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

 It is currently 21 Aug 2018, 16:59

### 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

# In the sequence of positive numbers x1, x2, x3, ..., what

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Feb 2010
Posts: 163
In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

21 Jun 2010, 15:58
3
23
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:06) correct 30% (00:56) wrong based on 897 sessions

### HideShow timer Statistics

In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

21 Jun 2010, 16:33
13
9
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$ --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find $$x_1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$ --> we have the relationship between $$x_5$$ and $$x_4$$, also insufficient to find $$x_1$$ (we cannot extrapolate the relationship between $$x_5$$ and $$x_4$$ to all consecutive terms in the sequence).

(1)+(2) From (1) $$x_5=\frac{x_4}{2}$$ --> $$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$ --> $$x_4=1$$ --> $$x_4=1=x_1*(\frac{1}{2})^3$$ --> $$x_1=8$$. Sufficient.

_________________
##### General Discussion
Intern
Joined: 21 Jun 2010
Posts: 6
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

22 Jun 2010, 11:45
1
why is it so that we are doing the (1/2) 3 times?
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

22 Jun 2010, 12:34
3
ruchichitral wrote:
why is it so that we are doing the (1/2) 3 times?

$$x_i=\frac{x_{(i-1)}}{2}$$, so every next term is preivious term times $$\frac{1}{2}$$ --> $$x_4=x_3*\frac{1}{2}=x_2*\frac{1}{2}*\frac{1}{2}=x_1*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=x_1*(\frac{1}{2})^3$$.
_________________
Intern
Joined: 24 May 2010
Posts: 4
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

24 Aug 2010, 06:39
1
Thanks Bunuel,

But how do you account for the fact that x4 could be equal to zero.

By taking both the statements together, one of the solutions is also x4 = 0. It nowhere mentions in the question that the sequence has all distinct numbers. Or may be I am unaware that sequence is meant to consist of distinct numbers only.
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

24 Aug 2010, 06:45
1
jainsaurabh wrote:
Thanks Bunuel,

But how do you account for the fact that x4 could be equal to zero.

By taking both the statements together, one of the solutions is also x4 = 0. It nowhere mentions in the question that the sequence has all distinct numbers. Or may be I am unaware that sequence is meant to consist of distinct numbers only.

Stem says: "In the sequence of positive numbers ..."
_________________
Intern
Joined: 24 May 2010
Posts: 4
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

24 Aug 2010, 06:49
Oooops !!! missed that one.

Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

04 Jun 2013, 05:06
1
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
_________________
Manager
Joined: 28 Feb 2012
Posts: 112
GPA: 3.9
WE: Marketing (Other)
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

05 Jun 2013, 04:38
1 st.) Does not tell us anything. It only tells us the sequence formula and how each term in the sequence are related, but no numbers.

2 st.) Again this statement tells us the relation of X5 and X4, no real numbers. Not sufficient.

Combining two statements we see that according to the first formula X4+1=2 which means that X4=1. Solving it for X3=X2/2, X4=X2/4--->1=X2/4---> X2=4. X2=X1/2--->X1=8

_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Intern
Joined: 28 Jan 2013
Posts: 31
Re: In the sequence of positive numbers  [#permalink]

### Show Tags

24 Oct 2013, 07:01
4
abhisheksharma85 wrote:
In the sequence of positive numbers X1, X2, X3, ..... What is the value of X1

(1) Xi = Xi-1 / 2 for all integers i > 1

(2) X5 = X4 / X4+1

Guys, I need to know how to solve this question.. Thanks..

from 1, simply put the values of i = 2,3 or 4 but we can not find the value of X1

we can only know

X2 = X1 / 2 or
X3 = X2 / 2 = X1 / 4 or
X4 = X1 / 8 or
X5 = X1 / 16 etc....
insufficient

from 2, X5 = X4 / X4+1
cannot find X1 , insufficient

combine 1+2, X5 = X1 / 16
and X4 = X1 / 8

so, X1 / 16 = (X1 / 8)/((X1 / 8)+1)

can find X1 hence sufficient

Note : you will find two values of X1 from above quadratic equation i.e X1 = 0 and X1 = 8,
since it is given that X1 is positive so we cant take X1=0 hence sufficient
Manager
Joined: 11 Sep 2013
Posts: 156
Concentration: Finance, Finance
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

26 Oct 2013, 14:30
Bunuel wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$ --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find $$x_1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$ --> we have the relationship between $$x_5$$ and $$x_4$$, also insufficient to find $$x_1$$ (we cannot extrapolate the relationship between $$x_5$$ and $$x_4$$ to all consecutive terms in the sequence).

