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

 It is currently 17 Jun 2019, 21:57

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

If x, y, and z are integers, what is the remainder when xyz is divided

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55631
If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

18 Apr 2016, 01:17
00:00

Difficulty:

45% (medium)

Question Stats:

53% (01:04) correct 47% (01:39) wrong based on 233 sessions

HideShow timer Statistics

If x, y, and z are integers, what is the remainder when xyz is divided by 2?

(1) 6xy is even.
(2) 9zx is even.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7752
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

18 Apr 2016, 03:34
Bunuel wrote:
If x, y, and z are integers, what is the remainder when xyz is divided by 2?

(1) 6xy is even.
(2) 9zx is even.

We have to find if xyz is EVEN or ODD..
firstly XYZ must be x*y*z and not three digit number otherwise it would have been specified

(1) 6xy is even.
It is possible that xy is also even ans will be 0..
Nothing is known of z and xy could also be ODD, that is 6xy may be EVEN because of 6.. ans can be 1
Insuff

(2) 9zx is even.
xz is clearly EVEN here..
xyz will be EVEN and remainder will be 0..
Suff

B
_________________
Manager
Joined: 17 Nov 2014
Posts: 51
Location: India
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

19 Apr 2016, 00:21
We have to find if atleast one of the numbers is even or not
Statement 1: 6xy is even.
X and Y may or may not be even
For example x=1, Y= 1 6xy = even even when X,Y are odd,
Suppose X=2, Y= 5 still 6xy is even
So X,Y may or may not be even NS

Statement 2:
9XZ = even, it means at least one og X or Z is even.
So, xyz will be divisible by 2

Option B

Posted from my mobile device
Intern
Joined: 15 Mar 2017
Posts: 38
Location: India
GMAT 1: 720 Q50 V37
GPA: 4
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

17 Aug 2017, 07:44
Very simple trick for above question

Statement 1: 6xy can be even because of 6 or xy.
Not sufficient

Statement 2: 9xz is even because of either x or z
Hence remainder always 0
Sufficient
_________________
You give kudos, you get kudos. :D
Intern
Joined: 21 Sep 2018
Posts: 3
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

10 Jan 2019, 07:08
i am trying to get my head around this question, please correct me where I go wrong:

a) 6xy=EVEN, regardless what xy is, if we have 6 (EVEN), result would always be EVEN, so R=0. Example: 6*2*2=24, 6*3*3=54, 6*2*3=36
I can't understand why A is not sufficient (

b) 9zx=EVEN, so for it to be EVEN we need at least one even number, and then it would divide by 2 with R=0. Sufficient

Explanation above indicated that we don't have information about z, so A is insufficient, but do we have to now what Z is, no matter what, because we have 6, it would result in EVEN and would divide by 2 with R0

Intern
Joined: 16 Jun 2018
Posts: 15
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

08 Apr 2019, 23:32
nuraisma wrote:
i am trying to get my head around this question, please correct me where I go wrong:

a) 6xy=EVEN, regardless what xy is, if we have 6 (EVEN), result would always be EVEN, so R=0. Example: 6*2*2=24, 6*3*3=54, 6*2*3=36
I can't understand why A is not sufficient (

b) 9zx=EVEN, so for it to be EVEN we need at least one even number, and then it would divide by 2 with R=0. Sufficient

Explanation above indicated that we don't have information about z, so A is insufficient, but do we have to now what Z is, no matter what, because we have 6, it would result in EVEN and would divide by 2 with R0

Same Issue here as well
Intern
Joined: 30 Mar 2018
Posts: 27
Location: India
Concentration: Marketing, Nonprofit
GMAT 1: 650 Q44 V35
WE: Research (Non-Profit and Government)
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

09 Apr 2019, 01:36
louhit wrote:
nuraisma wrote:
i am trying to get my head around this question, please correct me where I go wrong:

a) 6xy=EVEN, regardless what xy is, if we have 6 (EVEN), result would always be EVEN, so R=0. Example: 6*2*2=24, 6*3*3=54, 6*2*3=36
I can't understand why A is not sufficient (

b) 9zx=EVEN, so for it to be EVEN we need at least one even number, and then it would divide by 2 with R=0. Sufficient

Explanation above indicated that we don't have information about z, so A is insufficient, but do we have to now what Z is, no matter what, because we have 6, it would result in EVEN and would divide by 2 with R0

Same Issue here as well

6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.
Intern
Joined: 16 Jun 2018
Posts: 15
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

09 Apr 2019, 01:53
swatato wrote:
louhit wrote:
nuraisma wrote:
i am trying to get my head around this question, please correct me where I go wrong:

a) 6xy=EVEN, regardless what xy is, if we have 6 (EVEN), result would always be EVEN, so R=0. Example: 6*2*2=24, 6*3*3=54, 6*2*3=36
I can't understand why A is not sufficient (

b) 9zx=EVEN, so for it to be EVEN we need at least one even number, and then it would divide by 2 with R=0. Sufficient

Explanation above indicated that we don't have information about z, so A is insufficient, but do we have to now what Z is, no matter what, because we have 6, it would result in EVEN and would divide by 2 with R0

Same Issue here as well

6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.

Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

Posted from my mobile device
Intern
Joined: 30 Mar 2018
Posts: 27
Location: India
Concentration: Marketing, Nonprofit
GMAT 1: 650 Q44 V35
WE: Research (Non-Profit and Government)
If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

09 Apr 2019, 02:08
Quote:
Quote:
6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.

Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

Posted from my mobile device

Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.
Intern
Joined: 16 Jun 2018
Posts: 15
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

09 Apr 2019, 02:11
swatato wrote:
Quote:
Quote:
6xy is even, meaning 6 times xy is even. But we don't know if xy is even on its own. It could 3*1 = 3, which is odd. Now if Z were odd, we would have a range of possibilities for remainders when xyz/2. Hence it is insufficient.

Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

Posted from my mobile device

Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.

Isint z = 6 from statement 1? Which means xyz is even ?
Intern
Joined: 30 Mar 2018
Posts: 27
Location: India
Concentration: Marketing, Nonprofit
GMAT 1: 650 Q44 V35
WE: Research (Non-Profit and Government)
Re: If x, y, and z are integers, what is the remainder when xyz is divided  [#permalink]

Show Tags

09 Apr 2019, 02:14
louhit wrote:
swatato wrote:
Quote:

Thanks for the reply. I totally get your explanation but what i am struggling to understand that if 6 is multiplied by x and y, the result will always be even. Why do we need to determine x and y nature. Because as per your example 6 multiplied by 3 and 1 will give 18 which is still give remainder 0. Sorry if i am making this tough but need bit of clarity if i am able to understand the question/solution right or not. Thanks

Posted from my mobile device

Because the question is asking you for the remainder when xyz is divided by 2. Not 'what is the remainder when 6xy divided by 2'

If xy are odd and by some chance z is odd too, then you will have a range of remainders, not one, single answer, which is what the question is asking you for.

Unless you know clearly what x, y and z are in terms of even/odd, you will not be able to answer the main question: What is the remainder when xyz is divided by 2.

Isint z = 6 from statement 1? Which means xyz is even ?

Nope. z is not 6. It doesn't say that anywhere in the statement. For DS questions statements must be interpreted as they are presented.
Re: If x, y, and z are integers, what is the remainder when xyz is divided   [#permalink] 09 Apr 2019, 02:14
Display posts from previous: Sort by