GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 Jan 2020, 00:24

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60728
If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0  [#permalink]

Show Tags

New post 30 Oct 2018, 04:16
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:32) correct 39% (01:08) wrong based on 71 sessions

HideShow timer Statistics

Intern
Intern
avatar
B
Joined: 07 Jun 2018
Posts: 22
Location: India
Concentration: Entrepreneurship, Marketing
Schools: Wharton '21, Haas '21
Re: If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0  [#permalink]

Show Tags

New post 30 Oct 2018, 04:28
let's say 1) is true:
Then a^2 + b^2 = a^2 + 2*ab + b^2 = (a + b)^2 = 1 (given)
Taking square root of both sides,
(a + b) = +-1
Hence, 1) alone is not sufficient.

With 2) alone as true,
a^2 + b^2 = a^2 = 1
Therefore, a = +-1
Hence, (a + b) = +-1
2) Alone is not sufficient.

If 1) and 2) are both true, then b = 0 and then a = +-1, again.
Therefore, we cannot say from the given two conditions whether (a+b) = 1 for sure.

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 26 Mar 2019
Posts: 108
Concentration: Finance, Strategy
Re: If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0  [#permalink]

Show Tags

New post 05 Dec 2019, 09:40
Quote:
If a^2 + b^2 = 1, is (a + b) = 1?

(1) ab = 0
(2) b = 0


From the task description we have that \(a^2 + b^2 = 1\). Note that in the task it is not specified that both a and b are integers. Since then, it can be possible that \(a =\frac{\sqrt{3}}{2}\) and \(b=\frac{1}{2}\). In this case \(a^2 + b^2 = (\frac{1}{2})^2 + (\frac{\sqrt{3}}{2})^2 = \frac{1}{4} + \frac{3}{4} = 1\)
Even though both \(a^2\) and \(b^2\) are positive, it is not necessarily that \(a\) and \(b\) are also positive. It is possible that \(a = 0\) and \(b = -1\): \(a^2 + b^2 = (0)^2 + (-1)^2 = 0 + 1= 1\)
Let us look closer to each statement.

Statement 1:
1) \(ab = 0\)
Since \(ab = 0\), we can conclude that either \(a\) or \(b\) is equal to \(0\). However, if we assume that \(b = 0\), \(a\) can be both \(1\) and \(-1\). In case \(a = -1\), \(a + b = (-1) + 0 = -1\) and in case \(a = 1\), \(a + b = 1 + 0 = 1\).
The statement is clearly insufficient.

Statement 2:
2) \(b = 0\)
This statement states the same thing that the statement 1 and thus, it is also insufficient.

Both statements 1 and 2 together state the same thing and for this reason both of them are insufficient.

Answer is E.
GMAT Club Bot
Re: If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0   [#permalink] 05 Dec 2019, 09:40
Display posts from previous: Sort by

If a^2 + b^2 = 1, is (a + b) = 1? (1) ab = 0 (2) b = 0

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne