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When 15x is divided by 2y, the quotient is x
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27 Feb 2017, 08:27
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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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Re: When 15x is divided by 2y, the quotient is x
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27 Feb 2017, 08:52
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
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27 Feb 2017, 10:33
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
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27 Feb 2017, 11:23
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
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27 Feb 2017, 14:15
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
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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??



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Re: When 15x is divided by 2y, the quotient is x
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21 Jul 2017, 02:10
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
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21 Jul 2017, 05:13
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
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21 Jul 2017, 05:22
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
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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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Re: When 15x is divided by 2y, the quotient is x
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25 Aug 2018, 23:51
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
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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 Answer: E
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Re: When 15x is divided by 2y, the quotient is x
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18 Nov 2019, 08:49






