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

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Senior Manager
Joined: 21 Oct 2013
Posts: 435
Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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29 Aug 2014, 12:42
1
7
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Difficulty:

65% (hard)

Question Stats:

56% (01:08) correct 44% (01:01) wrong based on 325 sessions

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Is |a| > |b|?

(1) b < -a
(2) a < 0
Math Expert
Joined: 02 Sep 2009
Posts: 46213
Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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29 Aug 2014, 14:35
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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.

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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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31 Aug 2015, 23:18
2
goodyear2013 wrote:
Is |a| > |b|?

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

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)
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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14 Nov 2016, 08:23
goodyear2013 wrote:
Is |a| > |b|?

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

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|.

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Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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Updated on: 12 Feb 2017, 17:55
Bunuel wrote:
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.

Bunuel, What does it means?
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Originally posted by hazelnut on 19 Jan 2017, 04:12.
Last edited by hazelnut on 12 Feb 2017, 17:55, edited 1 time in total.
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Posts: 46213
Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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19 Jan 2017, 04:16
ziyuenlau wrote:
Bunuel wrote:
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.

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:
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.
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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22 Jan 2017, 06:19
goodyear2013 wrote:
Is |a| > |b|?

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

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.
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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05 Mar 2018, 01:13
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Re: Is |a| > |b|? (1) b < -a (2) a < 0   [#permalink] 05 Mar 2018, 01:13
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