|
|
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.
28 Aug 2023, 01:30
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:16) correct
24%
(01:15)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are integers and \(N=(a^4)(b^3)+1\). Is N odd?
(1) \(a^4\) is even
(2) \(b^2\) is odd
(1) \(a^4\) is even
(2) \(b^2\) is odd
30 Aug 2023, 04:50
Kudos
Bookmarks
If an and b are integers and \(N=(a^4)(b^3)+1\). Is N odd?
If ab is odd, that is both an and b are odd then N is even.
If any of an and b is even, then N is odd.
(1) \(a^4\) is even
\(N=(a^4)(b^3)+1=even*b+1=even+1=odd\)
Sufficient
(2) \(b^2\) is odd
\(N=(a^4)(b^3)+1=a*odd+1\)
If a is odd, then N is even, but if a is even, then N is odd.
Insufficient
A
If ab is odd, that is both an and b are odd then N is even.
If any of an and b is even, then N is odd.
(1) \(a^4\) is even
\(N=(a^4)(b^3)+1=even*b+1=even+1=odd\)
Sufficient
(2) \(b^2\) is odd
\(N=(a^4)(b^3)+1=a*odd+1\)
If a is odd, then N is even, but if a is even, then N is odd.
Insufficient
A
25 Sep 2023, 02:35
Kudos
Bookmarks
Q: if a and b are integers, and N = \((a^4)(b^3)\) + 1, is N odd?
For N to be odd we need a construction of Even + Odd (since 1 is odd, \((a^4)(b^3)\) needs to be even for N to be odd)
1) \(a^4\) = even
If \(a^4\) is even, it doesn't matter whether \(b^3\) is even or odd, since (even)(odd) or (even)(even) will always be even. When taken this into consideration we get: (even)(odd or even) + odd = even, this directly answers the prompt, so keep this one
2) \(b^2\) = odd
If \(b^2\) is odd, that means that \(b^3\) must be odd as well, since any odd number multiplied by an odd number will remain odd. I'll test some cases where a^4 is odd and even, since in this statement no information for \(a^4\) is given
Case 1: \(b^3\) is odd and \(a^4\) is even: just like in statement 1 (even)(odd) + (odd) = odd
Case 2: \(b^3\) is odd and \(a^4\) is odd: (odd)(odd) + (odd) = even
Since we got 2 different outcomes, we can eliminate this choice
Answer: A
For N to be odd we need a construction of Even + Odd (since 1 is odd, \((a^4)(b^3)\) needs to be even for N to be odd)
1) \(a^4\) = even
If \(a^4\) is even, it doesn't matter whether \(b^3\) is even or odd, since (even)(odd) or (even)(even) will always be even. When taken this into consideration we get: (even)(odd or even) + odd = even, this directly answers the prompt, so keep this one
2) \(b^2\) = odd
If \(b^2\) is odd, that means that \(b^3\) must be odd as well, since any odd number multiplied by an odd number will remain odd. I'll test some cases where a^4 is odd and even, since in this statement no information for \(a^4\) is given
Case 1: \(b^3\) is odd and \(a^4\) is even: just like in statement 1 (even)(odd) + (odd) = odd
Case 2: \(b^3\) is odd and \(a^4\) is odd: (odd)(odd) + (odd) = even
Since we got 2 different outcomes, we can eliminate this choice
Answer: A
