1001^2 - 999^2 / 101^2 - 99^2 ?
a) 10
b) 20
c) 40
d) 80
e) 100
Answer is a. Can someone please explain it.
Thanks,
Vito
Can someone help me with this problem?
This topic has expert replies
GMAT/MBA Expert
- beatthegmat
- Site Admin
- Posts: 6773
- Joined: Mon Feb 13, 2006 8:30 am
- Location: Los Angeles, CA
- Thanked: 1249 times
- Followed by:994 members
What is the source of this question?
Beat The GMAT | The MBA Social Network
Community Management Team
Research Top GMAT Prep Courses:
https://www.beatthegmat.com/gmat-prep-courses
Research The World's Top MBA Programs:
https://www.beatthegmat.com/mba/school
Community Management Team
Research Top GMAT Prep Courses:
https://www.beatthegmat.com/gmat-prep-courses
Research The World's Top MBA Programs:
https://www.beatthegmat.com/mba/school
-
- Senior | Next Rank: 100 Posts
- Posts: 87
- Joined: Fri Jun 09, 2006 2:47 am
- Thanked: 2 times
Based on (a + b)^2 = a^2 + b^2 + 2*a*b
and (a - b)^2 = a^2 + b^2 - 2*a*b:
(1001^2 - 999^2) / (101^2 - 99^2)
= (1000 + 1)^2 - (1000 - 1)^2 / (100 + 1)^2 - (100 - 1)^2
= (1000^2 + 1^2 + 2*1*1000) - (1000^2 + 1^2 - 2*1*1000) / (100^2 + 1^2 + 2*1*100) - (100^2 + 1^2 - 2*1*100)
= 4000/400
= 10
and (a - b)^2 = a^2 + b^2 - 2*a*b:
(1001^2 - 999^2) / (101^2 - 99^2)
= (1000 + 1)^2 - (1000 - 1)^2 / (100 + 1)^2 - (100 - 1)^2
= (1000^2 + 1^2 + 2*1*1000) - (1000^2 + 1^2 - 2*1*1000) / (100^2 + 1^2 + 2*1*100) - (100^2 + 1^2 - 2*1*100)
= 4000/400
= 10
GMAT/MBA Expert
- Stacey Koprince
- GMAT Instructor
- Posts: 2228
- Joined: Wed Dec 27, 2006 3:28 pm
- Location: Montreal, Canada
- Thanked: 639 times
- Followed by:694 members
- GMAT Score:780
Alternatively, using Raj's suggestion (this is the shortcut):
1001^2 - 999^2 / 101^2 - 99^2
(1001 + 999)(1001 - 999) / (101 + 99)(101-99)
(2000)(2)
(200)(2)
cross off 2's, cross off two zero's each from top and bottom
20/2
10
1001^2 - 999^2 / 101^2 - 99^2
(1001 + 999)(1001 - 999) / (101 + 99)(101-99)
(2000)(2)
(200)(2)
cross off 2's, cross off two zero's each from top and bottom
20/2
10
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
In solving this question, let us first recall the algebraic equation
a^2 - b^2 = (a-b)(a+b)
(1001^2 - 999^2) / (101^2 - 99^2)
solving the numerator first,
1001^2 - 999^2 = (1001-999)(1001+999)
=(2)(2000)
=4000
let solve the denominator
101^2 - 99^2 = (101-99)(101+99)
=2*200
=400
Solving mathematically using the division method,
numerator/denominator= 4000/400
=10
we got 10 as the answer which is option A
a^2 - b^2 = (a-b)(a+b)
(1001^2 - 999^2) / (101^2 - 99^2)
solving the numerator first,
1001^2 - 999^2 = (1001-999)(1001+999)
=(2)(2000)
=4000
let solve the denominator
101^2 - 99^2 = (101-99)(101+99)
=2*200
=400
Solving mathematically using the division method,
numerator/denominator= 4000/400
=10
we got 10 as the answer which is option A
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can see that both the numerator and denominator are differences of two squares. Therefore, the numerator can be factored and simplified as:
(1001 - 999)(1001 + 999) = 2(2000) = 4000
Similarly, the denominator can be factored and simplified as:
(101 - 99)(101 + 99) = 2(200) = 400
Therefore, the quotient is 4000/400 = 10.
Answer: A
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews