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

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BrentGMATPrepNow
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When 15x is divided by 2y, the quotient is x [#permalink] New post   27 Feb 2017, 09:27
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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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vitaliyGMAT
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   27 Feb 2017, 09:52
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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

Answer E
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   27 Feb 2017, 11:33
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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

Answer E
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When 15x is divided by 2y, the quotient is x [#permalink] New post   27 Feb 2017, 12:23
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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
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   27 Feb 2017, 15:15
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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

Answer: E
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   21 Jul 2017, 02:42
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??
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   21 Jul 2017, 03:10
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Adityagmatclub 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.
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   21 Jul 2017, 06:13
Bunuel wrote:
Adityagmatclub 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?
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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   21 Jul 2017, 06:22
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pulkitaggi wrote:
Bunuel wrote:
Adityagmatclub 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] New post   21 Jul 2017, 07:25
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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Re: When 15x is divided by 2y, the quotient is x [#permalink] New post   26 Aug 2018, 00:51
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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] New post   18 Nov 2019, 09:49
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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

Answer: E
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