|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:54) correct
42%
(02:42)
wrong
based on 186
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are positive integers, is \(ab + b^a + 1\) odd?
(1) \((a+b)\) is odd.
(2) (\(a+1)^b + (b+2)^{(a+1)}\) is even.
(1) \((a+b)\) is odd.
(2) (\(a+1)^b + (b+2)^{(a+1)}\) is even.
22 Sep 2021, 02:44
Kudos
Bookmarks
Bunuel
\(ab + b^a + 1\)
Case I: If b is even, then \(ab + b^a + 1=E+E+1\) = odd irrespective of the value of a.
(b:E,a:E) and (b:E,a:O) will give answer as ODD.
Case II: If b is odd, then \(ab + b^a + 1=a*O+O+1=a*O+E\) will depend on the value of a. If a is odd, answer is odd, and if a is even, answer is even.
(b:O,a:E) and (b:O,a:O) will give answer as EVEN and ODD respectively.
Let us see the statements.
(1) \((a+b)\) is odd.
This means both are of opposite property.
It can lead to (b:O,a:E), giving result as even and (b:O,a:E), giving result as odd.
Insufficient
(2) \((a+1)^b + (b+2)^{(a+1)}\) is even.
Thus (a+1) and (b+2) are both either odd or even.
This tells us that a and b are opposite in property.
Same as I above.
It can lead to (b:O,a:E), giving result as even and (b:O,a:E), giving result as odd.
Insufficient
Combined
Nothing new.
E
Archit3110
Major Poster
22 Sep 2021, 08:25
Kudos
Bookmarks
target is \(ab + b^a + 1\) odd
#1
\((a+b)\) is odd.
possible when either of a or b is even and other is odd
so we get yes and no to target
#2
(\(a+1)^b + (b+2)^{(a+1)}\) is even.
possible when ( a+1) + ( b+2) are both odd or both are even
i.e. same as #1 either of a or b is even and other is odd
again we get yes and no to target
from 1 &2 nothing can be determined
option E is correct
#1
\((a+b)\) is odd.
possible when either of a or b is even and other is odd
so we get yes and no to target
#2
(\(a+1)^b + (b+2)^{(a+1)}\) is even.
possible when ( a+1) + ( b+2) are both odd or both are even
i.e. same as #1 either of a or b is even and other is odd
again we get yes and no to target
from 1 &2 nothing can be determined
option E is correct
Bunuel
