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

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

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08 Mar 2012, 22:57
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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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09 Mar 2012, 01:03
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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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

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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09 Mar 2012, 09:53
1
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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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.
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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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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!
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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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10 Nov 2016, 13:22
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
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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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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?
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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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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
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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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16 Mar 2017, 07:08
1
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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17 Mar 2018, 18:05
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Re: If a, b and c are positive integers, what is the value of (a + b)(c +   [#permalink] 17 Mar 2018, 18:05
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