Data Sufficiency

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab greater than or equal to 0

Anyone want to help me clarify this question.

OA is E. I initially chose C.

Thanks

tisrar02 wrote:If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab greater than or equal to 0

Anyone want to help me clarify this question.

OA is E. I initially chose C.

Thanks

We are given |a| > |b|
We need to find whether a · |b| < a - b or rephrased we need to find:
Is a(|b|-1) + b < 0

Since a and b are integers, our best test cases are probably to start with -2, -1, 0, 1,2 .
we are given |a| > |b|.
With that in mind, let's look at the statements.

1. a < 0.
Let a=-2.
Let b=0, then
a(|b|-1) + b = (-2)(-1) +0 = 2 which is greater than 0.
Let b = -1,
a(|b|-1) + b = (-1)(1-1) + -1 = 0 - 1 = -1 which is less than 0.
Insufficient.

2. ab>=0
Using the same 2 cases as above, still insufficient.

Together, still using the same cases as used in 1, still insufficient.

Hence E is correct.

Let me know if this helps

Hey Eagleeye,

Thank you for the question debrief. Would you say that typically with these types of questions, you would use -2, -1, 0, 1, 2 to test out if the question is sufficient or not. I usually struggle with these types of questions because they can get so time consuming.

Thanks

tisrar02 wrote:If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab greater than or equal to 0

Anyone want to help me clarify this question.

OA is E. I initially chose C.

Thanks

Statement 1 only....

Lets' take couple of values that satisfy |a| > |b|. These could be..

1. a=8, & b=2

2. a=-8, & b=-2;

For first set of values, put it in a·|b| < a - b => 8.2 <(8-2) => 16<6 => Decision--NO.

For second set of values, put it in a·|b| < a - b => -8.2 <(-8+2) => -16<-6 => Decision--Yes.

Statement 1 is not sufficient.

Statement 2 only....

It is clear that the values, we took for statement 1 also satisfy 'ab greater than or equal to 0'

Hence statement 2 itself and even combined together is not sufficient. Ans. E.

tisrar02 wrote:Hey Eagleeye,

Thank you for the question debrief. Would you say that typically with these types of questions, you would use -2, -1, 0, 1, 2 to test out if the question is sufficient or not. I usually struggle with these types of questions because they can get so time consuming.

Thanks

Ya, there are a few things you can be mindful of:

1. If one of the numbers can be 0, you almost always should test the 0 case.
2. If the numbers are positive integers, test 1, 2, 3, 20, 30 etc.
3. If the numbers are integers -2,-1,0,1,2 might help you disprove some stuff.
4. If the numbers can be anything, -2,-1,-0.5,0,0.5,1,2 may be appropriate. Almost always test the 0, -0.5, +0.5 case, because they are critical in so many inequalities questions.

Selecting numbers is pretty much an art form which comes with experience as you practice more and more, but these hints above should help you get your thinking started if you are stuck.

tisrar02 wrote:If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab greater than or equal to 0

Anyone want to help me clarify this question.

OA is E. I initially chose C.

Thanks

DS problems becomes much easier if we understand how they are written.
Let the STATEMENTS guide you.
Statement 1 is clearly insufficient on its own.
So what is the purpose of statement 1?
It likely has some EFFECT ON STATEMENT 2.
If a<0, the result in statement 2 is that b≤0.
So let's start with these two cases: a<0 and b=0, a<0 and b<0.
The question stem requires |a| > |b|.

Case 1: a=-2 and b=0
Plugging these values into a · |b| < a - b, we get:
-2 * |0| < -2 - 0
0 < -2.
NO.

Case 2: a=-2, b=-1
Plugging these values into a · |b| < a - b, we get:
-2 * |-1| < -2 - (-1)
-2 < -1
YES.

Since in the first case the answer is NO, and in the second case the answer is YES, and each case satisfies both statements, the correct answer is E.

When a statement is clearly insufficient on its own, ask yourself how it affects the OTHER statement.
There is a good chance that the first statement will restrict the second in an important way.