Doubt on |x|

[mehravikas]

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

[bsandhyav]

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

Well i'm not the best when it comes to modulus questions ....but i'll give it a try

1. x=-a

if a>=0 |x|=a

if a<0 |x|= -a

So Insuuficient


2. x<0

No information about A

So Insufficient

Taking (1) & (2) together

x=-a & x<0

=> x is negative => a is positive

therefore |x|=a--->Proved

IMO:C

[mehravikas]

What is your answer to the first question?

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

Well i'm not the best when it comes to modulus questions ....but i'll give it a try

1. x=-a

if a>=0 |x|=a

if a<0 |x|= -a

So Insuuficient


2. x<0

No information about A

So Insufficient

Taking (1) & (2) together

x=-a & x<0

=> x is negative => a is positive

therefore |x|=a--->Proved

IMO:C

[bsandhyav]

Answer to the 1st Question is A since it is clearly mentioned that x= -5 & |-5| = 5

i.e |x|=a

[mehravikas]

Lets say for question 2 you plug in some values:

Case 1: Let a = 5

|x| = 5, i.e. x = 5 or -5

Statement 1: x = -5
Statement 2: x < 0

If x < 0, then x = -5, true....

Case 2: Let a = -5

|x| = -5, i.e. x = 5 or -5

Statement 1: x = - (-5) -> x = 5
Statement 2: x < 0

If x < 0, then x = 5....

Can we conclude the answer to be C? in both cases how does statement 2 helps i.e. x < 0?

Answer to the 1st Question is A since it is clearly mentioned that x= -5 & |-5| = 5

i.e |x|=a

[chetanojha]

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

|x|=5?

Since anything inside modulus is converted into positive sign, so in this case you always have to consider two case. Since you does not know the sign of the number inside variable x.
i) x=5 (if x is positive)
ii)x=-5 (if x is negative)

Now above you have two values of x i.e.5 and -5. Look at the options now.

1. x=-5. This is same as the one we have done above. Hence this is sufficient to answer the question.

2. x<0. This could be anything viz. -4,-3,-2,-1,-5 etc. Hence It does not give you YES/NO answer hence NOT SUFFICIENT.

Therefore, your answer is A.

SAME for question 2 as well.

[mehravikas]

That's what I think as well.

statement 2 is not needed in both the questions:

|x| = 5 or |x| = a

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

|x|=5?

Since anything inside modulus is converted into positive sign, so in this case you always have to consider two case. Since you does not know the sign of the number inside variable x.
i) x=5 (if x is positive)
ii)x=-5 (if x is negative)

Now above you have two values of x i.e.5 and -5. Look at the options now.

1. x=-5. This is same as the one we have done above. Hence this is sufficient to answer the question.

2. x<0. This could be anything viz. -4,-3,-2,-1,-5 etc. Hence It does not give you YES/NO answer hence NOT SUFFICIENT.

Therefore, your answer is A.

SAME for question 2 as well.

[tohellandback]

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

in question one
its A. 1 alone is sufficient

BUT in 2
both statements are required
statement 1 is sufficient ONLY WHEN YOU KNOW THAT a is positive.
lets take this example
if a=3,|x|=3, which is a
if a=-3, |x|=3, which is -a
so it can not be concluded that |x|=a
|x|= |a| is the correct conclusion and after than it will depend upon whether a is negative or positive
in the given question, statement 2 makes it clear that a is positive.
so both are required and answer is C

[mehravikas]

Thanks it makes sense now...!!

I was not considering that a could be positive or negative.

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

in question one
its A. 1 alone is sufficient

BUT in 2
both statements are required
statement 1 is sufficient ONLY WHEN YOU KNOW THAT a is positive.
lets take this example
if a=3,|x|=3, which is a
if a=-3, |x|=3, which is -a
so it can not be concluded that |x|=a
|x|= |a| is the correct conclusion and after than it will depend upon whether a is negative or positive
in the given question, statement 2 makes it clear that a is positive.
so both are required and answer is C

[tohellandback]

Thanks it makes sense now...!!

I was not considering that a could be positive or negative.

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

in question one
its A. 1 alone is sufficient

BUT in 2
both statements are required
statement 1 is sufficient ONLY WHEN YOU KNOW THAT a is positive.
lets take this example
if a=3,|x|=3, which is a
if a=-3, |x|=3, which is -a
so it can not be concluded that |x|=a
|x|= |a| is the correct conclusion and after than it will depend upon whether a is negative or positive
in the given question, statement 2 makes it clear that a is positive.
so both are required and answer is C

Just in case you wanted it algebraically,
if x=-a
|x|=|-a|
|x|=|-1|*|a| (this is where you were wrong)
|x|=|a|

[mehravikas]

would this be a good way to solve such problems:

|x| = a

Case 1 - a = 5

therefore x = -5 or +5

statement 1 - x = -a -> x = -5
Insufficient as we do not know whether x is less than 0.
statment 2 - x < 0 therefore x = -a i.e. -5

Case 2 - a = -5
statement 1 - x = -a -> x = -(-5) = 5
Insufficient as we do not know whether x is less than 0.
statment 2 - x < 0 therefore x = -a i.e. 5

Therefore |x| = |a|

Thanks it makes sense now...!!

I was not considering that a could be positive or negative.

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

in question one
its A. 1 alone is sufficient

BUT in 2
both statements are required
statement 1 is sufficient ONLY WHEN YOU KNOW THAT a is positive.
lets take this example
if a=3,|x|=3, which is a
if a=-3, |x|=3, which is -a
so it can not be concluded that |x|=a
|x|= |a| is the correct conclusion and after than it will depend upon whether a is negative or positive
in the given question, statement 2 makes it clear that a is positive.
so both are required and answer is C

Just in case you wanted it algebraically,
if x=-a
|x|=|-a|
|x|=|-1|*|a| (this is where you were wrong)
|x|=|a|

[Stuart@KaplanGMAT]

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

You make is sound like these two question are identical, when in fact they're quite different. Due to the differences, the second would be rated as considerably more difficult than the first.

In the first case, we know that 5 is a positive number; in the second case, a could be either positive or negative. It's this distinction that leads to two different answers. When you see absolute value, you should always ask "do I know the signs involved?" If you don't, watch for funny stuff to happen.

Others have given great algebraic explanations, so no need for me to repeat those. Picking numbers is a great way to work through the second question.

[mehravikas]

Hi Stuart,

would this be a good way to solve such problems:

|x| = a

Case 1 - a = 5

therefore x = -5 or +5

statement 1 - x = -a -> x = -5
Insufficient as we do not know whether x is less than 0.
statment 2 - x < 0 therefore x = -a i.e. -5

Case 2 - a = -5
statement 1 - x = -a -> x = -(-5) = 5
Insufficient as we do not know whether x is less than 0.
statment 2 - x < 0 therefore x = -a i.e. 5

Therefore |x| = |a|

Is |x| = 5?

1. x = -5
2. x < 0

If your answer to the above question is A then what should the answer to this one:

Is |x| = a?

1. x = -a
2. x < 0

You make is sound like these two question are identical, when in fact they're quite different. Due to the differences, the second would be rated as considerably more difficult than the first.

In the first case, we know that 5 is a positive number; in the second case, a could be either positive or negative. It's this distinction that leads to two different answers. When you see absolute value, you should always ask "do I know the signs involved?" If you don't, watch for funny stuff to happen.

Others have given great algebraic explanations, so no need for me to repeat those. Picking numbers is a great way to work through the second question.