GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:00 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The second, the first and the third term of an AP whose comm

Author Message
TAGS:

Hide Tags

Manager  Status: Taking heavily leveraged but calculated risks at all times
Joined: 04 Apr 2010
Posts: 177
Concentration: Entrepreneurship, Finance
Schools: HBS '15, Stanford '15
GMAT Date: 01-31-2012
The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

1
18 00:00

Difficulty:   75% (hard)

Question Stats: 58% (02:40) correct 42% (02:17) wrong based on 132 sessions

HideShow timer Statistics

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|

Originally posted by Anasthaesium on 08 Dec 2011, 08:15.
Last edited by Bunuel on 12 Jul 2013, 13:01, edited 1 time in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India

Show Tags

4
12
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, $$\frac{(a-d)}{a} = \frac{(a+d)}{(a-d)}$$

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

$$d^2 - 2ad = ad$$

$$d^2 - 3ad = 0$$

$$d(d - 3a) = 0$$

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

Common ratio $$= \frac{(a-d)}{a} = \frac{(a - 3a)}{a} = -2$$
_________________
Karishma
Veritas Prep GMAT Instructor

General Discussion
Manager  Joined: 24 Oct 2011
Posts: 83
Location: India
GMAT Date: 11-29-2011
GPA: 3.5
WE: Web Development (Computer Software)

Show Tags

1
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  Status: Taking heavily leveraged but calculated risks at all times
Joined: 04 Apr 2010
Posts: 177
Concentration: Entrepreneurship, Finance
Schools: HBS '15, Stanford '15
GMAT Date: 01-31-2012

Show Tags

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.
Manager  Joined: 24 Oct 2011
Posts: 83
Location: India
GMAT Date: 11-29-2011
GPA: 3.5
WE: Web Development (Computer Software)

Show Tags

1
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'.
Manager  Joined: 12 Oct 2011
Posts: 170

Show Tags

I am getting the ratio as -1/2. Can someone please explain how it is -2?
_________________
Consider KUDOS if you feel the effort's worth it
Intern  Joined: 28 Feb 2011
Posts: 33

Show Tags

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
Manager  Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 134
Location: India
WE: Information Technology (Investment Banking)

Show Tags

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.
Manager  Joined: 12 Oct 2011
Posts: 170

Show Tags

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.
_________________
Consider KUDOS if you feel the effort's worth it
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India

Show Tags

1
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

Manager  Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 134
Location: India
WE: Information Technology (Investment Banking)

Show Tags

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.
Manager  Joined: 12 Oct 2011
Posts: 170

Show Tags

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. _________________
Consider KUDOS if you feel the effort's worth it
Intern  Joined: 18 Jul 2013
Posts: 33
The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

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,a-d, a+d.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

2
2
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,a-d, 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
a-d, a, a+d (with d as the common difference)

When you put them in this order: second, first and third
a, a-d, a+d - this is a GP

A GP has common ratio so (a-d)/a = (a+d)/(a-d) = 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/
_________________
Karishma
Veritas Prep GMAT Instructor

Manager  S
Joined: 23 Jan 2016
Posts: 181
Location: India
GPA: 3.2
Re: The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

this does not look like a GMAT question. Please let me know if im wrong.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User Joined: 09 Sep 2013
Posts: 11378
Re: The second, the first and the third term of an AP whose comm  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: The second, the first and the third term of an AP whose comm   [#permalink] 07 Feb 2019, 19:51
Display posts from previous: Sort by

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