GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 05:48

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

If x and y are integers, is x+y an even number?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are integers, is x+y an even number?  [#permalink]

Show Tags

New post 20 Apr 2018, 01:08
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:22) correct 41% (01:46) wrong based on 81 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x+y\) an even number?

1) \(x+3y\) is even
2) \((x-1)(y-1)\) is odd

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x and y are integers, is x+y an even number?  [#permalink]

Show Tags

New post 20 Apr 2018, 01:42
1
Statement1:

x+3y is even.

Now as MULTIPLICATION BY AN ODD INTEGER DOESN’T CHANGE THE ODD/EVEN NATURE OF AN INTEGER.

Hence x +y is even (same as x+3y or 3x+5y etc)

SUFFICIENT



Statement 2:

(x-1)(y-1) is odd

Since the product of two integers are odd only if both of them are odd,

(x-1) is odd, hence x =odd+1 = even.

Similarly, (y-1) is odd, hence y= odd+1 = even.

Hence, x+y = even+even = even

SUFFICIENT.



Answer D
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4009
Location: Canada
Re: If x and y are integers, is x+y an even number?  [#permalink]

Show Tags

New post 20 Apr 2018, 07:00
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x+y\) an even number?

1) \(x+3y\) is even
2) \((x-1)(y-1)\) is odd


Target question: Is x+y an even integer?

Statement 1: x+3y is even
There are 4 possible cases to consider. Let's test them all
Case a: x is ODD and y is ODD. Notice that x +3y = ODD + (3)(ODD) = ODD + ODD = EVEN. In this case, x + y = ODD + ODD = EVEN. So, the answer to the target question is YES, x+y IS even
Case b: x is ODD and y is EVEN. Notice that x +3y = ODD + (3)(EVEN) = ODD + EVEN= ODD. This does NOT meet the requirement that x+3y is even, so IGNORE case b
Case c: x is EVEN and y is ODD. Notice that x +3y = EVEN + (3)(ODD) = EVEN + ODD= ODD. This does NOT meet the requirement that x+3y is even, so IGNORE case c
Case d: x is EVEN and y is EVEN. Notice that x +3y = EVEN + (3)(EVEN) = EVEN+ EVEN= EVEN. In this case, x + y = EVEN + EVEN = EVEN. So, the answer to the target question is YES, x+y IS even
So, cases a and d are the only to possible cases.
Since both cases yields the SAME answer to the target question (YES, x+y IS even), statement 1 is SUFFICIENT

Statement 2: (x-1)(y-1) is odd
If the product of two integers is ODD, then the two integers must each be ODD
So, (x-1) must be ODD, and (y-1) must be ODD
If (x-1) is ODD, then we can be certain that x is EVEN
If (y-1) is ODD, then we can be certain that y is EVEN
If x and y are both EVEN, then x+y = EVEN + EVEN = EVEN
So, the answer to the target question is YES, x+y IS even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are integers, is x+y an even number?  [#permalink]

Show Tags

New post 22 Apr 2018, 18:27
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since both conditions are satisfied only when x is even and y is even, x + y must be an even number.
Thus, both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
There are two ways in which x + 3y can be even.
If x and y are both even, then x + y is even.
If x and y are both odd, then x + y is even too.
Thus, condition 1) is sufficient.


Condition 2)
Since (x-1)(y-1) is odd, both x -1 and y – 1 must be odd.
So, x and y must both be even.
It follows that x + y is even.
Thus, condition 2) is sufficient too.

Therefore, D is the answer.

Answer: D

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: If x and y are integers, is x+y an even number?   [#permalink] 22 Apr 2018, 18:27
Display posts from previous: Sort by

If x and y are integers, is x+y an even number?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne