Is |a^2 - b^2|

Question

Is |a^2 - b^2| < 10?

(1) |a - b| < 5
(2) |a + b| < 2

*An answer will be posted in 2 days.

HARRY113 · Answer

My Answer is C)

Below is my explanation, Please feel free to correct me, if wrong.
given |(a+b)(a-b)| < 10 --> A

a) |a-b| < 5
Let a = 10 , b = 7 : Above eq A is not satisfied
a = 3 , b = -2 : Above eq A is satisfied
Therefore, Not Suff.

b) |a+b| <2
If a = 1, b = 1/2 : Eq A is satisfied
a = 10 , b = -9 : Eq A is not satisfied.
Therefore, Not Suff.

a + b => Sufficient. Hence, C

MathRevolution · Answer

Since there are 2 variables in the original condition, the correct answer is C.

- 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 independent equations ensures a solution.

tinalongmao · Answer

Could I seperate the equation |(a+b)(a-b)|<10 as |a+b|*|a-b|<10?

abhimahna · Answer

Yes, you could.

Remember, Product and Division in absolute values could be separated.

I mean if we have |a/b|, we can write it as |a|/|b|

or |a*b|=|a|*|b|

MikeScarn · Answer

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Thanks,

Bunuel · Answer

Is |a^2 - b^2| < 10?

(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.
If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.
If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.

cruiseav · Answer

Can we write  |xy| = |x|*|y| , isn't it fundamentally wrong

abhimahna · Answer

We can always do so. It is absolutely correct. Check my comments here: https://gmatclub.com/forum/is-a-2-b-2-1 ... l#p1711648

Bunuel · Answer

Yes, we can. Why do you say that? In mathematics it's called multiplicativity: |xy| = |x|*|y| is true for all numbers x and y.

stoned · Answer

st.1  distance of a from b is 5 --- they could be any number in the number line
 st.2  distance of a from -b is 2 --- they could be any number in number line

when taken together only a set of values will satisfy the conditions that a is at distance 2 from -b and a distance 5 from b.

am i doing this right  Bunuel ?

Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2

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