If a and b are non-zero integers, and a/b > 1, then which of the following must be true?
A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3
If b is positive, then we have that a>b>0.
If b is negative, then we have that a<b<0.
A. a > b. Not necessarily true.
B. 2a > b. Not necessarily true.
C. a^2< b^2 --> |a|<|b|. Not necessarily true.
D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.
E. a^3 < b^3 --> a<b. Not necessarily true.
Answer: D.
Hope it's clear.
A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3
If b is positive, then we have that a>b>0.
If b is negative, then we have that a<b<0.
A. a > b. Not necessarily true.
B. 2a > b. Not necessarily true.
C. a^2< b^2 --> |a|<|b|. Not necessarily true.
D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.
E. a^3 < b^3 --> a<b. Not necessarily true.
Answer: D.
Hope it's clear.