BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The product (1−1/2)(1−1/3)(1−1/4)(1−1/5)...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

The product (1−1/2)(1−1/3)(1−1/4)(1−1/5)...

by BTGmoderatorLU » Sat Oct 21, 2017 6:57 pm
The product
$$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right).........\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)$$
equals...

$$A:\frac{1}{10}$$

$$B:\frac{1}{20}$$

$$C:\frac{3}{20}$$

$$D:\frac{3}{10}$$

$$E:\frac{7}{20}$$

The OA is B.

Can any expert help me with this PS question please? Thanks.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Oct 22, 2017 3:57 am
LUANDATO wrote:The product
$$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right).........\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)$$
equals...

$$A:\frac{1}{10}$$

$$B:\frac{1}{20}$$

$$C:\frac{3}{20}$$

$$D:\frac{3}{10}$$

$$E:\frac{7}{20}$$
In the solution below, all of the values in red CANCEL OUT.

$$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right).........\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)$$

= (1/2)(2/3)(3/4)....(17/18)(18/19)(19/20).

= 1/20.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Nov 20, 2019 6:02 pm
BTGmoderatorLU wrote:The product
$$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right).........\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)$$
equals...

$$A:\frac{1}{10}$$

$$B:\frac{1}{20}$$

$$C:\frac{3}{20}$$

$$D:\frac{3}{10}$$

$$E:\frac{7}{20}$$

The OA is B.

Can any expert help me with this PS question please? Thanks.

Solving the product for the 1st four parentheses, we have:

(1/2) x (2/3) x (3/4) x (4/5) x ... x (18/19) x (19/20)

After cross canceling, we see that only the numerator of the first fraction and the denominator of the last fraction remain. Thus, the product of the entire expression is 1/20.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1