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

 It is currently 20 Oct 2019, 15:32

### 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

# The product of all positive even numbers less than or equal to 20 is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58434
The product of all positive even numbers less than or equal to 20 is  [#permalink]

### Show Tags

13 Dec 2015, 05:09
00:00

Difficulty:

95% (hard)

Question Stats:

39% (02:23) correct 61% (02:18) wrong based on 189 sessions

### HideShow timer Statistics

The product of all positive even numbers less than or equal to 20 is closest to which of the following?

A. 10^6
B. 10^7
C. 10^8
D. 10^9
E. 10^10

_________________
Intern
Joined: 30 May 2014
Posts: 15
WE: Information Technology (Consulting)
Re: The product of all positive even numbers less than or equal to 20 is  [#permalink]

### Show Tags

14 Dec 2015, 06:14
1
Bunuel wrote:
The product of all positive even numbers less than or equal to 20 is closest to which of the following?

A. 10^6
B. 10^7
C. 10^8
D. 10^9
E. 10^10

2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20

Replacing closest digits to 10 (6,8,12,14) with 10 and closest to 20 (16,18) with 20.

==>(2 * 4) * (10 * 10 * 10 * 10 * 10) * (20 * 20 * 20)
==>8 * (10^5) * (8 * 10^3)
==>64 * 10^8
==>64 is closest to 50
==>50 * 10^ 8
==>5 * 10^9

Intern
Joined: 26 Dec 2014
Posts: 4
The product of all positive even numbers less than or equal to 20 is  [#permalink]

### Show Tags

28 Dec 2015, 15:50
1
$$n = 2*4*6*8*10*12*14*16*18*20 = (2^1^0)(1*2*3*4*5*6*7*8*9*10) = (2^1^0)10!$$

Now:
$$1*10 = 10$$
$$2*5 = 10$$
$$3*4 = 10$$ (More than 10)
$$6*8 = 50$$ (Less than 50)
$$9*7 = 60$$ (More than 60)
$$2^1^0 = 1000$$ (More than 1000)

Therefore:
$$n = 1000*(3*10^6) = 3*10^9$$, which is closer to $$10^9$$

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: The product of all positive even numbers less than or equal to 20 is  [#permalink]

### Show Tags

03 Nov 2018, 17:54
Bunuel wrote:
The product of all positive even numbers less than or equal to 20 is closest to which of the following?

A. 10^6
B. 10^7
C. 10^8
D. 10^9
E. 10^10

2 x 4 x 6 x … x 20 = (2 x 1) x (2 x 2) x (2 x 3) x … x (2 x 10) = 2^10(1 x 2 x 3 x … x 10) = 2^10 x 10!

2^10 = 1024 is approximately 10^3.

10! = 7! x 8 x 9 x 10 = 5040 x 720 is approximately 5000 x 700 = 35 x 10^5. Since 35 is less than 50, we can round it down to 10, so 35 x 10^5 is approximately 10 x 10^5 = 10^6.

Therefore, 2^10 x 10! is approximately 10^3 x 10^6 = 10^9.

Alternate Solution:

We can group the numbers in the product to create 10s or 100s.

2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 can be broken down into:

10 = 10^1

8 x 12 = 96 ≈ 100 = 10^2

6 x 16 = 96 ≈ 100 = 10^2

2 x 4 x 14 = 112 ≈ 10^2

The remaining two factors are 18 x 20 = 360 = 3.6 x 10^2

We combine all of these factors, obtaining 3.6 x 10^9, which is closest to answer choice D.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: The product of all positive even numbers less than or equal to 20 is   [#permalink] 03 Nov 2018, 17:54
Display posts from previous: Sort by