(1)+(2) From (1) $$x_5=\frac{x_4}{2}$$ --> $$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$ --> $$x_4=1$$ --> $$x_4=1=x_1*(\frac{1}{2})^3$$ --> $$x_1=8$$. Sufficient.

last part is not clear. (1/2)^3 how did u get it?
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: GMAT Prep Question 2  [#permalink]

### Show Tags

27 Oct 2013, 07:00
Raihanuddin wrote:
Bunuel wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$ --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find $$x_1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$ --> we have the relationship between $$x_5$$ and $$x_4$$, also insufficient to find $$x_1$$ (we cannot extrapolate the relationship between $$x_5$$ and $$x_4$$ to all consecutive terms in the sequence).

(1)+(2) From (1) $$x_5=\frac{x_4}{2}$$ --> $$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$ --> $$x_4=1$$ --> $$x_4=1=x_1*(\frac{1}{2})^3$$ --> $$x_1=8$$. Sufficient.

last part is not clear. (1/2)^3 how did u get it?

Or from $$x_i=\frac{x_{(i-1)}}{2}$$:

$$x_2=\frac{x_1}{2}$$;

$$x_3=\frac{x_2}{2}=\frac{x_1}{4}$$;

$$x_4=\frac{x_3}{2}=\frac{x_1}{8}$$.

Hope it's clear.
_________________
Manager
Joined: 22 Apr 2013
Posts: 91
Location: India
Concentration: Finance
GMAT 1: 660 Q48 V33
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

29 Oct 2013, 04:15
What would the difficulty level of this question be? Is it above 700 level?
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

29 Oct 2013, 06:48
akashb106 wrote:
What would the difficulty level of this question be? Is it above 700 level?

No, I'd say it's around 600-650, not more.
_________________
Intern
Joined: 06 Jan 2014
Posts: 41
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

21 Jan 2014, 13:21
This is what I understand thus far

testprep2010 wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$

when combined we can infer that $$x_4+1$$ $$=2$$ thus $$x_4=1$$

and so if you can get a number for one answer, you can get a number for any answer and thus the answer is C?
Senior Manager
Joined: 15 Aug 2013
Posts: 268
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

17 Jun 2014, 17:18
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

I tried to do this by plugging in numbers and after 3+ minutes, I chose "Neither Suff" b/c I wasn't seeing any trends.

A and B are both insufficient because we don't have a starting point. When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

18 Jun 2014, 05:29
russ9 wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

I tried to do this by plugging in numbers and after 3+ minutes, I chose "Neither Suff" b/c I wasn't seeing any trends.

A and B are both insufficient because we don't have a starting point. When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?

On DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get an YES answer with one chosen number(s) and a NO with another.

You can easily see that (1) and (2) are not sufficient alone: different numbers plugged there will lead to different values of x1. When you take the statements together you are able to find the value of x4, and then the value of x1, so no need to plug-in there.
_________________
Manager
Joined: 28 Dec 2013
Posts: 68
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

06 Jul 2014, 09:51
Bunuel wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$ --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find $$x_1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$ --> we have the relationship between $$x_5$$ and $$x_4$$, also insufficient to find $$x_1$$ (we cannot extrapolate the relationship between $$x_5$$ and $$x_4$$ to all consecutive terms in the sequence).

(1)+(2) From (1) $$x_5=\frac{x_4}{2}$$ --> $$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$ --> $$x_4=1$$ --> $$x_4=1=x_1*(\frac{1}{2})^3$$ --> $$x_1=8$$. Sufficient.

Bunuel: to get x4 = 1 do we cross multiply? Can you show the steps to attain this value ?
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

06 Jul 2014, 12:10
sagnik242 wrote:
Bunuel wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$ --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find $$x_1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$ --> we have the relationship between $$x_5$$ and $$x_4$$, also insufficient to find $$x_1$$ (we cannot extrapolate the relationship between $$x_5$$ and $$x_4$$ to all consecutive terms in the sequence).

(1)+(2) From (1) $$x_5=\frac{x_4}{2}$$ --> $$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$ --> $$x_4=1$$ --> $$x_4=1=x_1*(\frac{1}{2})^3$$ --> $$x_1=8$$. Sufficient.

Bunuel: to get x4 = 1 do we cross multiply? Can you show the steps to attain this value ?

Sure.

$$\frac{x_4}{2}=\frac{x_4}{x_4+1}$$;

Reduce by x4: $$\frac{1}{2}=\frac{1}{x_4+1}$$;

Cross-multiply: $$x_4+1=2$$ --> $$x_4=1$$.

Hope it's clear.
_________________
Intern
Joined: 15 May 2014
Posts: 9
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

### Show Tags

06 Jul 2014, 20:39
Bunnuel,

Are AP and GP formulas and concepts required for GMAT? Its obvious that knowing them can be helpful like it helped here, but does GMAT need you to know these thoroughly?
Re: In the sequence of positive numbers x1, x2, x3, ..., what &nbs [#permalink] 06 Jul 2014, 20:39

Go to page    1   2    Next  [ 26 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.