ziyuenlau wrote:If a*b≠0. Is |a|/|b|=a/b ?
(1) |a*b|=a*b
(2) |a|/|b|=|a/b|
Official Answer : D
How do we able to arrive and solve Statement (2) is sufficient?
Hi ziyuenlau,
We are given that ab≠0.
We have to see whether |a|/|b|=a/b.
Let's take four cases.
Case 1: a = 3 and b = 2, thus |a|/|b| = 3/2 and a/b = 3/2. The answer is YES.
Case 2: a = -3 and b = -2, thus |a|/|b| = |-3|/|-2| = 3/2 and a/b = -3/-2 = 3/2. The answer is YES.
Case 3: a = -3 and b = 2, thus |a|/|b| = |-3|/|2| = 3/2 and a/b = -3/2 = -3/2. The answer is NO.
Case 4: a = 3 and b = -2, thus |a|/|b| = |3|/|-2| = -3/2 and a/b = 3/-2 = -3/2. The answer is NO.
This means that if the signs of a and b are same, the answer is yes, else no.
Let's take each statement one by one.
S1: |a*b|=a*b
Since LHS [|a*b|] is positive, the RHS a*b must be positive.
=> a and b must be either both positive or negative. This falls in case 1 and case 2. The answer is YES. Sufficient.
S2: |a|/|b|=|a/b|
Since RHS |a/b| is positive whether a and b have the same sign or the opposite signs, thus |a|/|b| may or may not be equal to a/b. Insufficient.
The correct answer:
A
Hope this helps!
Relevant book:
Manhattan Review GMAT Data Sufficiency Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations:
New York |
Warsaw |
Cape Town |
Madrid | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
