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The second, the first and the third term of an AP whose comm

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Manager
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The second, the first and the third term of an AP whose comm [#permalink]  08 Dec 2011, 07:15
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35% (medium)

Question Stats:

57% (02:29) correct 42% (01:25) wrong based on 19 sessions
The second, the first and the third term of an AP whose common difference is non zero but lesser than 200, form a GP in that order. What is the common ration of that GP?

A. 1
B. -1
C. 2
D. -2
E. |1|
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Jul 2013, 12:01, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Progessions Ap/Gp/both?? [#permalink]  08 Dec 2011, 08:44
1
KUDOS
its D

think A.P to be a-d,a,a+d.
G.P will be a,a-d,a+d

which means (a-d)^2 = a^2 + ad
that means d=3
and G.P is -1,2,-4 and A.P is 2,-1,-4. so G.P common ratio is -2 .....
Manager
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Re: Progessions Ap/Gp/both?? [#permalink]  08 Dec 2011, 09:00
avenkatesh007 wrote:
its D

which means (a-d)^2 = a^2 + ad
that means d=3

Can you please elaborate on how you solved the quad with two unknowns variables.
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Re: Progessions Ap/Gp/both?? [#permalink]  08 Dec 2011, 09:13
1
KUDOS
d=3a
here I assumed 'a' to be 1 coz in G.P ratio will be a+d:a kind of.so it wont matter what 'a' is.......else u can substitute direct values interms of 'a'.
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Re: Progessions Ap/Gp/both?? [#permalink]  03 Jan 2012, 03:43
I am getting the ratio as -1/2. Can someone please explain how it is -2?
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Re: Progessions Ap/Gp/both?? [#permalink]  03 Jan 2012, 14:02
avenkatesh007 wrote:
its D

think A.P to be a-d,a,a+d.
G.P will be a,a-d,a+d

which means (a-d)^2 = a^2 + ad
that means d=3
and G.P is -1,2,-4 and A.P is 2,-1,-4. so G.P common ratio is -2 .....

Hi,

Can you please explain how did u get:

Thanks,
Anu
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Re: Progessions Ap/Gp/both?? [#permalink]  04 Jan 2012, 20:49
anuu wrote:
avenkatesh007 wrote:
its D

think A.P to be a-d,a,a+d.
G.P will be a,a-d,a+d

which means (a-d)^2 = a^2 + ad
that means d=3
and G.P is -1,2,-4 and A.P is 2,-1,-4. so G.P common ratio is -2 .....

Hi,

Can you please explain how did u get:

Thanks,
Anu

for GP we use b^2=ac

so using that (a-d)^2 = a(a+d)

by solving this we get d=3a

but the common difference is comming to be -1/2
can anyone please comment on this.
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Re: Progessions Ap/Gp/both?? [#permalink]  05 Jan 2012, 20:23
subhajeet, I have cited the same problem above. Even I am getting the ratio as -1/2. Wonder if we are missing something vital here.
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Re: Progessions Ap/Gp/both?? [#permalink]  06 Jan 2012, 03:15
Expert's post
Anasthaesium wrote:
The second, the first and the third term of an AP whose common difference is non zero but lesser than 200, form a GP in that order. What is the common ration of that GP?

a)1
b)-1
c)2
d)-2
e)|1|

Detailed algebraic explanation:

Let the 3 terms of the AP be (a-d), a and (a+d)
Terms of the GP: a, (a-d), (a+d) in that order.
In a GP, terms next to each other have the same ratio.
So, \frac{(a-d)}{a} = \frac{(a+d)}{(a-d)}

(a-d)^2 = a(a+d)

d(d - 3a) = 0

We know that d is not 0 from the question. So d = 3a

Common ratio = \frac{(a-d)}{a} = \frac{(a - 3a)}{a} = -2
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4032 Location: Pune, India Followers: 859 Kudos [?]: 3616 [1] , given: 144 Re: Progessions Ap/Gp/both?? [#permalink] 06 Jan 2012, 03:17 1 This post received KUDOS Expert's post siddharthmuzumdar wrote: subhajeet, I have cited the same problem above. Even I am getting the ratio as -1/2. Wonder if we are missing something vital here. You probably got d = 3a but after that, substituted d in a/(a-d) as one would naturally since (a-d) is smaller than a. But, the terms in the GP are a, (a-d), (a+d) in that order. So the common ratio is (a-d)/a or (a+d)/(a-d) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Progessions Ap/Gp/both?? [#permalink]  06 Jan 2012, 03:56
VeritasPrepKarishma wrote:
siddharthmuzumdar wrote:
subhajeet, I have cited the same problem above. Even I am getting the ratio as -1/2. Wonder if we are missing something vital here.

You probably got d = 3a but after that, substituted d in a/(a-d) as one would naturally since (a-d) is smaller than a. But, the terms in the GP are a, (a-d), (a+d) in that order. So the common ratio is (a-d)/a or (a+d)/(a-d)

Karishma: U got me right. I was indeed making the same mistake as you have mentioned here. Thanks for the reply.
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Re: Progessions Ap/Gp/both?? [#permalink]  07 Jan 2012, 01:32
VeritasPrepKarishma wrote:
siddharthmuzumdar wrote:
subhajeet, I have cited the same problem above. Even I am getting the ratio as -1/2. Wonder if we are missing something vital here.

You probably got d = 3a but after that, substituted d in a/(a-d) as one would naturally since (a-d) is smaller than a. But, the terms in the GP are a, (a-d), (a+d) in that order. So the common ratio is (a-d)/a or (a+d)/(a-d)

Grrr....I am just cursing myself for such silly mistakes.
Thanks a ton for pointing it out.
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Re: Progessions Ap/Gp/both??   [#permalink] 07 Jan 2012, 01:32
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