Problem Solving

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.

srcc25anu wrote:Q7. Male % in senior class = ???
given: 72% males applied to college
80% females applied to college

stat 1: total students in senior class = 840
doesnt tell us about number of males
hence not sufficient

stat 2: 75% of students in senior class have applied to college
still doesnt tell us the number of males versus females in the class hence not sufficient

Together they are sufficient hence C

.72x + .8 (840-x) = .75*840 hence we can solve for x that is total number of males in senior class

Q7 the answer is B.

72%*M + 80%*F = 75%(M+F)
Won't let you find the actual value of M and F, but you don't really need it: you just need the fraction M/M+F, and that is possible to find:
72M+80F = 75M+75F
5F = 3M
F = 3/5M

so the fraction of the class that are male is
M/M+F = M/ M+3M/5, and the Ms will cancel out to leave a single fraction. Stat. (2) is actually sufficient.