If x^a*x^b = x^c, is what is c/(a+b)?

Question

GMATBusters’ Quant Quiz Question -2

For past quiz questions, click  here

If  x^a*x^b = x^c,  is what is  \frac{c}{(a+b)} ?

(1) a, b are integers
(2) a, and b are positive numbers

GMATBusters · Answer

Official Solution:

if a+b = c, then  x^a*x^b = x^c  
but vice versa is tricky. 
  if x = 1 or 0, then we can have  x^a*x^b = x^d , where d is any number 
 similarly, if x = -1, x^n will always = 1 , if n is even 
 hence  if,  x^a*x^b = x^c . it is not necessary that c = a+b

If  x^a*x^b = x^c,  is what is  \frac{c}{(a+b)}   ?

(1) a, b are integers
if x  
eq{0}  1, 0, -1. then we can say c=a+b, but 
if x = 1, 0, -1. then we can't say c=a+b
Not Sufficient

(2) a, and b are positive numbers
if x  
eq{0}  1, 0, -1. then we can say c=a+b, but 
if x = 1, 0, -1. then we can't say c=a+b
Not Sufficient

Even after combining both statements 1 & 2, we can find value of  \frac{c}{(a+b)} 
Hence,  Answer is E

Raxit85 · Answer

If x^a∗x^b=x^c, is what is c/(a+b)?
We need unique value of c/a+b.
 x^a∗x^b=x^c
x^a+b=x^c
a+b =c
1) a, b are integers
If a = 2 and b = 3, then c = 5. So, 5/5 = 1
If a = 5, b = 7, then c = 12, So, 12/12=1
If a = -1, b = 2, then c = 1, 1/1= 1.
Sufficient.

2) a, and b are positive numbers
If a = 2 and b = 3, then c = 5. So, 5/5 = 1
If a = 1/2, b = 2, then c=2.5 (5/2), so 5/2 divided by 5/2 = 1
If a = 3/2, b = 2/3, then c=13/6, so 13/6 divided by 13/6 = 1
So sufficient.

Ans. D

uc26 · Answer

As per exponents rule,  x^a*x^b= x^a+x^b .
So  x^a+x^b=x^c 
Here there are two situations possible. If a and b have different signs adding upto zero, there can be a possibility like-
 1^-2* 1^2= 1^1 
 1^0= 1^1 
However c/a+b= 1/0 here is undefined because the denominator is zero.

The other case can be where a+b=c
And here c/a+b= 1
Thus, we need to know the positive/ negative nature of a and b.

1) Does not give us the required information regarding the positive/ negative nature of a and b. No sufficient.
2) a and b are positive integers. So the answer would be 1. Sufficient.

Answer: B

Archit3110 · Answer

given
x^a* x^b = x^c 
a+b=c
need to find c/a+b
#1
a,b are integers 
we can have
(-1)^1*(-1)^2 = (-1)^√1 
(-1)^3 = (-1)^√1
we get c/(a+b) =√1 /3 or c can be any odd value 
or 
2^2*2^3 = 2^5
2^5=2^5
we get c/(a+b) = 5/5 ; 1
insufficient

#2 a, and b are positive numbers

again same as #1
(-1)^1*(-1)^2 = (-1)^√1 
(-1)^3 = (-1)^√1
we get c/(a+b) =√1 /3 
or 
2^2*2^3 = 2^5
2^5=2^5
we get c/(a+b) = 5/5 ; 1
insufficient
From 1&2 nothing can be determined
OPTION E

If x^a∗x^b=x^c,, is what is c/(a+b)?
1) a, b are integers
2) a, and b are positive numbers

ashwini2k6jha · Answer

Answer E
c/a+b=?
State1:Not sufficient
x^a+b-c=1
case 1, x^2+2-4=1
c/a+b=1
case 2, 1^2+3-1=1
c/a+b=1/5
State:2not sufficient
a,b>0
x^a+b-c=1
case 1, x^2+2-4=1
c/a+b=1
case2, let x=1, 1^2+3-1=1
c/a+b=1/5
statement 1+2,
both case apply in this case also
Hence not sufficient
Answer E

Kinshook · Answer

If  x^a∗x^b=x^c,  is what is c/(a+b)
If x=0 or 1; a,b & c can take multiple values.

1) a, b are integers
Since x may be 0 or 1 or -1
NOT SUFFICIENT

2) a, and b are positive numbers 
Since x may be 0 or 1 or -1
NOT SUFFICIENT

(1) + (2) 
1) a, b are integers
2) a, and b are positive numbers 
Since x may be 0 or 1 or -1
NOT SUFFICIENT

IMO E

LJg-XeHs6Ik

1BlackDiamond1 · Answer

Answer is D.

Statement 1 is sufficient to answer the question.
Statement 2 is sufficient to answer the question.

freedom128 · Answer

x^a*x^b = x^c
--> x^(a+b) = x^c

Q. c/(a+b)?

(1) a, b are integers 
If a=1, b=-1, c=0, and x is not 1, then c/(a+b) is undefined. 
If a=1, b=2, c=3, and x is not 1, then c/(a+b)=1
NOT SUFFICIENT

(2) a, and b are positive numbers 
If a=1, b=2, c=3, and x is not 1, then c/(a+b)=1
If a=1, b=2, c=9, and x=1, then c/(a+b)=1/3
We need to know x
NOT SUFFICIENT

Combined 
If a=1, b=2, c=3, and x is not 1, then c/(a+b)=1
If a=1, b=2, c=9, and x=1, then c/(a+b)=1/3
We need to know x to determine exact value of c/(a+b)
NOT SUFFICIENT