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The second, the first and the third term of an AP whose comm [#permalink]
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08 Dec 2011, 08:15
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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
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Last edited by Bunuel on 12 Jul 2013, 13:01, edited 1 time in total.
Renamed the topic and edited the question.



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Re: Progessions Ap/Gp/both?? [#permalink]
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08 Dec 2011, 09:44
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its D
think A.P to be ad,a,a+d. G.P will be a,ad,a+d
which means (ad)^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 .....



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Re: Progessions Ap/Gp/both?? [#permalink]
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08 Dec 2011, 10:00
avenkatesh007 wrote: its D
which means (ad)^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]
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08 Dec 2011, 10:13
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(ad)^2 = a^2 +ad a^22ad+d^2=a^2+ad d^2=3ad 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]
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03 Jan 2012, 04:43
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]
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03 Jan 2012, 15:02
avenkatesh007 wrote: its D
think A.P to be ad,a,a+d. G.P will be a,ad,a+d
which means (ad)^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: (ad)^2 = a^2+ad Thanks, Anu



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Re: Progessions Ap/Gp/both?? [#permalink]
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04 Jan 2012, 21:49
anuu wrote: avenkatesh007 wrote: its D
think A.P to be ad,a,a+d. G.P will be a,ad,a+d
which means (ad)^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: (ad)^2 = a^2+ad Thanks, Anu for GP we use b^2=ac so using that (ad)^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]
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05 Jan 2012, 21:23
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]
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06 Jan 2012, 04:15
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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 (ad), a and (a+d) Terms of the GP: a, (ad), (a+d) in that order. In a GP, terms next to each other have the same ratio. So, \(\frac{(ad)}{a} = \frac{(a+d)}{(ad)}\) \((ad)^2 = a(a+d)\) \(d^2  2ad = ad\) \(d^2  3ad = 0\) \(d(d  3a) = 0\) We know that d is not 0 from the question. So d = 3a Common ratio \(= \frac{(ad)}{a} = \frac{(a  3a)}{a} = 2\)
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Re: Progessions Ap/Gp/both?? [#permalink]
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06 Jan 2012, 04:17
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/(ad) as one would naturally since (ad) is smaller than a. But, the terms in the GP are a, (ad), (a+d) in that order. So the common ratio is (ad)/a or (a+d)/(ad)
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Re: Progessions Ap/Gp/both?? [#permalink]
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06 Jan 2012, 04:56
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/(ad) as one would naturally since (ad) is smaller than a. But, the terms in the GP are a, (ad), (a+d) in that order. So the common ratio is (ad)/a or (a+d)/(ad) 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]
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07 Jan 2012, 02:32
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/(ad) as one would naturally since (ad) is smaller than a. But, the terms in the GP are a, (ad), (a+d) in that order. So the common ratio is (ad)/a or (a+d)/(ad) Grrr....I am just cursing myself for such silly mistakes. Thanks a ton for pointing it out.
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The second, the first and the third term of an AP whose comm [#permalink]
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18 Nov 2014, 10:43
Hi Karishma,
I am bit confuse with this AP and GP, is it Arithmetic progression and geometric progression. And how do we decide this sequence of a,ad, a+d.



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Re: The second, the first and the third term of an AP whose comm [#permalink]
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18 Nov 2014, 23:37
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taleesh wrote: Hi Karishma,
I am bit confuse with this AP and GP, is it Arithmetic progression and geometric progression. And how do we decide this sequence of a,ad, a+d. Yes, AP is Arithmetic Progression, GP is Geometric Progression. The second first and third terms of an AP form a GP when put in that order. How do we express the terms of AP? Three terms can be expressed as ad, a, a+d (with d as the common difference) When you put them in this order: second, first and third a, ad, a+d  this is a GP A GP has common ratio so (ad)/a = (a+d)/(ad) = Common Ratio More on AP and GP: http://www.veritasprep.com/blog/2012/03 ... gressions/http://www.veritasprep.com/blog/2012/03 ... gressions/http://www.veritasprep.com/blog/2012/04 ... gressions/
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Re: The second, the first and the third term of an AP whose comm [#permalink]
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27 Apr 2016, 09:33
this does not look like a GMAT question. Please let me know if im wrong.



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Re: The second, the first and the third term of an AP whose comm [#permalink]
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27 Apr 2016, 19:46
abypatra wrote: this does not look like a GMAT question. Please let me know if im wrong. The concept could easily be tested this way in GMAT though the wording of the question would be much more explicit.
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Re: The second, the first and the third term of an AP whose comm [#permalink]
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