Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 08:48

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The product of all the prime numbers less than 20 is closest

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [0], given: 2677

The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 01:21
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

46% (01:00) correct 54% (01:11) wrong based on 400 sessions
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

Diagnostic Test
Question: 15
Page: 22
Difficulty: 650
[Reveal] Spoiler: OA

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [2] , given: 2677

Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 01:22
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
SOLUTION

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);

2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}.

Answer: C.

Approach #2:

2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)

2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 285
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 16

Kudos [?]: 150 [0], given: 23

GMAT ToolKit User GMAT Tests User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 02:17
Hi,

Difficulty level: 650

Product of prime numbers less than 20 = 2*3*5*7*11*13*17*19
=(2*5)*3*(7*13)*(11*17)*19
=3*10*91*189*19
~(30)*(90*19)*190
~5700*1710
~5700*1700
~9690000 (=10^6)


Thus, Answer is (D)

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep


Last edited by cyberjadugar on 02 Jul 2012, 02:39, edited 2 times in total.
1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 67

Kudos [?]: 498 [1] , given: 43

GMAT Tests User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 02:25
1
This post received
KUDOS
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

Diagnostic Test
Question: 15
Page: 22
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


The product is 2*3*5*7*11*13*17*19 = 10 * 21 * 11*(13*17) * 19 \approx10*20*10*15^2*20=900*10^4\approx10^7.

Therefore, answer C
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 285
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 16

Kudos [?]: 150 [0], given: 23

GMAT ToolKit User GMAT Tests User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 02:45
Hi,

The magnitude of error depends on the approximation done in the question.

For example: 51*671=34221
50*671=33550 (error = 671)
51*670=34170 (error = 51)

Thus, the when the larger number is approximated the error is less.

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 160
Followers: 1

Kudos [?]: 18 [0], given: 11

Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 04:53
cyberjadugar wrote:
Hi,

The magnitude of error depends on the approximation done in the question.

For example: 51*671=34221
50*671=33550 (error = 671)
51*670=34170 (error = 51)

Thus, the when the larger number is approximated the error is less.

Regards,


your answer '9690000' is closer to 10000000 than 1000000
then why D instead of C.
i got the same and chose D :(
Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 285
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 16

Kudos [?]: 150 [0], given: 23

GMAT ToolKit User GMAT Tests User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 04:58
kashishh wrote:
cyberjadugar wrote:
Hi,

The magnitude of error depends on the approximation done in the question.

For example: 51*671=34221
50*671=33550 (error = 671)
51*670=34170 (error = 51)

Thus, the when the larger number is approximated the error is less.

Regards,


your answer '9690000' is closer to 10000000 than 1000000
then why D instead of C.
i got the same and chose D :(

Hi,

I believe you are right and answer should be (C).

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Intern
Intern
avatar
Joined: 14 Apr 2012
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 02 Jul 2012, 11:58
2*3*5*7*11*13*17*19 = 210*(10+1)(10+3)(10+7)(10+9)
210 ~ 10*10*2
So the original equation will be equivalent to 10*10*2*(10+1)(10+3)(10+7)(10+9)
The highest order of the equation will be 10^6, and other part of expression will not make it closer to 10^7.
I have solved it mostly on hunch, no sure how correct I am.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [1] , given: 2677

Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 06 Jul 2012, 02:12
1
This post received
KUDOS
Expert's post
SOLUTION

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);

2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}.

Answer: C.

Approach #2:

2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)

2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
avatar
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 65
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14
GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 18 [1] , given: 60

Reviews Badge
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 25 Oct 2013, 03:45
1
This post received
KUDOS
I have approached in the following way:-

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 10 x 21x 11 x 13 x 17 x 19 = 10 x 10 x 2.1 x 10 x 1.1 x 10 x 1.3 x 10 x 1.7 x 10 x 1.9 = 10^6 x (2.1 x1.1 x 1.3 x 1.7 x 1.9)

The approximation of the (2.1 x 1.7 x 1.9 x 1.3 x 1.1) will be close to 10, so the answer is 10^7
Intern
Intern
avatar
Joined: 15 Sep 2013
Posts: 5
Schools: Darden
Followers: 0

Kudos [?]: 0 [0], given: 55

GMAT ToolKit User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 05 Mar 2014, 10:48
Similar to Bunuel's first approach:
I thought it was easiest to just do :
2*3*5*7 = 210
11 roughly 10
13 roughly 10
17 roughly 20
19 roughly 20
so 210*10*10*20*20 = 8*10^6 = 10^7
Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 799
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 194 [0], given: 164

Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 06 Mar 2014, 20:40
Product of Prime no between 1 & 20 =

(2*3*5*7)*(11*13)* (17*19)

210 * 143 * 323

(10^2+10) * (10^1+43) * (10^3+23)

(10^3+4300+10^2+430) * (10^3+23)

5830 * (10^3+23)

5830000 + 134090

= 6974090 this is near to 10^7

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 30 May 2013
Posts: 193
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 25 [0], given: 72

GMAT ToolKit User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 10 Mar 2014, 09:15
2*19 =~40
3*17=~60
5*13=~50 (More than 50)
7*11=~70 (")

=40*60*50*70
=4*6(10^2)*5*7(10^2)
=2*(10^1*10^2)*3.5(10^1*10^2)
=7*10^6
=~10^7

Like this any prime number can be multiplied with.
Intern
Intern
avatar
Joined: 12 Feb 2011
Posts: 36
Followers: 0

Kudos [?]: 1 [0], given: 1186

GMAT ToolKit User
Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 11 Apr 2014, 18:07
Can anyone comment on my method's effectiveness/efficiency:
Prime numbers < 20 are: 2, 3, 5, 7, 11, 13, 17, 19 (Count = 8)
Median = 9 (through (7+11)/2)
So product should be approx. close to 9^8 which in turn is closest to 10^7, thus answer is 10^7.

Thanks for reviewing.
Re: The product of all the prime numbers less than 20 is closest   [#permalink] 11 Apr 2014, 18:07
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic The product of all the prime numbers less than 20 is closest melissawlim 7 20 Jan 2010, 05:27
1 Experts publish their posts in the topic The product of all the prime numbers less than 20 is closest JuliaS 2 21 Jan 2008, 21:05
The product of all the prime numbers less than 20 is closest netcaesar 8 12 Jan 2008, 10:20
2 The product of all the prime numbers less than 20 is closest gablaze23 9 02 Aug 2007, 07:07
The product of all the prime number less than 20 is closest Paul 4 06 Jan 2006, 17:20
Display posts from previous: Sort by

The product of all the prime numbers less than 20 is closest

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.