vaibhav101 wrote:is modulus a+modulus b> modulus a+b?
1) $$a^2>b^2$$
2) b. modulus a<0
We have to determine whether |a| + |b| > |a + b|?
|a| + |b| > |a + b| is poosible only if a and b are opposite in sign. Let's take two cases.
Case 1: Say a = 2 and b = -1
We have |a| + |b| > |a + b| => |2| + |-1|
? |2 - 1| => 2 + 1
? 1. We see that 3 > 1. The answer is Yes.
Case 2: Say a = 2 and b = 1
We have |a| + |b| > |a + b| => |2| + |1|
? |2 + 1| => 2 + 1
? 3. We see that 3
= 3. The answer is No.
Let's see each statement one by one.
(1) a^2 > b^2
Both the cases discussed above are applicable here too. Insufficient.
(2) b.|a| < 0
Since |a| is a positive quantity (irrespective of whether a is positive or negative), and b.|a| is negative, it implies that b is negative.
If a and both are negative, the answer is NO. Say a = b = -1. Then |a| + |b|
= |a + b|. The aswer is No.
However, if a is positive and b is negative, the answer is Yes. Say a = 1 and b = -1. Then |a| + |b|
> |a + b|. The aswer is Yes.
(1) and (2) together:
Both the cases discussed above are applicable here too. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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