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

 It is currently 16 Oct 2019, 13:16 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.  A geometric sequence is a sequence in which each

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: A geometric sequence is a sequence in which each  [#permalink]

Show Tags

3
1 00:00

Difficulty:   35% (medium)

Question Stats: 66% (01:17) correct 34% (01:21) wrong based on 220 sessions

HideShow timer Statistics

rakeshd347 wrote:
v, w, x, y, z
A geometric sequence is a sequence in which each term after
the first is equal to the product of the preceding term and a
constant. If the list of numbers shown above is an geometric
sequence, which of the following must also be a geometric
sequence?

I. 2v, 2w, 2x, 2y, 2z
II. v + 2, w + 2, x + 2, y + 2, z + 2
III.\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

KUDOS please if you like my question.

We know that v,w,x,y,z are in GP. Thus, w/v = x/w = y/x = z/y = r(some constant, called the common ratio)

I. A multiplication by a constant (2) will not change the ratio, as evident.
III. The ratio for these terms will be another constant $$\sqrt{r}$$

E.

_________________
Manager  Joined: 04 Mar 2013
Posts: 58
Location: India
Concentration: Strategy, Operations
Schools: Booth '17 (M)
GMAT 1: 770 Q50 V44 GPA: 3.66
WE: Operations (Manufacturing)
Re: A geometric sequence is a sequence in which each  [#permalink]

Show Tags

1
Can be done quite easily if 4 nos are considered instead of the variables

For example

1, 2, 4, 8

I multiply 2 : 2, 4, 8, 16 ; they are still in GP
II Add 2: 3, 4, 6, 10 ; not in GP
III Square root : 1, \sqrt{2}, 2, 2\sqrt{2} ; still in GP

So clearly I and III i.e E is the correct answer
_________________
When you feel like giving up, remember why you held on for so long in the first place.
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: A geometric sequence is a sequence in which each  [#permalink]

Show Tags

rakeshd347 wrote:
v, w, x, y, z

A geometric sequence is a sequence in which each term after the first is equal to the product of the preceding term and a constant. If the list of numbers shown above is an geometric sequence, which of the following must also be a geometric sequence?

I. 2v, 2w, 2x, 2y, 2z
II. v + 2, w + 2, x + 2, y + 2, z + 2
III. $$\sqrt{v}$$, $$\sqrt{w}$$, $$\sqrt{x}$$, $$\sqrt{y}$$, $$\sqrt{z}$$

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

Similar question from OG13:
Quote:
p, r, s, t, u

An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. 2p, 2r, 2s, 2t, 2u
II. p-3, r-3, s-3, t-3, u-3
III. p^2, r^2, s^2, t^2, u^2

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Discussed here: an-arithmetic-sequence-is-a-sequence-in-which-each-term-59035.html
_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A geometric sequence is a sequence in which each  [#permalink]

Show Tags

I. 2v, 2w, 2x, 2y, 2z

Multiplication by 2 keeps the GP sequence intact

II. v + 2, w + 2, x + 2, y + 2, z + 2

Addition breaks the GP sequence in this case

III.$$\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}$$

Square rooting is nothing but changing the power from 1 to $$\frac{1}{2}$$ ; it still keeps the GP sequence intact

_________________
Kindly press "+1 Kudos" to appreciate Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
A geometric sequence is a sequence in which each  [#permalink]

Show Tags

mau5 wrote:
rakeshd347 wrote:
v, w, x, y, z
A geometric sequence is a sequence in which each term after
the first is equal to the product of the preceding term and a
constant. If the list of numbers shown above is an geometric
sequence, which of the following must also be a geometric
sequence?

I. 2v, 2w, 2x, 2y, 2z
II. v + 2, w + 2, x + 2, y + 2, z + 2
III.\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

KUDOS please if you like my question.

We know that v,w,x,y,z are in GP. Thus, w/v = x/w = y/x = z/y = r(some constant, called the common ratio)

I. A multiplication by a constant (2) will not change the ratio, as evident.
III. The ratio for these terms will be another constant $$\sqrt{r}$$

E.

Let the common ratio of the terms in GP be r.
So, w = vr
x = vr^2
y = vr^3
z = vr^4

Now lets start checking I , II & III

I. 2v, 2w, 2x, 2y, 2z = 2v, 2vr, 2vr^2, 2vr^3, 2vr^4 Common ratio = r. So, GP
II. (v+2), (w+2), (x+2), (y+2), (z+2) = 2v+2, 2vr+2, 2vr^2 +2 , 2vr^3 +2, 2vr^4 +2 . Not in GP.
III. $$\sqrt{v},\sqrt{w},\sqrt{x},\sqrt{y},\sqrt{z}, = \sqrt{2v}, \sqrt{2vr}, \sqrt{2vr^2},\sqrt{2vr^3},\sqrt{2vr^4}$$

Common ration = $$\sqrt{r}$$. So, GP

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish". A geometric sequence is a sequence in which each   [#permalink] 05 Jul 2017, 06:17
Display posts from previous: Sort by

A geometric sequence is a sequence in which each

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  