If a, b, and c are positive integers, what is the value of c?

Question

If a, b, and c are positive integers, is c a prime number?

(1) a + b = c
(2) a! + b! = c

M36-74

Archit3110 · Answer

Here there is no relation is given among a,b,c

so from 1:
a+b=c
2+1=3 yes or 2+4=6 no
not sufficient

from 2:
a!+b!=c
1!+2!=3 yes
or 2!+3!= 8 no

combining we get 1+2=3 and 1!+2!=3 or 2+2=4 , not sufficient IMO E

NCRanjan · Answer

IMO E

If a, b, and c are positive integers, is c a prime number?

(1) a + b = c
(2) a! + b! = c

stmt1 
1+1= 2 Yes
1+2=3 Yes
2+2=4 No
2+4 = 8 No

Stmt 2 
a!+b!=c
1!+1!=2 Prime yes
1!+2!=3 Prime yes
2!+2!=4 Not PRime No

Combined
a+b =c
1+2=3 Yes
1!+2!=3 Yes

2+2=4 No
2!+2!=4 No

hence NS

saurabh9gupta · Answer

Just wanted to add.. question stem does not say that a and b are distinct.. they can be same.

a+b=c
1+1=2 yes
2+4=6 no

a!+b!=c
1!+1!=2 yes
2!+2!=4 no

Combined..
Test using a=b=1 and a=b=2
E

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Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Kinshook · Answer

Asked: If a, b, and c are positive integers, is c a prime number?

(1) a + b = c
If a = 1; b = 2; c = 3 is a prime number
But if a = 1; b=3; c =4 is NOT a prime number 
NOT SUFFICIENT

(2) a! + b! = c
If a = 1; b = 2; c = 3 is a prime number
But if a =2; b =3; c = 8 is NOT a prime number
NOT SUFFICIENT

(1) + (2) 
(1) a + b = c
(2) a! + b! = c
If a = b = 1; c =2 is a prime number
If a = 1; b = 2; c = 3 is a prime number
But if a = b =2; c =4 is NOT a prime number
NOT SUFFICIENT

IMO E

exc4libur · Answer

(1) a + b = c: 1+1=2=prime; 1+3=4≠prime, insufic.

(2) a! + b! = c: 1!+2!=3=prime; 2!+3!=8≠prime, insufic.

(1 & 2): a!+b!=a+b; 1!+1!=1+1=2=prime; 2!+2!=2+2=4≠prime, insufic.

Answer (E)

Bunuel · Answer

Official Solution:

If  a ,  b , and  c  are positive integers, is  c  a prime number? 
 
(1)  a + b = c . Clearly insufficient.
 
(2)  a! + b! = c . Clearly insufficient.
 
(1)+(2) From above we have  a + b = a! + b! . Now, obviously if  a  and  b  are large enough numbers, then  a! + b!  will be more than  a + b . So, let's test small numbers:  a=b=1 ,  a=1  and  b=2  (or vise versa) and  a=b=2  work. In the first two cases  c  is a prime (2 or 3) but for the third case  c  is not a prime (4). Not sufficient.

Answer: E

If a, b, and c are positive integers, what is the value of c?

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