It is currently 17 Oct 2017, 19:39

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 to which

Author Message
Manager
Joined: 10 Nov 2010
Posts: 247

Kudos [?]: 401 [0], given: 22

Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
The product of all the prime numbers less than 20 is closest to which [#permalink]

Show Tags

08 Mar 2011, 08:34
2
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

36% (01:01) correct 64% (00:55) wrong based on 73 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

[Reveal] Spoiler:
2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

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

_________________

The proof of understanding is the ability to explain it.

Kudos [?]: 401 [0], given: 22

Manager
Joined: 02 Apr 2010
Posts: 102

Kudos [?]: 138 [0], given: 18

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

Show Tags

08 Mar 2011, 09:06
As you don't have to know the exact result but rather the magnitude I would just round when multiplying, i.e.:

2*3*5*7 = 210 (use 200)
200*11= 2200 (use 2,000)
2,000*13= 26000 (use 20,000)
20,000*17 = 340,000 (use 300,000)
300,000*19 = 5,700,000 (use 6,000,000)

Now since you rounded to a lower number most of the time and the result is still larger than 5,000,000 it is clear that the answer is C) 10^7.

I don't know why the answer is given as D) but I think it's wrong.

Kudos [?]: 138 [0], given: 18

Manager
Joined: 14 Feb 2011
Posts: 185

Kudos [?]: 152 [0], given: 3

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

Show Tags

08 Mar 2011, 09:32
GMATD11 wrote:
15.) 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

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

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17) or 10*21*209*221
Now take out power of 10 from each number and rewrite

10*10*100*100*(1*2.1*2.09*2.21) or 10^6*(1*2.1*2.09*2.21)

Which is greater than 10^6 and closer to 10^7, so answer should be C.

Are you sure OA is correct?

Kudos [?]: 152 [0], given: 3

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 396 [0], given: 123

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

Show Tags

08 Mar 2011, 09:43
2*3*5*7*11*13*17*19

6 * 35 * 7 * 143 * 340 i.e.(17 * 20)
6 * 245 * 143 * 340
6 * 2.5 * 1.4 * 3.4 * 10^6
15 * 5 * 10^6
75 * 10^6
7.5 * 10^7

Kudos [?]: 396 [0], given: 123

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

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

Show Tags

16 May 2016, 19:58
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.
_________________

Kudos [?]: 273 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128621 [0], given: 12180

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

Show Tags

16 May 2016, 22:04
GMATD11 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

[Reveal] Spoiler:
2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

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

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);

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

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)

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
_________________

Kudos [?]: 128621 [0], given: 12180

Chat Moderator
Joined: 04 Aug 2016
Posts: 574

Kudos [?]: 85 [0], given: 139

Location: India
GPA: 4
WE: Engineering (Telecommunications)
Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

Show Tags

05 Aug 2017, 00:28
Bunuel wrote:
GMATD11 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

[Reveal] Spoiler:
2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/the-product-o ... 35192.html

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);

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

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)

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/the-product-o ... 35192.html

The OA is marked as 'D' for this question. Why do we have 2 threads with same question? Is it to keep number of posts readable?

Kudos [?]: 85 [0], given: 139

Re: The product of all the prime numbers less than 20 is closest to which   [#permalink] 05 Aug 2017, 00:28
Display posts from previous: Sort by