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

 It is currently 15 Oct 2019, 15:09 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.  When 15x is divided by 2y, the quotient is x

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

Hide Tags

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4002
When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

3
Top Contributor
7 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:52) correct 29% (02:11) wrong based on 303 sessions

HideShow timer Statistics

When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

_________________
Senior Manager  B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
2
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

Hi

We have:

15x = 2y*x + x

14x = 2x*y

y = 7

Intern  S
Joined: 11 Aug 2016
Posts: 46
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38 GPA: 3.95
WE: Design (Manufacturing)
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

When A is divided by B and the quotient is Q and the remainder is R, then
A=B*Q+R ... equation 1

For our case,
A=15x, B=2y , Q=x and R=x

Putting all the values in equation 1, we get
15x=2y*x+x
=>14x=2xy
=> y=7 which is less than 8

VP  P
Joined: 07 Dec 2014
Posts: 1222
When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

15x=2xy+x
y=7
testing possible values of x,
x=any positive integer≥1
thus, A,B,C and D are false,
and only y<8 is true
E
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4002
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
Top Contributor
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

------NOW ONTO THE QUESTION------------------------------

When 15x is divided by 2y, the quotient is x, and the remainder is x.
Applying the above rule, we can write: 15x = (2x)(y) + x
Subtract x from both sides to get: 14x = 2xy
Divide both sides by 2x to get: y = 7

_________________
Manager  B
Joined: 22 May 2017
Posts: 84
GMAT 1: 580 Q41 V29 GMAT 2: 580 Q43 V27 Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??

If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, $$15 = 2xy + x = x(2y + 1)$$

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.
_________________
Manager  B
Joined: 02 Mar 2017
Posts: 71
GMAT 1: 700 Q51 V34 Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

Bunuel wrote:
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??

If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, $$15 = 2xy + x = x(2y + 1)$$

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.

(5,1) also. Right?
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
pulkitaggi wrote:
Bunuel wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

Just for curiousity, if we change the question and replaces 15X with only 15 what will the Answer??

If it were: when 15 is divided by 2y, the quotient is x, and the remainder is x.

Then, $$15 = 2xy + x = x(2y + 1)$$

In this case, (x, y) can be (1, 7) or (3, 2) only. So, both A and E will be correct.

(5,1) also. Right?

No, x = 5 and y = 1 does not work. Though these numbers fit the formula they do not satisfy the conditions given in the stem: 15 divided by 2y = 2 gives the quotient 7 and the remainder of 1, not 5 and 5. The point is that the remainder (x= 5 in this case) cannot be more than the divisor (2y = 2 in this case)
_________________
Manager  G
Joined: 18 Jan 2017
Posts: 127
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

We know that --> Dividend = Quotient * Divisor + Remainder

we have, 15x = (2x) * y + x
14x = 2x * y
y = 14x/2x
y = 7

y < 8
Therefore, E
_________________
A KUDO = A Thank-you. If this post helped you, please send a KUDO across.

YOU CAN LEARN ANYTHING!
MY GMAT BLOG ---> https://gmatclub.com/forum/a-fitness-mat-some-music-few-books-and-the-gmat-245808.html
Manager  B
Joined: 17 Jun 2017
Posts: 60
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

Show Tags

1
GMATPrepNow wrote:
When 15x is divided by 2y, the quotient is x, and the remainder is x. If x and y are positive integers, which of the following must be true?

A) x is odd
B) x < y
C) 3y < 20x
D) x < 3
E) y < 8

*kudos for all correct solutions

We can use this formula to get this one , otherwise taking numbers will take too long ,as I tried taking numbers for this one .
Dividend = Divisor * Quotient + Remainder
Then , it comes
15x = 27*x + x
7 = Y
From options E Y < 8 (Y less than 8) Re: When 15x is divided by 2y, the quotient is x   [#permalink] 26 Aug 2018, 00:51
Display posts from previous: Sort by

When 15x is divided by 2y, the quotient is x

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

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