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**soha****Real Member**- Registered: 2006-07-07
- Posts: 2,530

Four numbers are in AP. If their sum is 20 and sum of their squares is 120 then the numbers are

A) 1,4,7,9 B) 3,5,7,9 C) 2,4,6,8 D) 2,4,8,12

"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"

- David O. McKay

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi soha;

C is the correct answer.

2 + 4 + 6 + 8 = 20

4 + 16 + 36 + 64 = 120

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

bobbym

u only need to find the SUM OF THE NUMBERS because all other answer options don't add up to 20.

In an Aptitude Test this can save a lot of time...

If two or more thoughts intersect, there has to be a point!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi ZHero;

I know. I just wanted to show soha that I picked the right one.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**soha****Real Member**- Registered: 2006-07-07
- Posts: 2,530

It is given that the numbers are in Ap....

Is there any way we can find it by arithmetic progression????

"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"

- David O. McKay

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi soha;

A and D are not arithmetic progressions. B and C are, and only C's 4 numbers add up to 20.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**soha****Real Member**- Registered: 2006-07-07
- Posts: 2,530

Got it !!!!!!!!!!!!!!

*Last edited by soha (2010-03-21 20:00:52)*

"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"

- David O. McKay

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,379

If it was not a multiple choice question, how would we know the answer? Just curious.

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi Monox D. I-Fly

Yes, it can be done although the algebra gets a little complicated at times. If you call the first term 'a', and the common difference 'd' then you can form two equations. Make d the subject of the first and substitute into the second to get a. Then calculate d.

There are two answers but the second is just the first with the order of terms reversed.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,379

I have tried. Stuck at 2a + 3b = 10 and

.Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi Monox D. I-Fly

Yes, that's how I started. If you have two independent equations and two unknowns then you can find both values. Here's how:

Use the 'easier' one to make b the subject. (Can alternatively make a the subject)

So

Substitute all the b values in the second equation using this, so you have an equation with just a.

Simplify.

You end up with a quadratic.

Solve to get two values for a. Use the above to get the value of b in each case.

These give rise to two possible APs. One is the one you know about. The other is the same four numbers in the reverse order.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**Alg Num Theory****Member**- Registered: 2017-11-24
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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,379

Ah, okay. Thank you everyone!

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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