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DS - Odd even

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Thu Jun 21, 2012 12:03 am

If x and y are integers and (x^2)y + 5x is odd, which of the following must be even?

(A) x

(B) y

(C) xy + 5

(D) xy - 5

(E) y + 5

Last edited by karthikpandian19 on Thu Jun 21, 2012 5:50 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 21, 2012 12:03 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jun 21, 2012 12:44 am

karthikpandian19 wrote:If x and y are integers and x2y + 5x is odd, which of the following must be even?

I'm assuming the underlined term is xÂ²y

Algebraic Approach:
(xÂ²y + 5x) = x(xy + 5) is odd
Hence, both x and (xy + 5) is odd.

As (xy + 5) is odd, xy must be even.
Now, as x is odd, y must be even

The correct answer is B.

Last edited by Anurag@Gurome on Thu Jun 21, 2012 5:12 am, edited 1 time in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jun 21, 2012 2:23 am

karthikpandian19 wrote:If x and y are integers and x2y + 5x is odd, which of the following must be even?

(A) x

(B) y

(C) xy + 5

(D) xy - 5

(E) y + 5

Try to show that the answers DON'T have to be even.

xÂ²y + 5x = x(xy + 5).
For this product to be odd, factors x and xy+5 must both be odd.
Let x=1 and xy+5 = 7.
Solving the second factor for y, we get:
1*y + 5 = 7
y=2.

Now we plug x=1 and y=2 into the answers and eliminate any answer choice that does not yield an even result.

A: x=1. Eliminate A.
B: y=2. Hold onto B.
C: xy+5 = 1*2 + 5 = 7. Eliminate C.
D: xy-5 = 1*2 - 5 = -3. Eliminate D.
E: y+5 = 2+5 = 7. Eliminate E.

The correct answer is B.

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sams_online: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Sep 04, 2010 11:39 pm

by sams_online » Thu Jun 21, 2012 5:11 am

Anurag@Gurome wrote:
karthikpandian19 wrote:If x and y are integers and x2y + 5x is odd, which of the following must be even?
I'm assuming the underlined term is xÂ²y

Algebraic Approach:
(xÂ²y + 5x) = x(xy + 5) is odd
Hence, both x and (xy + 5) is odd.

As (xy + 5) is odd, xy must be even.
Now, as x is even, y must be even

The correct answer is B.

Correction: as x is odd, y must be even

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jun 21, 2012 5:23 am

samvit wrote:Correction: as x is odd, y must be even

Thanks for pointing the typo.
Edited my reply.

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Thu Jun 21, 2012 5:50 am

OA is B

Regards,
Karthik
The source of the questions that i post from JUNE 2013 is from KNEWTON

---If you find my post useful, click "Thank"

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