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

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Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 14 Jul 2016, 21:34
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:36) correct 39% (01:50) wrong based on 147 sessions

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

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

*An answer will be posted in 2 days.

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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 14 Jul 2016, 22:45
1
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
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 18 Jul 2016, 09:16
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.
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 19 Jul 2016, 01:55
Could I seperate the equation |(a+b)(a-b)|<10 as |a+b|*|a-b|<10?
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 19 Jul 2016, 03:44
1
tinalongmao wrote:
Could I seperate the equation |(a+b)(a-b)|<10 as |a+b|*|a-b|<10?


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|
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 18 Mar 2018, 15:03
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.


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,
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 18 Mar 2018, 21:40
msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.


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,


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.
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Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 20 Mar 2018, 08:59
Bunuel wrote:
msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.


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,


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.


Can we write |xy| = |x|*|y|, isn't it fundamentally wrong
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 20 Mar 2018, 09:04
cruiseav wrote:
We cannot write |xy| = |x|*|y|, it is fundamentally wrong


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
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 20 Mar 2018, 09:08
cruiseav wrote:
Bunuel wrote:
msurls wrote:
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,


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.


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


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.
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

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New post 08 Aug 2019, 13:12
Bunuel wrote:
msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.


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,


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.

Bunuel

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

Can you multiply 1 and 2 and retain the inequality because LHS and RHS are both positive so no question of sign change?
if yes then |a-b| |a+b| < 10---> |a2-b2| < 10..Is this true?
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Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2   [#permalink] 08 Aug 2019, 13:12
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