3. if c and d are integers, is c even?
a. C(d+1) is even
b. (c+2)(d+4) is even
Answer is C.
Stat. (1): either C is even, (in which case D can be anything) and the answer is yes
OR
d+1 is even (in which case C can anything - even or odd) and the answer is a possible no.
insufficient.
Stat. (2): the same.
either C+2 is even (which means that c is even), (in which case D can be anything) and the answer is yes
OR
d+4 is even (in which case C can anything - even or odd) and the answer is a possible no.
Insufficient.
combined, c cannot be odd. If C is odd, then both d+1 and d+4 have to be even, which contradics: d cannot be both odd and even. Thus, each statement eliminates the alternative scenario of the other one, and we remain with only one possible scenario: C is even, and the answer is yes. Sufficient.
a. C(d+1) is even
b. (c+2)(d+4) is even
Answer is C.
Stat. (1): either C is even, (in which case D can be anything) and the answer is yes
OR
d+1 is even (in which case C can anything - even or odd) and the answer is a possible no.
insufficient.
Stat. (2): the same.
either C+2 is even (which means that c is even), (in which case D can be anything) and the answer is yes
OR
d+4 is even (in which case C can anything - even or odd) and the answer is a possible no.
Insufficient.
combined, c cannot be odd. If C is odd, then both d+1 and d+4 have to be even, which contradics: d cannot be both odd and even. Thus, each statement eliminates the alternative scenario of the other one, and we remain with only one possible scenario: C is even, and the answer is yes. Sufficient.
