If a

Question

If a < 0, is |a| - a - |2a| = ?

A. a
B. -1
C. 0
D. 1
E. –a

json · Answer

|a|-|2a| = -|a|

-a - |a| and a <0:
-a - (-a) = 0

gmatophobia · Answer

As a < 0

|a| = -a 
 |2a| = -2a

Substituting the values

-a -a - (-2a)

-2a + 2a = 0

Option C

BrushMyQuant · Answer

Given that a < 0 and we need to find the value of |a| - a - |2a|

a < 0
=> a can be taken as -k where k > 0
=> |a| - a -|2a| = |-k| -(-k) -|-2k|
= k + k - 2k (as k> 0 => |-k| =k)
= 2k - 2k
= 0

So, Answer will be C
Hope it helps!

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eaat · Answer

Sorry, can someone explain this to me? Isn't the absolute value of negative a, a? How is it negative a

|a| - a - |2a| = ?

I did:
|-a| = a
- a = a
|-2a| = 2a

a + a - 2a = 0

eaat · Answer

Since we're given a<0, that is why I substituted -a into the equation therefore turning this |a| - a - |2a| into |-a| - -a - |-2a| ; is that wrong? and then I solved each set

Bunuel · Answer

If a < 0, is |a| - a - |2a| = ?

A. a
B. -1
C. 0
D. 1
E. –a

Since a < 0, |a| = -a and |2a| = -2a.

So:

|a| - a - |2a| = -a - a - (-2a) = -2a + 2a = 0

Answer: C.

a < 0 means a is already negative. It does not mean replace every a with -a.

For example, if a = -3:

|a| - a - |2a| = |-3| - (-3) - |-6| = 3 + 3 - 6 = 0

So the answer is 0.

eaat · Answer

I'm not sure I understand this part:

*  |a| = -a; isn't an absolute value always positive? How can it yield a negative number? 
 * |2a| = -2a; same as above

For example, if a = -3:

|a| - a - |2a| = |-3| - (-3) - |-6| = 3 + 3 - 6 = 0

Yes this is what I ended up getting: a + a - 2a = 0

Sorry my formatting was weird, but I did this:
|a| given that a<0 doesn't this become |-a| = a
- a given than a<0 doesn't this become -(-a) = a
|2a| given that a<0 doesn't this become |-2a| = 2a

So we get a + a - 2a which matches 3 + 3 - 6 = 0

Bunuel · Answer

The key point is that -a does not mean “a negative number.” It means “the opposite of a.”

So if a is negative, then -a is positive. For example, if a = -3, then -a = 3.

So, yes, absolute value always gives a nonnegative result. However, when a is negative, |a| = -a = -(negative) = positive.

This is the basic absolute value property being used here.

eaat · Answer

I understand, I think I'm flipping it around.

Yes this is clear thank you very much!  |a| = -a = -(negative) = positive.

If I did |a| = |-a| = a is this also correct, or did I just get lucky for this question?

I ended up with a + a - 2a

Bunuel · Answer

|a| = |-a| is true for any value of a.

If a < 0, then |a| = -a and in this case -a is positive, so |-a| = -a. So, as you can see  |a| = |-a|.

If a > 0, then |a| = a and in this case -a is negative, so |-a| = -(-a) = a. So, as you can see here also |a| = |-a|.

If a < 0, is |a| - a - |2a| = ?

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If a < 0, is |a| - a - |2a| = ?

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