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Re: M09-22
[#permalink]
11 Oct 2023, 16:55
11 Oct 2023, 16:55
1
Kudos
Pretty good reasoning there in the solution! I did it algebraically the whole way which took a little longer I suppose.
I multiplied both sides with |x|, resulting in
x < x*|x|
x|x| -x > 0
This gives rise to 2 cases:
1. x > 0 AND |x| - 1 > 0
Solving for |x| > 1 gives rise to x > 1 or x < -1. Since x has to fulfil condition x > 0 as well, x can only be > 1.
2. x < 0 AND |x| - 1 < 0
Solving for |x| < 0 gives rise to -1 < x < 1. Since x NEEDS to be smaller than 0 as well, condition becomes -1 < x < 0.
I multiplied both sides with |x|, resulting in
x < x*|x|
x|x| -x > 0
This gives rise to 2 cases:
1. x > 0 AND |x| - 1 > 0
Solving for |x| > 1 gives rise to x > 1 or x < -1. Since x has to fulfil condition x > 0 as well, x can only be > 1.
2. x < 0 AND |x| - 1 < 0
Solving for |x| < 0 gives rise to -1 < x < 1. Since x NEEDS to be smaller than 0 as well, condition becomes -1 < x < 0.
Re: M09-22
[#permalink]
08 Jun 2024, 09:21
08 Jun 2024, 09:21
Hi Bunuel, Don't we consider |x| as always +x and not -x? Cause whatever x be any sort of real number it will always come out positive. Although I understand that if we have a function inside a mod, the we consider both negative and positive. But, pls let me know foe this case. I always get confused in this
Re: M09-22
[#permalink]
08 Jun 2024, 10:38
08 Jun 2024, 10:38
Expert Reply
tanishqgirotra
Hi Bunuel, Don't we consider |x| as always +x and not -x? Cause whatever x be any sort of real number it will always come out positive. Although I understand that if we have a function inside a mod, the we consider both negative and positive. But, pls let me know foe this case. I always get confused in this
You should brush up fundamentals:
10. Absolute Value
- Theory
Math: Absolute value (Modulus)
Absolute Value: Tips and hints
Properties of Absolute Values on the GMAT
Absolute modulus : A better understanding
GMAT Question Patterns: Abolute Value
The Reason Behind Absolute Value Questions on the GMAT
For more check Ultimate GMAT Quantitative Megathread
Hope it helps.
