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

 It is currently 16 Oct 2019, 00:09 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  M08-26

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58364

Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 85% (00:46) correct 15% (01:59) wrong based on 102 sessions

HideShow timer Statistics

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58364

Show Tags

1
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

_________________
Intern  Joined: 13 Feb 2014
Posts: 7
Location: India
Concentration: Leadership, General Management
Schools: HBS '18, ISB '16, IIMA
GMAT Date: 12-14-2014
GPA: 3.5
WE: Engineering (Consumer Electronics)

Show Tags

this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.
Math Expert V
Joined: 02 Sep 2009
Posts: 58364

Show Tags

ramarao443 wrote:
this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.

xy always means x multiplied by y, if it's not stated otherwise. If it were two digit number xy, then it would be explicitly mentioned.
_________________
Retired Moderator G
Joined: 26 Nov 2012
Posts: 575

Show Tags

Bunuel wrote:
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.
Math Expert V
Joined: 02 Sep 2009
Posts: 58364

Show Tags

msk0657 wrote:
Bunuel wrote:
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.

We are given that $$x$$ and $$y$$ are positive integer and $$xy$$ (the product of x and y) is divisible by 4.

(B) says that if $$x$$ is odd then $$y$$ is a multiple of 4. Now, if x is odd, then for xy to be divisible by 4, y must be a multiple of 4. So, option B must be true.
_________________
Intern  B
Joined: 16 Dec 2016
Posts: 4

Show Tags

if x =1 and y=4 then none of the options r true
Math Expert V
Joined: 02 Sep 2009
Posts: 58364

Show Tags

sushanttinku wrote:
if x =1 and y=4 then none of the options r true

B says: If x is odd then y is a multiple of 4.

If x = 1 = odd and y = 4 = multiple of 4 (recall that an integer IS a multiple of itself).
_________________ Re: M08-26   [#permalink] 16 Mar 2018, 00:00
Display posts from previous: Sort by

M08-26

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

Moderators: chetan2u, Bunuel

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