sukhman wrote:For non-zero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0
(2) abcd = -4
Dear Sukman,
I'm happy to help.
When we multiply or divide four numbers, any combination of multiplying vs. dividing, the result is positive if
(a) all four are positive
(b) two are positive, two are negative
(c) all four are negative
You see, the product or quotient of two negatives is positive, so as long as there are an even number of negatives, the result will be positive.
Statement #1:
ad + bc = 0
ad = -bc
So if ad is positive, bc is negative, or vice versa, which means we have an odd number of negatives, and the quotient would be negative. This gives us a definitive "no" answer, so we are able to answer the prompt question. This statement, alone and by itself, is
sufficient.
Statement #2:
abcd = -4
This also indicates an odd number of negative signs, so the quotient would be negative. This gives us a definitive "no" answer, so we are able to answer the prompt question. This statement, alone and by itself, is
sufficient.
Both statements sufficient. Answer = [spoiler]
(D)[/spoiler]
In this one, it's very important not to confuse the answer to the
prompt question (Is ab/cd positive? No) with the
sufficiency question (Is the statement sufficient to give a definitive answer to the prompt question? Yes)
See:
https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/
Let me know if you have any further questions.
Mike
