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.

_________________

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?

25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership