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

Question

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

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

subhashghosh · Answer

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

devinawilliam83 · Answer

How have you identified the values of here, have u tested numbers and picked up the first non fraction values. ?

subhashghosh · Answer

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)!

mvictor · Answer

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.

GSBae · Answer

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!

MHI · Answer

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

georgekaterji · Answer

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?

awdxzs · Answer

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

GSBae · Answer

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.

Kinshook · Answer

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

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

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GMAT Data Sufficiency (DS) Questions

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

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