Is |a| > |b|? (1) b < -a (2) a < 0

Bunuel,
This is a very silly question. Kindly pardon me, when i approached this Q i chose (A)
b < -a is the same as -a > b which means lal > lbl right ?

And another doubt, when do u substitute values for Inequalities / Solve the inequality / use the number line. I am very naive in using the number line so .. kindly mention when to use which approach.

Thanks

Yes, \(-a > b\) is the same as \(b < -a\), but it does NOT mean that \(|a| > |b|\). Consider: \(a=-1\) and \(b=-2\) --> \(-a=1>-2=b\) but \(|a|=1<2=|b|\).

As for your other question: it really depends on the particular problem at hand and personal preferences to choose which approach to take.

@Bunuel

I have this doubt:

b<-a...let say a= -3 and b=-5, (as given b<-a..it means b is also negative.). so mod of b> mod of a...hence A is suff. ?

One example is NOT enough to say that a statement is sufficient.

Consider a=-5 and b=-3, to get the different answer.

Question: Is |a| > |b|?
We need to find whether absolute value of a is more than absolute value of b.

Statement II is certainly not sufficient alone.

Statement I: b < -a
To analyse it, we need to consider two cases: 'a is positive' and 'a is negative'. Let's start with a is negative since that is stmnt II. If we see that it is not sufficient, we know that the answer would be (E).

If a is negative (say -5), -a is positive(say 5). We know that b is less than 5. b could be 2 or it could be -10. In one case, |b| is less than |a| and in the other, it is greater.

Hence, both statements together are not sufficient. Answer (E)

We need to determine whether |a| > |b|.

Statement One Alone:

b < -a

We can rearrange the inequality in statement one to read:

b + a < 0

We do not have enough information to determine whether |a| > |b|.

For instance, if a = -3 and b = 2, |a| IS greater than |b|. However, if a = -1 and b = -2, |a| IS NOT greater than |b|. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

a < 0

Just knowing that a < 0 is not enough information to answer the question. Similar to statement one, if a = -3 and b = 2, |a| IS greater than |b|; however, if a = -1 and b = -2, |a| IS NOT greater than |b|. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that b + a < 0 and a < 0. However, we still do not have enough information to determine whether |a| > |b|. As mentioned above, if a = -3 and b = 2, |a| IS greater than |b|; however, if a = -1 and b = -2, |a| IS NOT greater than |b|.

Answer: E

Bunuel, What does it means?

The absolute value of a number is the value of a number without regard to its sign.

For example, \(|3| = 3\); \(|-12| = 12\); \(|-1.3|=1.3\)...

Another way to understand absolute value is as the distance from zero. For example, \(|x|\) is the distance between x and 0 on a number line.

From that comes the most important property of an absolute value: since the distance cannot be negative, an absolute value expression is ALWAYS more than or equal to zero.

Here are the topics that will help you to brush up fundamentals on absolute values:


Hope it helps.

We can rephrase this question as: "Is a farther away from zero than b, on the number-line?" We can solve this question by picking numbers:

Since Statement 2 is less complex than Statement 1, begin with Statement 2 and a BD/ACE grid.

(1) INSUFFICIENT: Picking values that meet the criteria b < -a demonstrates that this is not enough information to answer the question

(2) INSUFFICIENT:  We have no information about b.

(1) AND (2) INSUFFICIENT: Picking values that meet the criteria b < -a and a < 0 demonstrates that this is not enough information to answer the question.

Hi Bunuel !!

Just a quick question for statement 1. It says b<-a,, then shouldnt b be a negative that is smaller than a (lets say a=-4 b=-10),,then then they become absolute values then |b| must be larger than |a| (i.e. |-10|>|-4|).. Wouldnt it then be sufficient to say no to the question stem ?

Not necessarily. Consider b = -3 and a = 1.

Let's take statement (2) to begin with.

a<0 . This tells us nothing about b. Hence, options B and D are elimated.

b < -a . a can be positive or negative. If, a is positive, -a is negative and hence b has to be negative (and |b| will be greater than a)
If a is negative, b would be less than -a no matter whether |b| will be greater than or less than or equal to |a|

Therefore statement (1) alone cannot be used to solve this problem. Hence, option A is also eliminated.

Now, lets see if both statement (a) and (b) together can be used to solve this problem.

Since a is negative as per statement (2), b would be less than -a no matter whether |b| will be greater than or less than or equal to |a|

Hence, we cannot say if |a| > |b| or not.

Therefore, the answer is option E

Remember the 12TEN mnemonic when answering DS questions!

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