Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]
27 Jul 2012, 08:29
If a, b, c, and d are integers and ab^2c^3d^4 > 0, which of the following must be positive?
I. a^2cd II. bc^4d III. a^3c^3d^2
A) I only B) II only C) III only D) I and III E) I, II, and III
Since given that a*b^2*c^3*d^4 > 0, then we know that none of the unknowns is zero. Therefore, b^2>0 and d^4>0, which means that we can safely reduce by them to get a*c^3>0 (so, the given expression does not depend on the value of b or d: they can be positive as well as negative).
Next, a*c^3>0 means that a and c must have the same sign: they are either both positive or both negative.
Evaluate each option:
I. a^2cd. Since d can positive as well as negative then this option is not necessarily positive.
II. bc^4d. Since d can positive as well as negative then this option is not necessarily positive.
III. a^3c^3d^2. Since a*c^3>0, then a^3*c^3>0 and as d^2>0, then their product, (a^3*c^3)*d^2 must be positive too.