|
|
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.
08 Apr 2021, 13:00
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
30% (02:24) correct
70%
(01:53)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b, and c are all integers, is \(ab + bc + ca + a^2 odd\)?
(1) a is odd.
(2) (b + c) is odd.
(1) a is odd.
(2) (b + c) is odd.
Bunuel
a(b+c+a) + bc
1) a is odd. No info about b and c -> INSUFFICIENT
2) (b+c) is odd. Meaning either b or c is even. So, bc is even
Case 1: a is odd
odd(odd+odd) + even
odd*even + even = even
Case 2: a is even
even(odd+even) + even
even*odd + even = even
Either ways, x is not odd.
Answer B
Posted from my mobile device
08 Apr 2021, 14:14
Kudos
Bookmarks
ab+bc+ca+a^2 is odd?
(1) a is odd.
(2) (b + c) is odd. So:
ab+bc+ca+a^2=(a+b)(a+c)
We now condition for:
Addition / Subtraction:
even +/- even = even;
even +/- odd = odd;
odd +/- odd = even. Also we now rules for:
Multiplication:
even * even = even;
even * odd = even;
odd * odd = odd.
In this case we have combinations:
(a+b)(a+c)
(odd+odd)(odd+even)=even*odd=even
(odd+even)(odd+odd)=odd*even=even
So, ab+bc+ca+a^2 is not odd!
(1) a is odd.
(2) (b + c) is odd. So:
ab+bc+ca+a^2=(a+b)(a+c)
We now condition for:
Addition / Subtraction:
even +/- even = even;
even +/- odd = odd;
odd +/- odd = even. Also we now rules for:
Multiplication:
even * even = even;
even * odd = even;
odd * odd = odd.
In this case we have combinations:
(a+b)(a+c)
(odd+odd)(odd+even)=even*odd=even
(odd+even)(odd+odd)=odd*even=even
So, ab+bc+ca+a^2 is not odd!
