Modulus question!! got stuck

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nroy347: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Apr 02, 2012 9:53 am

by nroy347 » Mon Aug 27, 2012 3:31 am

Hello...
The question I am unabe to solve..PLEASE HELP !!

If x is an integer, how many possible values of x exist for x^2+|5|x+6 ?
[A] 4
2
[C] 3
[D] 1
[E] 0

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Source: Beat The GMAT — Problem Solving | Mon Aug 27, 2012 3:31 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Mon Aug 27, 2012 6:33 am

nroy347 wrote:Hello...
The question I am unabe to solve..PLEASE HELP !!

If x is an integer, how many possible values of x exist for x^2+|5|x+6 ?
[A] 4
2
[C] 3
[D] 1
[E] 0

Not sure if it is a correct method, but let me try:

I think the equation is x^2+|5|x+6 = 0.

Two cases arise: 5 can be either -5 or +5

Case 1: If +5 => x^2+5x+6 = 0 => x=-2 or x=-3. Plug back these two values in original equation and you can see they work.

Case2: If -5 => x^2-5x+6 = 0 => x=+2 or x=+3. Plug back these two values in original equation and you can see they DO NOT work.

So, we have two solutions. Ans B.

- VK

I will (Learn. Recognize. Apply)

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nroy347: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Apr 02, 2012 9:53 am

by nroy347 » Mon Aug 27, 2012 7:03 am

Hi..

No the answer which was given was E!! I got the answer B but I dont know how come E!!

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vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Mon Aug 27, 2012 7:25 am

I don't think 0 is the answer because the Determinant (b^2 - 4ac) is positive. Therefore two solutions exist.

Maybe experts can help.

- VK

I will (Learn. Recognize. Apply)

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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

by cypherskull » Mon Aug 27, 2012 8:54 am

Hey Vinayak

I got B as the answer too.

However, I wanted to point out (or rather confirm) the following:

Two cases arise: 5 can be either -5 or +5

As far as I know, |5| cannot have +5 or -5 as its value. Modulus of any positive or negative value is always positive.

This applies to the cases where the value within the modulus is unknown - say |X|. If X (without mods) < 0, |X| = -X. If X > 0, |X| = X.

Besides, I think this question as it stands will always yield B as the answer. Its just a guess but maybe the question is - x^2 + |5x| + 6 = 0.

Regards,
Sunit

________________________________

Kill all my demons..And my angels might die too!

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vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Mon Aug 27, 2012 8:58 am

Thanks, Sunit. I applied + and - by seeing the modulus. You are right, if it is |5| it is just simply 5 not -5.

- VK

I will (Learn. Recognize. Apply)

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