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# Is |a| > |b|?

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07 Feb 2011, 18:38
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Is |a| > |b|?

(1) b < -a
(2) a < 0
[Reveal] Spoiler: OA

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10 Feb 2011, 09:07
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ajit257 wrote:
Is |a| > |b|?

(1) b < -a

(2) a < 0

just not getting absolutes. Please can some one help in understanding this topic better.

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.

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08 Feb 2011, 01:19
I used substitution;

Q: Is |a| > |b|?

(1) b < -a

b+a < 0
This equation will hold true for ;
1. a: +ve; b: -ve
2. a: -ve; b: -ve
3. a: -ve; b:+ve

Substitution;
case: I
"a" can be a very big -ve number and "b", a very small positive
a=-100
b=+5
Thus; |a|>|b|. Answer to the Q: TRUE

Converse can also be true;
case II.
"a" can be a very small +ve number and "b", a very big negative
a=+5
b=-100
Thus; |a|<|b|. Answer to the Q: FALSE

Ideally, we have proven that the statement is NOT SUFFICIENT. But, we'll see other two cases as well

case III:
"a" can be a very small -ve number and "b", a very big negative
a=-5
b=-100
Thus; |a|<|b|. Answer to the Q: FALSE

case IV:
"a" can be a very big -ve number and "b", a very small negative
a=-100
b=-5
Thus; |a|>|b|. Answer to the Q: TRUE

(2) a < 0
a: -ve

Doesn't tell us anything about b;
b can be a bigger positive or bigger negative.
Not sufficient.

Combining both the statements;
a: +ve; b: -ve --- We can count this one out as a=-ve

a: -ve; b: -ve. Here b can be a bigger negative OR b can be a smaller negative both will have opposite results. NOT SUFFICIENT.

Already proven that combining both is NOT SUFFICIENT.

a: -ve; b:+ve; "a" can be a small negative and "b", a very big postive OR "a" can be a big negative and b, a very small postive. NOT SUFFICIENT.

Ans : "E"
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10 Feb 2011, 08:22
Hi..

Im having trouble understanding the first statement.
if b< -a , then you cant have that a is grater then b?

you haven have a 5 for b, and a has to be negative? or is it that you can enter a negative A and with the negative in the statement it changes it to a positive??

5<- (-10)

we would get
5<10 and that is true... for the statemnte

and the same thing can go for
-5<-(-1)
you would get
-5<1 and that is true for statement one but contradicts the above and you can go take of A and D , and statement two is wrong that is why you get at E...

I seem to be a bit mixed up... can anyone help?
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 just not getting [#permalink]

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01 Feb 2012, 12:51
ajit257 wrote:
Is |a| > |b|?

(1) b < -a

(2) a < 0

just not getting absolutes. Please can some one help in understanding this topic better.

+1 E

This problem requires to pick numbers.

Stmnt (1): $$b < -a$$ ------ > $$b + a < 0$$
Picking numbers:
$$a = -1$$ , $$b = - 3$$ ---> $$-3-1< 0$$ ----> $$|b| > |a|$$
$$a = -3$$ , $$b = - 1$$ ---> $$-1-3< 0$$ ----> $$|a| > |b|$$
INSUFF

Stmnt (2): $$a < 0$$
There is not information about b.
INSUFF

Combining (1) and (2): We use the same examples in (1).
INSUFF

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

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15 Feb 2013, 02:20
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
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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15 Feb 2013, 04:11
Expert's post
thinktank wrote:
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.
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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09 May 2013, 22:55
Bunuel wrote:
thinktank wrote:
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. ?
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Re: Is |a| > |b|? (1) b < -a (2) a < 0 [#permalink]

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10 May 2013, 01:26
Expert's post
sunshinewhole wrote:
Bunuel wrote:
thinktank wrote:
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.
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Re: Is |a| > |b|? [#permalink]

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18 Dec 2013, 12:44
This question can be solved best on number line.
Is |a| > |b|? a and b can take any sign.
(1) b < -a
If a is positive -----------0---------a------- -=> b<-(a) --(b)-<--(-a)-----0-----a------ |b|>|a| Sufficient to say NO.
If a is negative ---(-a)------0----------- -=> b<-(-a) => b<a --b----(-a)----b-----0---b----a------- b can be anywhere less than a. Not Sufficient to tell distance of b from origin compared to a, thus Option 1 Insufficient.

(2) a < 0 Clearly insufficient as we do not know anything about position of b.

Option 1 and 2 together,
a is negative ---(-a)------0----------- -=> b<-(-a) => b<a --b----(-a)----b-----0---b----a------- b can be anywhere less than a. can not tell position of b comparative to a. Insufficient.

Ans E.
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Re: Is |a| > |b|? [#permalink]

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09 Jun 2015, 07:57
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Re: Is |a| > |b|? [#permalink]

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Re: Is |a| > |b|?   [#permalink] 30 Jun 2016, 03:10
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