Brushing up on the basics

Algebra Level 5

It is known that a 0 a \neq 0 and b 0 b \neq 0 satisfy

( ( a ) + b ) < 0 -(-(a)+b) < 0

Then, which of the following statements are true?

A) b > a \text{A) } b > a

B) a > b \text{B) } a > b

C) 1 a > 1 b \text{C) } \frac{1}{a} > \frac{1}{b}

D) 1 b > 1 a \text{D) } \frac{1}{b} > \frac{1}{a}

B and D B only A only B and C None of the above A and C A and D

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1 solution

Manuel Kahayon
Jan 1, 2017

Did you see that coming?

Let a = 3 + i a = 3+i and b = 4 + i b = 4+i . Since we cannot compare complex numbers using inequalities, then none of the above statements actually hold true! (I didn't say anything about a a and b b being real.)

So, the answer is None of the above. \large \boxed{\text{None of the above.}}

It made me cry.

Just Kidding

Achal Jain - 4 years, 5 months ago

I wonder who's gonna be the first solver...

Manuel Kahayon - 4 years, 5 months ago

Wicked man...... Seriously

Shubham Rustagi - 4 years, 5 months ago

I am the first solver yipee

Rohith M.Athreya - 4 years, 5 months ago

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Congratulations! Finally, a solver!

Manuel Kahayon - 4 years, 5 months ago

Wow , Caught in trap Great question

Pawan pal - 4 years, 5 months ago

I got the thought of complex no's after looking at the level of question ........ Good one .

Shubhendra Singh - 4 years, 5 months ago

Son of a Biscuit....

Zhang Xiaokang - 1 year, 6 months ago

this problem is simply awesome didn't thought about complex numbers!

Prakhar Bindal - 4 years, 5 months ago

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Even if u take real numbers A is true and either C or D are true since u can't decide which without the signs of a and b,it is none of the options

Rohith M.Athreya - 4 years, 5 months ago

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I Marked A Only . clever options @Manuel Kahayon

Prakhar Bindal - 4 years, 5 months ago

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@Prakhar Bindal I really made it look like it's not a trick question :P

BTW, A is supposed to be correct for all reals

Manuel Kahayon - 4 years, 5 months ago

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@Manuel Kahayon why A only if they are real the C is also true , isn't it ? and also i was also trapped in the wording , i would like if you wrote "must be true " there ! :)

A Former Brilliant Member - 4 years, 5 months ago

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@A Former Brilliant Member Option C is true o n l y only if a and b are positive .....if a is negative it is wrong

Sumanth R Hegde - 4 years, 5 months ago

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