Symmetry.

[lenagmat]

In the number line, is point A and B symmetry about the zero point?

1). The distance from 0 to A is equal to the distance from 1 to B
2). The distance from 0 to A plus the distance from 1 to B is less than 1

For me here is the main question is - the concept symmetry suppose the two distances to be equal or nor?

Becauce if we take statement 2 I do not see that distances are equal? BUT the answer B.

Please, help me.

[user123321]

In the number line, is point A and B symmetry about the zero point?

1). The distance from 0 to A is equal to the distance from 1 to B
2). The distance from 0 to A plus the distance from 1 to B is less than 1

For me here is the main question is - the concept symmetry suppose the two distances to be equal or nor?

Becauce if we take statement 2 I do not see that distances are equal? BUT the answer B.

Please, help me.

i think it may be B
or maybe i am wrong

my explanation is...
say lets assume both A,B are on x-axis for explanation sake
if A = -0.4 (took because A,B's distances sum from O,1 should add to 1) then B should be 0.4 or -0.4 distance from O
case I) A = -0.4, B = 0.4
OA = 0.4,1B = 1-0.4 = 0.6
OA+1B = 1.0
case II) A = 0.4, B = 0.4
OA = o.4,1B = 1-0.4 = 0.6
OA+1B = 1.0

So what this proves is if distances OA & 1B are summed up and if it is less than 1 then they cannot become symmetrical about zero point. they need to be atleast greater than or equal to 1
that's my thought.

user123321

[Aksenov]

Could you look at my approach?

ans is B
explanation:

the question is A= -B?
1. |A| = |1-B|
lets assume that A=-B =>
|A|=|1+A|
A = 1 => 1=2 => not true
A =-0.5 => 0.5=0.5 => true

therefore here is ambiguity

2. |A| + |1-B| < 1

if A=-B then |A| + |1+A| <1 - false for all A
A = 0.2 => 0.2 +1.2 >< 1
A =-0.2 => 0.2 + 0.8=1, 1 not less then 1 => false

ans B.

I will be very grateful if you could correct my explanation

[Max@Math Revolution]

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


==> Using the original condition we can transform the question and gain A=-B?

In case of 1), A=-0.5, B=0.5 yes, A=0.2, B=0.8 no therefore it is not sufficient.

In case of 2), from |A-0|+|B-1|<1 we get A=-B if A<0 and 0<B<1. Then |A|+|B-1|<1==> -A+1-B<1 ==> -A-B<0 ==> A+B>0 and since A+B = 0 is not possible, the answer is No. Therefore it is sufficient. (from A<0, 0<B<1, any number for A=-B does not satisfy |A|+|B-1|<1. A=-0.5, B=0.5 will be a good example. Therefore the answer is B

In the actual question,

In the number line, is zero point between point A and point B?
we get
1). The distance from 0 to A is equal to the distance from 1 to B
2). The distance from 0 to A plus the distance from 1 to B is less than 1

The solution can be derived by matching the number of equation with the number of variables. Since there are 2 variables (A, B) we need 2 equations thus the answer is likely C. Using 1) & 2) together,
if A=0.4, B=0.6 the answer is NO, if A=-0.4, B=0.6 the answer is yesê°€. Therefore the answer is E.




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[Aksenov]

Official answer is B. Not E.