November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 01 Nov 2013
Posts: 297
WE: General Management (Energy and Utilities)

If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
19 Mar 2015, 21:49
Question Stats:
45% (02:29) correct 55% (02:46) wrong based on 194 sessions
HideShow timer Statistics
If x and y are positive integers, is x^2 + x + y + 1 an even number? 1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50. 2. y^4/16 is an even number.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.
I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.Mohammad Ali



Intern
Joined: 18 Mar 2014
Posts: 6

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
20 Mar 2015, 01:48
1) is in the form of x(x+1) + y +1. No matter what the value of x is, we will still need to know whether y is even or odd to judge whether the whole thing is even or odd. Also x(x+1) is always even 2) No. is divisible by 16, hence it is even. Therefore according to the above rule, the whole expression in odd
Hence option B



Director
Joined: 07 Aug 2011
Posts: 539
Concentration: International Business, Technology

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
04 Apr 2015, 07:22
samichange wrote: If x and y are positive integers, is x^2 + x + y + 1 an even number?
1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50. 2. y^4/16 is an even number.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. X2 will be odd when x is odd , will be even when X is even . 4 possible scenarios for F(XY)=x^2 + x + y + 1 X=Odd , Y= Even , F(XY) = ODD X=Even , Y= Even , F(XY) = ODD X=Odd, Y=Odd, F(XY) = EVEN X=Even, Y=Odd F(XY)=EVEN 1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50. not sufficient as we do not know about Y (it may be odd or even) . 2. y^4/16 is an even number. clearly Y is even , let look at above scenarios. we see that whenever Y is EVEN F(XY) is ODD. so this statement is sufficient. not that hard question IMO.
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
04 Apr 2015, 08:38
samichange wrote: If x and y are positive integers, is x^2 + x + y + 1 an even number?
1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50. 2. y^4/16 is an even number.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. At first we should analyze question: exponents doesn't matter in the tasks about parity, so we have x + x = 2x and this part will be even, so for solving this task we should only know about parity of y 1) in this statement we don't have information about y insufficient2) exponents doesn't matter so we have y / 16 = a so y = 16a and we know that y is even sufficientand answer is B
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 537
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
09 Jun 2016, 14:37
samichange wrote: If x and y are positive integers, is x^2 + x + y + 1 an even number?
1. x is equal to half the sum of the HCF of 12, 26, and 48 and LCM of 25, 35, and 50. 2. y^4/16 is an even number.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. According to question , \(x^2\)+x=even number (no matter what x could be even or odd integer,) So basically the Scope of the answer lies on y (if y is odd,\(x^2\)+x+y+1=even,But if y is even \(x^2\)+x+y+1=odd) Statement 1. didn't say anything about y, InsufficientStatement 2. \(\frac{y^4}{16}\)=even,So y=even number. SufficientCorrect Answer B
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Current Student
Joined: 12 Aug 2015
Posts: 2632

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
21 Nov 2016, 04:43
This is a tremendous Question Testing our even/odd understanding We are asked if x^2+x+y+1 is even here let V=x^2+x+y+1 V=x(x+1)+y+1 V=Even+y+odd V=Odd+y If y is odd => V is even If y is even => V is odd So the Question is asking "IS Y ODD" Statement 1 x is some value Dont stress on this statement as no clue of y is mentioned hence insufficient Statement 2 y^4/16 => even hence y^4 must be even too so y*y*y*y is even => This can happen only if y is even So as y is even => x^2+x+y+1=> odd Hence sufficient Hence B
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Manager
Joined: 21 Jul 2017
Posts: 193
Location: India
Concentration: Social Entrepreneurship, Leadership
GPA: 4
WE: Project Management (Education)

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
19 Sep 2017, 10:04
sandeep4488 wrote: 1) is in the form of x(x+1) + y +1. No matter what the value of x is, we will still need to know whether y is even or odd to judge whether the whole thing is even or odd. Also x(x+1) is always even 2) No. is divisible by 16, hence it is even. Therefore according to the above rule, the whole expression in odd
Hence option B how is the whole expression odd?



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 267

Re: If x and y are positive integers, is x2 + x + y + 1 an even number?
[#permalink]
Show Tags
23 Sep 2017, 20:13
rever08 wrote: sandeep4488 wrote: 1) is in the form of x(x+1) + y +1. No matter what the value of x is, we will still need to know whether y is even or odd to judge whether the whole thing is even or odd. Also x(x+1) is always even 2) No. is divisible by 16, hence it is even. Therefore according to the above rule, the whole expression in odd
Hence option B how is the whole expression odd? hi here you can see, x(x+1) is a product of 2 consecutive numbers, and hence the product will always be an even number. So the odd even nature of the whole expression will rest on the oddeven nature of y only... statement 1 says nothing about y, not sufficient statement 2 says y is even, sufficient because, even + even + odd = odd cheers through the kudos button, if this helps thanks




Re: If x and y are positive integers, is x2 + x + y + 1 an even number? &nbs
[#permalink]
23 Sep 2017, 20:13






