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# If a, b, c, and d are positive integers, what is the value..

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Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
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Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
If a, b, c, and d are positive integers, what is the value.. [#permalink]

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22 Dec 2012, 07:46
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Question Stats:

72% (01:58) correct 28% (01:09) wrong based on 236 sessions

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

(1) 4a! = b!
(2) 5c! = d!
[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Last edited by daviesj on 22 Dec 2012, 08:31, edited 1 time in total.
Intern
Joined: 20 Dec 2012
Posts: 18
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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22 Dec 2012, 08:06
I just stumbled onto the "!" symbol in math, so I cannot solve this problem. However I've got a question!

(Let's say a = 2)
When it was 4a!, does that equal 4*1*2, or does it equal 1*2*1*2*1*2*1*2?

I'm a bit confused as of which order to do things.
Intern
Joined: 25 Jul 2012
Posts: 40
Concentration: Organizational Behavior, General Management
GMAT 1: 610 Q47 V26
GMAT 2: 640 Q49 V27
GPA: 4
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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22 Dec 2012, 08:22
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If a, b, c, and d are positive integers, what is the value of (a + b)(c + d)?
(1) 4a! = b!
(2) 5c! = d!

Hi,

Statement 1: 4a! = b! so (a,b) have only one valid case (3,4) so values are a=3 and b=4
Statement 1: 5c! = d! so (c,d) have only one valid case (4,5) so values are c=4 and b=5

Ans: (3+4)(4+5) => 7*9

C
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Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 152
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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22 Dec 2012, 08:25
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700+ questions are never much difficult,they are just tricky...

In this problem if you can see carefully, only one combination of a and b satisfies 4a! = b!...well, how's that?
simple for a=3... a! will be 3*2*1 and 4*a! will be 4*3*2*1 i.e. 4! so b=4...no other value of a would satisfy this..
Same is the case with 5c! = d! .i.e c=4 and d=5.

Sentence 1: not sufficient as it gives only the values of a & b
Sentence 2: not sufficient as it gives only the values of c & d

both sentences together: can solve the problem as we get all the values

Hope the point is clear..:)
_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Intern
Joined: 20 Dec 2012
Posts: 18
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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22 Dec 2012, 09:18
daviesj wrote:
700+ questions are never much difficult,they are just tricky...

In this problem if you can see carefully, only one combination of a and b satisfies 4a! = b!...well, how's that?
simple for a=3... a! will be 3*2*1 and 4*a! will be 4*3*2*1 i.e. 4! so b=4...no other value of a would satisfy this..
Same is the case with 5c! = d! .i.e c=4 and d=5.

Sentence 1: not sufficient as it gives only the values of a & b
Sentence 2: not sufficient as it gives only the values of c & d

both sentences together: can solve the problem as we get all the values

Hope the point is clear..:)

This explained my question aswell. Thanks
Intern
Joined: 23 May 2012
Posts: 3
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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23 Dec 2012, 04:28
If a, b, c, and d are positive integers, what is the value of (a + b)(c + d)?
(1) 4a! = b!
(2) 5c! = d!
all u need to know are values of positive integers a,b,c &d.
statement1:talks about only a and b .no info reg c&d .insuff
statement2:talks about only c&d.no info reg a&b.insuffi.
combining 1 &2
only values which will work for a&b are a=3,b=4,c&d are c=4,d=5.sufficient.
Manager
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If a,b,c,and d are positive integers,what is the value of [#permalink]

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02 Mar 2013, 12:15
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If a,b,c,and d are positive integers,what is the value of (a+b)(c+d)
(1)4a!=b!
(2)5c!=d!
Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 213
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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02 Mar 2013, 12:24
1
KUDOS
daviesj wrote:
700+ questions are never much difficult,they are just tricky...

In this problem if you can see carefully, only one combination of a and b satisfies 4a! = b!...well, how's that?
simple for a=3... a! will be 3*2*1 and 4*a! will be 4*3*2*1 i.e. 4! so b=4...no other value of a would satisfy this..
Same is the case with 5c! = d! .i.e c=4 and d=5.

Sentence 1: not sufficient as it gives only the values of a & b
Sentence 2: not sufficient as it gives only the values of c & d

both sentences together: can solve the problem as we get all the values

Hope the point is clear..:)

Hi Daviesj
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Re: If a,b,c,and d are positive integers,what is the value of [#permalink]

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02 Mar 2013, 19:27
We are given that a,b,c, and d are positive integers and need to find the value of (a+b) (c+d)

Consider statement (1) first
4a! = b!
This can only be true if a=3 and b=4. However this does not give us the value of c and d and is insufficient.

Consider statement (2) next
5c! = d!
This can only be true if d=5 and c=4. However this does not give us the value and a and b and is insufficient.

Combining both, we have the values of a,b,c, and d. Sufficient.

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Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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12 Aug 2014, 18:38
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).

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Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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25 Dec 2015, 06:56
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).

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Re: If a, b, c, and d are positive integers, what is the value.. [#permalink]

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29 Nov 2016, 05:22
4a!=b! means (b!/a!)=4, the only possibility is 4!/3!

5c!=d! means (d!/c!)=5, the only possibility is 5!/4!

C
Re: If a, b, c, and d are positive integers, what is the value..   [#permalink] 29 Nov 2016, 05:22
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