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

It is currently 24 Sep 2018, 14:34

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

In a certain sequence of 10 positive numbers, each number after the fi

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

Hide Tags

Manager
Manager
avatar
S
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
GMAT ToolKit User
In a certain sequence of 10 positive numbers, each number after the fi  [#permalink]

Show Tags

New post 29 May 2017, 10:16
10
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:18) correct 35% (01:44) wrong based on 105 sessions

HideShow timer Statistics

In a certain sequence of 10 positive numbers, each number after the first is square root of the previous number. If the first number is 9, how many numbers are less than 1?


A. 0
B. 1
C. 2
D. 3
E. 4
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: In a certain sequence of 10 positive numbers, each number after the fi  [#permalink]

Show Tags

New post 29 May 2017, 12:39
3
3
niteshwaghray wrote:
In a certain sequence of 10 positive numbers, each number after the first is square root of the previous number. If the first number is 9, how many numbers are less than 1?


A. 0
B. 1
C. 2
D. 3
E. 4


Here is a little trick: any positive integer root from a number more than 1 will be more than 1. So, it does not matter how many times we take the square root from 9, we'll still won't get a number less than 1. Meaning: \(\sqrt[1000000]{9}>1\).

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1343
Location: India
Premium Member
Re: In a certain sequence of 10 positive numbers, each number after the fi  [#permalink]

Show Tags

New post 29 May 2017, 23:08
So in this sequence we are going to start from 9 and take square roots.. so square root of 9 which is 3, .. then square root of 3 which is approx. 1.732, .. then sq root of 1.732 .. and so on...

Its tricky but interesting - as long as a number is > 1, its square root will also be > 1... so in this list no matter how many times we take the square root - ALL the numbers that we end up with will always be > 1 (though the numbers will keep on decreasing)

Hence all numbers are > 1. None of the numbers is < 1.

Thus option A
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3528
Location: United States (CA)
Re: In a certain sequence of 10 positive numbers, each number after the fi  [#permalink]

Show Tags

New post 01 Jun 2017, 10:25
niteshwaghray wrote:
In a certain sequence of 10 positive numbers, each number after the first is square root of the previous number. If the first number is 9, how many numbers are less than 1?


A. 0
B. 1
C. 2
D. 3
E. 4


We note the following fact: If x is greater than 1, then the square root of x is also greater than one. This is because the product of two numbers between 0 and 1 is again between 0 and 1; if the square root of x was less than 1, then x would have to be less than 1 as well.

Now we can conclude that all the numbers in the sequence are greater than 1, since the numbers in the sequence are obtained by taking square roots of numbers that are greater than 1. Thus, none of the numbers in the sequence are less than 1.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8174
Premium Member
Re: In a certain sequence of 10 positive numbers, each number after the fi  [#permalink]

Show Tags

New post 08 Sep 2018, 01:57
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In a certain sequence of 10 positive numbers, each number after the fi &nbs [#permalink] 08 Sep 2018, 01:57
Display posts from previous: Sort by

In a certain sequence of 10 positive numbers, each number after the fi

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.