cant figure this out

[spankincubus123]

if b<c,d and c>0 which of the following cannot be true if b,c and d are integers?

a. bcd>0
b. b+cd<0
c. b-cd>0
d. b/cd<0
e. (b^3)cd<0

how do i approach this. there seems to be some problem since i find all of the options to be both true/false and not only false as the question asks. HELP![/b]

[Jim@StratusPrep]

A) b could be positive and this would be true
B) b could be a large negative number to offset the positive number and this would be true
C) Since c and d are positive integers when you multiply them cd must get bigger or stay the same relative to both of the variables. Since b < c then you have a smaller number - a larger number which will always be negative
D) b could be negative
E) b could be negative

Answer is C.

[pemdas]

About your question

how do i approach this. there seems to be some problem since i find all of the options to be both true/false and not only false as the question asks. HELP![/b]

There are three cases: 1) Both CAN be true OR false, 2) One MUST be false, 3) One MUST be true.

The solution seems easy once you account for the restrictions c>0, d>0, b<c and the possibilities for b which can be either positive or negative or 0
a. bcd>0 CAN be true
b. b+cd<0 CAN be true
c. b-cd>0 CAN NOT be true, as cd is always positive and b<c suggests ONLY b*d(positive d)<c*d(~ the same). As bd<cd, b<cd too. Stop and mark the answer.
d. b/cd<0
e. (b^3)cd<0

c

[spankincubus]

Thanks guys it is C. Actually, After giving it a careful thought i was able to get the right answer. But Appreciate your inputs nevertheless. CheerS!