arabella wrote:

If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

(1) abc = 1

(2) ad = 1

\(d= 4-(a+b+c)\)

Statement 1: as all are integers so this implies that \(|a|=|b|=|c|=1\)

now if all are positive then \(d=4-(1+1+1)=1\)

but if any two are negative and the 3rd is positive then \(d=4-(1-1-1)=5\). Hence

insufficientStatement 2: this implies that \(|a|=|d|=1\). but \(d\) can be positive or negative. hence no unique value.

InsufficientCombining 1 & 2, if \(a=1\), then \(d=1\)

but if \(a=-1\), then either \(b\) or \(c\) is \(-1\) and the remaining is \(1\) for Statement 1 to hold true

so \(d=4-(-1-1+1)=5\)

but from statement 2, if \(a=-1\) then \(d=-1\). so this implies that \(a\) is not equal to \(-1\). Hence \(a=d=1\)

SufficientOption

C