Is |a| |b|? (1) b

Question

Is |a| > |b|?

(1) b < -a
(2) a < 0

Bunuel · Accepted Answer

Is |a| > |b|?

The question asks whether a is further from 0 than b.

(1) b < -a --> b + a < 0. The sum of two numbers is less than 0. This is clearly insufficient to say which one is further from 0. Not sufficient.

(2) a < 0. Also insufficient.

(1)+(2) The sum of a and b is less than 0 and a is negative. How can we say which one is further from 0? If a = -1 and b = -2, then b is further but if a = -2 and b = -1, then a is further. Not sufficient.

Answer: E.

Bunuel · Answer

This question can be very easily solved with number line approach. Is |a| > |b|? If we rephrase the question we'll get: on the number line does point a lie further from zero than point b ? Note that we are not interested in the signs of a and b . (1) b < -a --> b+a<0 , the sum of two numbers is less than zero. Now, if both numbers are negative (to the left of zero) than their sum will obviously be less than zero, and any from these two could be further from zero, thus this statement is not sufficient. (2) a < 0. Clearly insufficient. (1)+(2) Example from (1) is still valid (we considered a<0 in it, so 2 is satisfied), thus even taken together statements are not sufficient. Answer: E.

thinktank · Answer

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

Bunuel · Answer

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.

sunshinewhole · Answer

@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. ?

Bunuel · Answer

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

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

KarishmaB · 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)

JeffTargetTestPrep · Answer

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

BillyZ · Answer

Bunuel , What does it means?

Bunuel · Answer

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: Theory on Abolute Values: math-absolute-value-modulus-86462.html Absolute value tips: absolute-value-tips-and-hints-175002.html DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37 PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58 Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html Hope it helps.

BillyZ · Answer

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.

mikkkiia · Answer

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 ?

Bunuel · Answer

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

GMATwithAK · Answer

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

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