speedilly wrote:
Just to throw a wrench in here, we do have to consider the possibility that one of the a,b,c,d could be 1 or 0. For instance, if one of the statements read:

(1) 6c!=d!, then (c,d) could be (5,6) or it could also be (0,3) or (1,3).

However, neither 4 or 5 are factorial numbers so we're safe. Always good to think of these cases though!



what do you mean by "neither 4 or 5 are factorial numbers", and how are we safe, if c and d were 1 and 3, then the whole answer would change no?
avatar
B
awdxzs
Intern
Intern
Joined: 15 Oct 2014
Posts: 13
Own Kudos [?]: 2 [0]
Given Kudos: 150
Send PM
Reviews Badge
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   15 Mar 2017, 20:12
speedilly wrote:
Just to throw a wrench in here, we do have to consider the possibility that one of the a,b,c,d could be 1 or 0. For instance, if one of the statements read:

(1) 6c!=d!, then (c,d) could be (5,6) or it could also be (0,3) or (1,3).

However, neither 4 or 5 are factorial numbers so we're safe. Always good to think of these cases though!


Hi there
Your assumption is not true as the stem has mentioned that a,b,c,d are positive integer and '0' is not a positive integer.

Posted from my mobile device
avatar
B
GSBae
Manager
Manager
Joined: 23 May 2013
Posts: 170
Own Kudos [?]: 402 [1]
Given Kudos: 42
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M$)
GMAT 1: 760 Q49 V45
GPA: 3.5
Send PM
GMAT ToolKit User
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   16 Mar 2017, 07:08
1
Kudos
awdxzs wrote:
speedilly wrote:
Just to throw a wrench in here, we do have to consider the possibility that one of the a,b,c,d could be 1 or 0. For instance, if one of the statements read:

(1) 6c!=d!, then (c,d) could be (5,6) or it could also be (0,3) or (1,3).

However, neither 4 or 5 are factorial numbers so we're safe. Always good to think of these cases though!


Hi there
Your assumption is not true as the stem has mentioned that a,b,c,d are positive integer and '0' is not a positive integer.

Posted from my mobile device


Still, it's possible that one of them could be 1. If Statement 2 was instead 6c! = d!, then (c,d) has two possibilities and therefore the answer would be E.
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5343
Own Kudos [?]: 3964 [1]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   05 May 2022, 22:42
1
Bookmarks
Asked: If a, b and c are positive integers, what is the value of (a + b)(c + d)

(1) 4a! = b!
b = 4
a = 3
Since c & d are unknown
NOT SUFFICIENT

(2) 5c! = d!
d = 5
c = 4
Since a & b are unknown
NOT SUFFICIENT

(1) 4a! = b!
b = 4
a = 3
(2) 5c! = d!
d = 5
c = 4
(a + b)(c + d) = (3 + 4) (4 + 5) = 7*9 = 63
SUFFICIENT

IMO C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32658
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink] New post   20 May 2023, 07:02
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.
GMAT Club Bot
gmatclubot
Re: If a, b and c are positive integers, what is the value of (a + b)(c + [#permalink]
20 May 2023, 07:02
Moderator:
Bunuel
Math Expert
92900 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