Is n<0?
1) -n=|-n|
2)n^2=16
When we list numbers for statement 1, are we supposed to add zero? Is it valid to write -(-0)=|-0|?
Can someone explain this?
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Sure, n = 0 satisfies the equation -n=|-n|seyna wrote:Is n<0?
1) -n = |-n|
2) n² = 16
When we list numbers for statement 1, are we supposed to add zero? Is it valid to write -(-0)=|-0|?
Here's my full solution:
Target question: Is n less than zero?
Statement 1: -n = |-n|
There are several values of n that satisfy this condition. Here are two:
Case a: n = -1, in which case n IS less than 0
Case b: n = 0, in which case n is NOT less than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n² = 16
There are exactly two values of n that satisfy this equation:
Case a: n = -4, in which case n IS less than 0
Case b: n = 4, in which case n is NOT less than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells that n equals EITHER 4 or -4
Of these two possible values of n, only -4 meets the condition in statement 1 (-n = |-n|)
So, n MUST EQUAL -4, in which case n is definitely less than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
That's totally understandable; zero is a strange value in many ways.seyna wrote:Thank you!
I asked 'is it valid to write -(-0)=|-0|?' because since 0 is neither negative nor positive I was thinking -(-0)=|-0| might not be valid.
Another way to look at a negative sign in front of a variable, is to rewrite it as a product with (-1)
That is, -n is the same as (-1)(n)
So, when we test n = 0, we get: (-1)(0) = |(-1)(0)|
Simplify to get: 0 = 0
Cheers,
Brent
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
-(-0)=|-0| is valid. -0 and 0 are the same, so that equation is the same as 0 = |0|.seyna wrote:Is n<0?
1) -n=|-n|
2)n^2=16
When we list numbers for statement 1, are we supposed to add zero? Is it valid to write -(-0)=|-0|?
My approach to solving the question.
No rephrase needed: Is n < 0 ?
1) Since -n = |-n|, we can tell that -n is a value that doesn't change when you put it inside absolute value brackets. Only 0 and positive values don't change, so -n >= 0, which means n <= 0. We cannot definitively tell whether n<0. INSUFFICIENT
2) n=-4 or 4. We cannot tell whether it's less than 0. INSUFFICIENT
Together:
(1) told us that n<=0, so in (2) n cannot equal 4. n must be -4. Since we know n=-4, we can definitively answer the question. SUFFICIENT
Answer is C
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
Thank you. I got it.
Can you also explain this q.
(2^(4-1)^2)) / (2^(3-2)
The answers are:
a) 2^8
b)2^7
c)2^6
d)2^5
2)2^4
I think the answer should be c) because it's in exponent of an exponent form.
But it says the answer is a)
Can you also explain this q.
(2^(4-1)^2)) / (2^(3-2)
The answers are:
a) 2^8
b)2^7
c)2^6
d)2^5
2)2^4
I think the answer should be c) because it's in exponent of an exponent form.
But it says the answer is a)