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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
The Next Quiz will start on 7:30AM IST 16nd Feb (15th Feb, 9PM EST). The Quiz will be Live for 12 hrs. We will also have a webinar on the Quiz Questions on 10 PM, IST 16 Feb (11:30 AM, EST 16 Feb)
Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.
Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT
If x and y are integers, and N = (x + y)(2x – y)(x + 2y
[#permalink]
Show Tags
12 Apr 2017, 06:42
Top Contributor
5
00:00
A
B
C
D
E
Difficulty:
85% (hard)
Question Stats:
54% (02:46) correct 46% (02:34) wrong based on 198 sessions
HideShow timer Statistics
If x and y are integers, and N = (x + y)(2x – y)(x + 2y + 1), which of the following is true?
A) If N is even, then x must be even B) If N is odd, then x must be odd C) If N is even, then x and y must both be odd D) If N is odd, then y must be odd E) If N is even, then y must be even
Re: If x and y are integers, and N = (x + y)(2x – y)(x + 2y
[#permalink]
Show Tags
12 Apr 2017, 07:03
2
(x+y)*(2x-y)*(x+2y+1)
Result of multiplication is Odd in case all multiplicands are Odd
1) x+y = Odd (x or y should be Even, and y or x should be Odd) 2) 2x-y = Odd (2x Even, then y must be Odd) 3) x+2y-1 = Odd (2y - Even, 1 Odd, then x must be Even)
Re: If x and y are integers, and N = (x + y)(2x – y)(x + 2y
[#permalink]
Show Tags
13 Apr 2017, 09:53
1
Top Contributor
3
GMATPrepNow wrote:
If x and y are integers, and N = (x + y)(2x – y)(x + 2y + 1), which of the following is true?
A) If N is even, then x must be even B) If N is odd, then x must be odd C) If N is even, then x and y must both be odd D) If N is odd, then y must be odd E) If N is even, then y must be even
*kudos for all correct solutions
Given the various answer choices, it might be useful to take a systematic approach and first look at all 4 possible cases.
Case i) x is EVEN and y is EVEN Case ii) x is EVEN and y is ODD Case iii) x is ODD and y is EVEN Case iv) x is ODD and y is ODD
For each case, we can EITHER apply the rules for even and odd numbers (e.g., EVEN + ODD = ODD) OR we can just plug in some easy numbers. I’ll go the plugging in route.
For even numbers, I’ll plug in 0, and for odd numbers I’ll plug in 1. Here’s what we get: Case i) x = 0, y = 0, so N = (0)(0)(1) = 0. Result: N is EVEN Case ii) x = 0, y = 1, so N = (1)(-1)(3) = -3. Result: N is ODD Case iii) x = 1, y = 0, so N = (1)(2)(2) = 4. Result: N is EVEN Case iv) x = 1, y = 1, so N = (2)(1)(4) = 8. Result: N is EVEN
So, we have: Case i) x is EVEN and y is EVEN. N is EVEN Case ii) x is EVEN and y is ODD. N is ODD Case iii) x is ODD and y is EVEN. N is EVEN Case iv) x is ODD and y is ODD. N is EVEN
Now check the answer choices…. A) If N is even, then x must be even. FALSE. Cases iii and iv refute this statement. B) If N is odd, then x must be odd. FALSE. Case ii refutes this statement. C) If N is even, then x and y must both be odd. FALSE. Cases i and iii refute this statement. D) If N is odd, then y must be odd. TRUE. See case ii E) If N is even, then y must be even. FALSE. Case iv refutes this statement.
Re: If x and y are integers, and N = (x + y)(2x – y)(x + 2y
[#permalink]
Show Tags
14 Apr 2017, 01:05
2
GMATPrepNow wrote:
If x and y are integers, and N = (x + y)(2x – y)(x + 2y + 1), which of the following is true?
A) If N is even, then x must be even B) If N is odd, then x must be odd C) If N is even, then x and y must both be odd D) If N is odd, then y must be odd E) If N is even, then y must be even
Let's simplify N first.
2x=Even & 2y+1=Even + ODD=ODD
Hence.... N= (x + y)(E – y)(x + O)
Let see when is either Even or Odd..Here I will borrow Brent's table above
Case i) x is EVEN and y is EVEN.............N= (E+E) (E-E) (E+O)= EVEN
Case ii) x is EVEN and y is ODD..............N = (E+O) (E-O) (E+O)= ODD
Case iii) x is ODD and y is EVEN.............N = (O+E) (E-E) (O+O) = Even
Case iv) x is ODD and y is ODD............. N = (O+O) (E-O) (O+O) = Even
So we have one 3 cases with Even and 1 case with ODD.. So I will focus my effort when N is ODD....Eliminate A, C & E
Re: If x and y are integers, and N = (x + y)(2x – y)(x + 2y
[#permalink]
Show Tags
19 Jan 2019, 02:25
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________