Problem Solving

If ab≠0 and |a|<|b|, which of the following must be negative?
A) a/b−b/a
B) a−b/a+b
C)a^b−b^a
D) a(b/a−b)
E) b−a/b

OA Coming soon.

rakeshd347 wrote:If ab≠0 and |a|<|b|, which of the following must be negative?
A) a/b−b/a
B) a−b/a+b
C)a^b−b^a
D) a(b/a−b)
E) b−a/b

OA Coming soon.

As soon as I see a pretty weird looking VICs (variables in answer choices) my top strategy is plugging in numbers:

From the stem:
ab ≠ 0
a ≠ 0 and b ≠ 0

|a| < |b|
|SMALL NUMBER| < |BIG NUMBER|

So my sample values would be
a = -1 & b = 2 (-ive, +ive)
a = 1 & b = 2 (+ive, +ive)
a = 1 & b = -2 (+ive, -ive)

Since its a "must be negative" question no matter what the sign is, the result should always be negative. The moment we see a positive result we can ignore it. Also if we see a negative result we need to check all three possibilities.

A) a/b−b/a
-1/2 - 2/-1 = 1.5

B) a−b/a+b
-1-2 / -1+2 = -1.5
Check other possibilities.
1-2 / 1+2 = -1/3
1--2 / 1-2 = -3

We can stop here as all the signs have been checked.

[spoiler]OA : B[/spoiler]

Regards,
Vivek

rakeshd347 wrote:If ab≠0 and |a|<|b|, which of the following must be negative?
A) a/b−b/a
B) a−b/a+b
C)a^b−b^a
D) a(b/a−b)
E) b−a/b

OA Coming soon.

I did this question this way.
Every time you see an absolute value you can square both sides without any hesitation.
|a|<|b|--->a^2<b^2---->a^2-b^2<0
or (a+b)(a-b)<0
Since a+b and a-b are of opposite sign their multiplication and division can never be positive this is what answer
B says.