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M16#18

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Senior Manager
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Joined: 29 Sep 2009
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Location: Ann Arbor, MI
Schools: ROSS PT 2012
WE 1: Mech Engineer - General Electric - 2yrs
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M16#18 [#permalink] New post 13 Nov 2010, 10:12
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Is the product 2*x*5*y an even integer?

1. 2 + x + 5 + y is an even integer
2. x - y is an odd integer

(C) 2008 GMAT Club - m16#18

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys:
if x + y = Odd and
x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem.
Extrapolating from the official explanation:
x+y=n ....1
x-y=m.....2
1: x=n-y , subst in 2
2 can be re-written as 2y=(n-m)
LHS is always Even - this implies y is an Integer
Examine RHS : n-m , now difference of 2 Integers is Even when both are odd or both are even. Thus we can conclude the following:
if x+y = Odd and x-y = Odd then both x, and y are integers.
if x+y = Even and x-y = Even then both x, and y are integers.

FYI - O.A. is C
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Re: M16#18 [#permalink] New post 13 Nov 2010, 10:30
Expert's post
vicksikand wrote:
Is the product 2*x*5*y an even integer?

1. 2 + x + 5 + y is an even integer
2. x - y is an odd integer

(C) 2008 GMAT Club - m16#18

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys:
if x + y = Odd and
x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem.

O.A. is C


Question: is 2*x*5*y=even? As there is 2 as a multiple, then this expression will be even if 5xy=integer. Basically we are asked is 5xy=integer true?

Note that x and y may not be integers for 2*x*5*y to be even (example x=\frac{7}{9} and y=\frac{9}{7}) BUT if they are integers then 2*x*5*y is even.

(1) 2+x+5+y=even --> 7+x+y=even --> x+y=odd. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO)

(2) x-y=odd. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO)

(1)+(2) Sum (1) and (2) (x+y)+(x-y)=odd_1+odd_2 --> 2x=even --> x=integer --> y=integer --> Both x and y are integers. Hence sufficient.

Answer: C.

As for your question: if x+y=odd_1 and x-y=odd_2 then x and y must be integers (see proof above).

Hope it helps.

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Senior Manager
Senior Manager
User avatar
Joined: 29 Sep 2009
Posts: 396
Location: Ann Arbor, MI
Schools: ROSS PT 2012
WE 1: Mech Engineer - General Electric - 2yrs
WE 2: Lead Mech Engineer - Ingersoll Rand - 4 yrs
Followers: 2

Kudos [?]: 23 [0], given: 5

GMAT Tests User
Re: M16#18 [#permalink] New post 13 Nov 2010, 10:48
Bunuel
I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true:
if x+y=odd and
x-y=odd
then both x and y are always integers
similarly
if x+y=even and
x-y=even then both x and y are always integers.
This result may come in handy to save time solving some complex number prop problems.
Expert Post
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Joined: 02 Sep 2009
Posts: 18683
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Re: M16#18 [#permalink] New post 13 Nov 2010, 10:54
Expert's post
vicksikand wrote:
Bunuel
I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true:
if x+y=odd and
x-y=odd
then both x and y are always integers
similarly
if x+y=even and
x-y=even then both x and y are always integers.
This result may come in handy to save time solving some complex number prop problems.


I thought I answered this question.

If x+y=odd_1 and x-y=odd_2 then x and y must be integers: add them up (x+y)+(x-y)=odd_1+odd_2 --> 2x=even --> x=integer --> y=integer --> Both x and y are integers.

If x+y=even_1 and x-y=even_2 then x and y must be integers: add them up (x+y)+(x-y)=even_1+even_2 --> 2x=even --> x=integer --> y=integer --> Both x and y are integers.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M16#18   [#permalink] 13 Nov 2010, 10:54
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