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

It is currently 24 Sep 2018, 05:09

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

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

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

Hide Tags

Manager
Manager
avatar
B
Joined: 18 Jun 2017
Posts: 60
The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 10 Jul 2017, 01:07
Multiply 2,5,3,7 and get 210 now rest numbers 11,13,17,19 when multiplied beginning with 210 derived would add a digit more to the number each time and finally we get a 7 digit number, hence which should be near to 10^7.

Please advise if this is feasible solution when calculating other such problems.
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: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 12 Jul 2017, 17:02
Bunuel wrote:
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 need to determine the product of:

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19

Let’s group some of these numbers to get powers of 10:

5 x 19 is about 100 = 10^2

So, we are left with:

2 x 3 x 7 x 11 x 13 x 17

7 x 13 is about 100 = 10^2

So, we are left with:

2 x 3 x 11 x 17

2 x 3 x 17 is about 100 = 10^2

Finally, we have 11, which is about 10 = 10^1.

Thus, the product of all the prime numbers less than 20 is closest to 10^2 x 10^2 x 10^2 x 10^1 = 10^7.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 14 Aug 2017, 14:48
stonecold wrote:
High Quality Question from the Official Set.
Its always good to remember the first 10 primes
2
3
5
7
11
13
17
19
23
29

Now the product of all primes <20 => 2*3*5*7*11*13*19
Product => 210*143*323
Approximating => Product
=>200*150*300 => 9000000 which is close to 10^7
Hence C


hi
Every-time I attempted the problem I ended up with 10^6, and, very naturally, I also found some or many people here with such answer, everybody, however, is claiming the answer to be 10^7...

I have seen you online now, so can you please shed some light on this issue ...?

thanks in advance ..
Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 14 Aug 2017, 15:06
ScottTargetTestPrep wrote:
Bunuel wrote:
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 need to determine the product of:

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19

Let’s group some of these numbers to get powers of 10:

5 x 19 is about 100 = 10^2

So, we are left with:

2 x 3 x 7 x 11 x 13 x 17

7 x 13 is about 100 = 10^2

So, we are left with:

2 x 3 x 11 x 17

2 x 3 x 17 is about 100 = 10^2

Finally, we have 11, which is about 10 = 10^1.

Thus, the product of all the prime numbers less than 20 is closest to 10^2 x 10^2 x 10^2 x 10^1 = 10^7.

Answer: C



hi

I am very much worried about the question, especially because, in many ways we can end up with 10^6 depending on the errors that can stem from the numbers we can approximate in many ways .....
can you please shed some more light on this issue, especially on the number picking process, for example, we have multiplied 5x19, some other people can multiply 5x2, and so on ...
can you please provide some guiding principles to handle questions as such ...

thank you in advance ....
Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 15 Aug 2017, 11:49
Bunuel wrote:
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.


I think I have got this high quality official question...
2,3,5,7,11,13,17,19

2x5 =10
3x11 =30
7x13= 100
17x19 = 400

=10 x1.2 x 10^6
=1.2 x 10^7

cheers ...
Manager
Manager
User avatar
G
Joined: 07 Jun 2017
Posts: 175
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 04 Sep 2017, 00:17
It is
2*3*5*7*11*13*17*19
~10* 21* 140 * 400
~200 * 48000
~96 00 00 0
~ 10^ 7
_________________

Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post

Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 636
Location: India
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 23 Jan 2018, 17:41
Bunuel wrote:
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

It is a good idea to have the representation of numbers in the solution in terms of that in the problem.
Primes below 20 are 2,3,5,7,11,13,17,19.
So we have (10-8)(10-7)(10-5)(10-3)(10+1)(10+3)(10+7)(10+9)
Rearranging we have (10-8)*(10+9) * (10-7)*(10+7) * (10-3)*(10+3) *(10-5)*((10+1)

Approximately these 4 pairs are: 90*50*90*50= approximately 10^7
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2889
Location: Canada
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 02 May 2018, 09:05
1
Top Contributor
Bunuel wrote:
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


Since the answer choices are very spread apart (each number is 10 times greater than the next answer choice), we can be somewhat AGGRESSIVE with our estimation.

We have the product (2)(3)(5)(7)(11)(13)(17)(19)

Let's see if we can group the numbers to get some approximate powers of 10

First (2)(5)=10, so we get (2)(3)(5)(7)(11)(13)(17)(19) = (10)(3)(7)(11)(13)(17)(19)

Next, 11 is close enough to 10, so we get: (10)(3)(7)(11)(13)(17)(19) ≈ (10)(3)(7)(10)(13)(17)(19) [approximately]

Next, (7)(13)=91, which is pretty close to 100. So we get (10)(3)(7)(10)(13)(17)(19) ≈ (10)(3)(100)(10)(17)(19) [approximately]

Finally, 3(17)=51, and (51)(19) is very close to (51)(20), which is very close to 1000
So,(10)(3)(100)(10)(17)(19) ≈ (10)(1000)(100)(10) ≈ 10,000,000

Since 10,000,000 = 10^7, the best answer is C

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Manager
Manager
User avatar
S
Joined: 02 Aug 2017
Posts: 69
Concentration: Strategy, Nonprofit
Schools: ISB '20
GPA: 3.71
Re: The product of all the prime numbers less than 20 is closest  [#permalink]

Show Tags

New post 08 Aug 2018, 23:21
Bunuel wrote:
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


This is how we can easily solve the question by using pattern of (6n+-1) for prime numbers greater than 3 , and by using approximation of maximum and minimum values.

Give kudos if it helps

Posted from my mobile device
Attachments

15337956264012480907789642008657.jpg
15337956264012480907789642008657.jpg [ 2.28 MiB | Viewed 163 times ]


_________________


Everything is in flux, nothing stays still


MGMAT1 :590 Q42 V30 (07/07/18)
VERITAS :660 Q48 V33 (16/07/18)
GMATPREP1 :690 Q46 V36 (22/07/18)
GMATPREP2 :740 Q51 V39 (06/08/18)
ECONOMIST :740 Q49 V44 (11/08/18)
KAPLAN :690 Q49 V36 (17/08/18)
PRINCETON :690 Q48 V38 (26/08/18)
MGMAT2 :720 Q43 V45 (02/09/18)

GMAT Club Bot
Re: The product of all the prime numbers less than 20 is closest &nbs [#permalink] 08 Aug 2018, 23:21

Go to page   Previous    1   2   [ 29 posts ] 

Display posts from previous: Sort by

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

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

Events & Promotions

PREV
NEXT


cron
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®.