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Manager  Joined: 25 Aug 2011
Posts: 135
Location: India
GMAT 1: 730 Q49 V40 WE: Operations (Insurance)
If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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Question Stats: 66% (01:20) correct 34% (01:11) wrong based on 255 sessions

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

(1) 4a! = b!
(2) 5c! = d!
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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1
2
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
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Manager  Joined: 25 Aug 2011
Posts: 135
Location: India
GMAT 1: 730 Q49 V40 WE: Operations (Insurance)
Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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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

How have you identified the values of here, have u tested numbers and picked up the first non fraction values. ?
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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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)!
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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

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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!
Intern  Joined: 24 Jan 2016
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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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
Intern  Joined: 23 Oct 2016
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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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?
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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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.

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Re: If a, b and c are positive integers, what is the value of (a + b)(c +  [#permalink]

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

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