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

 It is currently 19 Jan 2019, 02:22

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# Are x and y integers?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Are x and y integers?  [#permalink]

### Show Tags

03 Jan 2016, 12:52
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

38% (01:28) correct 63% (01:12) wrong based on 84 sessions

### HideShow timer Statistics

Are x and y integers?

(1) The product xy is an integer.
(2) x + y is an integer.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7202
Re: Are x and y integers?  [#permalink]

### Show Tags

03 Jan 2016, 18:55
4
4
BrainLab wrote:
Bunuel wrote:
Are x and y integers?

(1) The product xy is an integer.
(2) x + y is an integer.

(1) 2*2 YES, 2*1/2 NO
(2) 2+2 YES, 0.5 + 0.5 NO
(1)+(2) hmm... for statement 1 to be an integer we need either 2 integers or reciprocals, but I don't think that there are reciprocals that total an integer, that's why only integer pair satisfies both expressions. Please correct me if I'm wrong...

Hi,
in these type of Q one should know that there are various complex numbers which can fit in..
say $$x=2+\sqrt{3}$$ and $$y=2-\sqrt{3}$$
so xy=(2+\sqrt{3})*(2-\sqrt{3})=1..
and x+y= 2+\sqrt{3}+2-\sqrt{3}=4..

here the reason is we can take these two as roots of an equation, then
the eq becomes..
z^2+(x+y)z+xy... this will always give you the roots x and y as int ,frac or complex number, even if the product and sum of roots are integer..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

##### General Discussion
Director
Joined: 10 Mar 2013
Posts: 503
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: Are x and y integers?  [#permalink]

### Show Tags

03 Jan 2016, 16:03
Bunuel wrote:
Are x and y integers?

(1) The product xy is an integer.
(2) x + y is an integer.

(1) 2*2 YES, 2*1/2 NO
(2) 2+2 YES, 0.5 + 0.5 NO
(1)+(2) hmm... for statement 1 to be an integer we need either 2 integers or reciprocals, but I don't think that there are reciprocals that total an integer, that's why only integer pair satisfies both expressions. Please correct me if I'm wrong...
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Joined: 18 Jul 2012
Posts: 5
Location: United States
GMAT 1: 470 Q41 V27
GPA: 3.87
WE: Consulting (Consulting)
Re: Are x and y integers?  [#permalink]

### Show Tags

03 Jan 2016, 18:10
I tried the following

For statement 1, x = 2 and y = 1/2, x*y = 2*1/2 = 1 (an integer) No
x= 2 and y = 1, x*y = 2*1 = 2(also an integer) Yes

For statement 2, x = 2.5,y=1.5, x+y = 2.5+1.5 (an integer) No
x= 2, y = 1, x+y = 2+1 = 3( an integer) Yes

Combining 1+2, we might arrive at an answer E, how ever consider the possibility that x = 0 and y = 0 , both are integers
and this would satisfy both the conditions and so the answer is C according to me.
Math Expert
Joined: 02 Aug 2009
Posts: 7202
Re: Are x and y integers?  [#permalink]

### Show Tags

03 Jan 2016, 18:57
Pragnya87 wrote:
I tried the following

For statement 1, x = 2 and y = 1/2, x*y = 2*1/2 = 1 (an integer) No
x= 2 and y = 1, x*y = 2*1 = 2(also an integer) Yes

For statement 2, x = 2.5,y=1.5, x+y = 2.5+1.5 (an integer) No
x= 2, y = 1, x+y = 2+1 = 3( an integer) Yes

Combining 1+2, we might arrive at an answer E, how ever consider the possibility that x = 0 and y = 0 , both are integers
and this would satisfy both the conditions and so the answer is C according to me.

Hi,
you can always find values of x and y as an integers satisfying the given conditions..
BUT we have to be sure that there are no values fittin as non integer, ecause the Q is a 'must ' Q..
hope it helped
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Non-Human User
Joined: 09 Sep 2013
Posts: 9436
Re: Are x and y integers?  [#permalink]

### Show Tags

09 Jun 2018, 11:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Are x and y integers? &nbs [#permalink] 09 Jun 2018, 11:17
Display posts from previous: Sort by