The product of all the prime numbers less than 20 is closest : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 08:47

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Jan 2012
Posts: 44
Location: United States
Concentration: Marketing, Technology
GMAT 1: Q42 V32
GMAT 2: 0 Q50 V35
GPA: 3.6
Followers: 1

Kudos [?]: 114 [4] , given: 5

The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

26 Jan 2012, 09:29
4
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

50% (01:59) correct 50% (01:10) wrong based on 416 sessions

### HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 May 2016, 21:01, edited 3 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93177 [5] , given: 10553

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

26 Jan 2012, 09:45
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
monikaleoster 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

Suggest method of solution.
The correct ans is C

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. One way:

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=~10*20*200*200=8*10^6=~10^7

Or:
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=~10*50*100*200=10^7.

P.S. Please format the questions properly.
_________________
Intern
Joined: 17 Jun 2012
Posts: 8
Followers: 0

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

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

23 Jun 2012, 20:52
2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
2000*5000
10,000,000

Posted from my mobile device
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 889 [1] , given: 43

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

23 Jun 2012, 23:21
1
KUDOS
melissawlim 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

Official Guide 12 Question

 Question: 15 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

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

My approximation would be 2x5x(3x7)x(11x19)x(13x17)~10x20x200x15x15=10,000x4x225=10,000x900~10,000,000.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 23 Jul 2010
Posts: 91
Followers: 0

Kudos [?]: 10 [0], given: 43

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

23 Mar 2013, 11:00
GMATBLACKBELT wrote:
gablaze23 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

Okay I have the solution to this.
But I am just wondering whether there is a shortcut?

My solution... hall ass.. 2*3*5*7=210*11=2310*13=30030*17=510510*19=9699690

Did you actually calculate this with a pen and paper or you used a calculator?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13453
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

07 Dec 2014, 12:18
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.
_________________
Current Student
Joined: 03 Feb 2013
Posts: 939
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Followers: 134

Kudos [?]: 843 [0], given: 546

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

21 Dec 2014, 07:24
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19

2* 5 = 10
11 = 10 approx.
3 * 7 = 21 = 20 approx = 10 *2 -Extra 2
19 = 10 * 2 - Extra 2
13 * 4 (2*2 extra) = 52 = 10 - Extra 5
17*5 = 105 - 100 approx
So 10 * 10 * 10 * 10 * 10 * 100 = 10^7 - C)
_________________

Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961
Prodigy for Tepper - CMU : http://bit.ly/cmuloan-kd

VP
Joined: 08 Jun 2010
Posts: 1401
Followers: 3

Kudos [?]: 113 [0], given: 812

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

29 Apr 2015, 22:58
hard one
thank you Bunuel for the best solution
Senior Manager
Joined: 10 Mar 2013
Posts: 290
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Followers: 11

Kudos [?]: 98 [0], given: 2405

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

01 Jan 2016, 17:56
2*3*5*7*11*13*17*19
2*3*5*7=210
11 ~=10
13*17=221
19 ~= 20

210*10*221*20
=2^3*10^6
~=C
Intern
Joined: 27 Oct 2015
Posts: 18
Followers: 2

Kudos [?]: 4 [0], given: 175

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

24 Jan 2016, 02:06
Dear Bunuel,
Thank you for elegant solution of the problem.
Could u plz share with similar questions,
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93177 [1] , given: 10553

Re: The product of all the prime numbers less than 20 is closest [#permalink]

### Show Tags

24 Jan 2016, 02:31
1
KUDOS
Expert's post
studentsensual wrote:
Dear Bunuel,
Thank you for elegant solution of the problem.
Could u plz share with similar questions,
Thanks

Similar question: the-product-of-all-positive-even-numbers-less-than-or-equal-to-20-is-209969.html
_________________
Re: The product of all the prime numbers less than 20 is closest   [#permalink] 24 Jan 2016, 02:31
Similar topics Replies Last post
Similar
Topics:
4 The product of all the prime numbers less than 20 is closest to which 6 14 Dec 2010, 17:18
9 The product of all the prime numbers less than 20 is closest to which 9 07 Dec 2010, 19:24
9 The product of all the prime numbers less than 20 is closest to which 7 26 Nov 2010, 07:20
4 The product of all the prime numbers less than 20 is closest 7 20 Jan 2010, 05:27
5 The product of all the prime numbers less than 20 is closest to which 6 12 Jun 2009, 20:28
Display posts from previous: Sort by