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

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GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
When 15x is divided by 2y, the quotient is x  [#permalink]

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27 Feb 2017, 08:27
3
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Difficulty:

45% (medium)

Question Stats:

67% (01:50) correct 33% (02:07) wrong based on 308 sessions

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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

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Joined: 13 Oct 2016
Posts: 352
GPA: 3.98
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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27 Feb 2017, 08:52
3
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

##### General Discussion
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Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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27 Feb 2017, 10:33
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

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
Joined: 07 Dec 2014
Posts: 1260
When 15x is divided by 2y, the quotient is x  [#permalink]

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27 Feb 2017, 11:23
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
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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27 Feb 2017, 14:15
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

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Joined: 22 May 2017
Posts: 82
GMAT 1: 580 Q41 V29
GMAT 2: 580 Q43 V27
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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21 Jul 2017, 01:42
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
Joined: 02 Sep 2009
Posts: 65808
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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21 Jul 2017, 02:10
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.
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GMAT 1: 700 Q51 V34
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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21 Jul 2017, 05:13
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
Joined: 02 Sep 2009
Posts: 65808
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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21 Jul 2017, 05:22
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)
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Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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21 Jul 2017, 06:25
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
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Joined: 17 Jun 2017
Posts: 58
Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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25 Aug 2018, 23:51
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)
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Re: When 15x is divided by 2y, the quotient is x  [#permalink]

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18 Nov 2019, 08:49
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 create the equation:

15x/(2y) = x + x/(2y)

15x = 2yx + x

14x = 2yx

Recall that x is a positive integer; thus we can divide each side by x:

14 = 2y

7 = y

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Re: When 15x is divided by 2y, the quotient is x   [#permalink] 18 Nov 2019, 08:49