Bunuel wrote:
If a and b are integers, what is the value of a+b?
(1) a·b=1
(2) a/b=1
Interpreting statement-1:
(1) Neither a, nor b is '0' (zero).
(2) Both have the same sign; either both of them +ve or both of them -ve.
(3) One is NOT the reciprocal of the other ( as both of them are INTEGERS).
(4) b = 1/a [or a =1/b]
(5) a + b = a + 1/a = (\(a^2\)+1)/a
Therefore, the product of two integers can be 1 in ONLY two possible scenarios, both are +1s or both are -1s.
If both are +ve, a+b =+2 and if both are -ve, then a+b = -2.
CONCLUSION: Can't come to a single value for a+b. Not sufficient.
Interpreting statement-2:
(1) Once again, neither a nor b is '0'.
(2) Both have the same sign; either both of them +ve or both of them -ve.
(3) a = b
(4) a + b = a + a = 2a [or 2b]
(5) The magnitude of the two integers is same.
If x = +5, y = +5; if x = -5 then y = -5 and so on.
CONCLUSION: a+b = could be any +ve or - ve integer. Not sufficient.
Combining both of them:(1) a+b = a+1/a = (a^2+1)/a (from statement 1)
(2) a+b = a+a = 2a (from statement 2)
(a^2+1)a = 2a
or, a^2+1 = 2a^2
or, a^2 = 1
.:. a = +/- 1
If a = 1, then b = 1 and if a = =1, then b = -1.
a + b = 1+1 = 2, or
a + b = -1 -1 = -2.
CONCLUSION: Together the statements are insufficient to come to a single value.
Therefore, IMO, the answer is 'E'.