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If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]
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12 Jun 2008, 04:45
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If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9
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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]
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12 Jun 2008, 07:49
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mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 Try each answer choices. For A: 1 + 3 + xy = 15; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3) For B: 1 + 5 + xy = 15; xy = 9 (no combination of xy = 9 and x + y = 5) For C: 1 + 6 + xy = 15; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2) For D: 1 + 8 + xy = 15; xy = 6 (no combination of xy = 6 and x + y = 8) For E: 1 + 9 + xy = 15; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9) Therefore, answer C.



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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]
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13 Jun 2008, 01:25
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mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 1 + x + y + xy = 15 1 + x + y (1+ x) = 15 (1 + x) (1+ y) = 3*5 x+y=(31)+(51) =2+4=6 C. 6



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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]
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13 Jun 2008, 03:23
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mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 1+x+y+xy=15 1+x + y(x+1)=15 (1+x)(1+y)=15 (1+x)(1+y)=3*5 this implies x=2 and y = 4 therefore x+y = 2 + 4 = 6 hence C is the answer
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Re: Arithmatic Problem [#permalink]
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12 Sep 2010, 07:58
I think this is how it is calculated;
Factors of 15 are 1,3,5,and 15.
So 1 + x + y +xy = (1+x)(1+y) = 15. Basically find product of two numbers that is equal to 15. This can be factorized as follows
1 + x = 3 and 1 + y = 5 (as product of 3x5 = 15) > x = 2 and y = 4
OR
1 + x = 15 and 1 + y = 1 (as product of 15x1 = 15) > x=14 and y=0
However problem indicates that x,y>0, so value of x = 2 and y = 4.
Value of x+y = 2+4 = 6
Ans C



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Re: Arithmatic Problem [#permalink]
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12 Sep 2010, 09:11
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Re: Arithmatic Problem [#permalink]
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12 Sep 2010, 09:26
I went by answe choices. x+y+xy=14 (given) If x+y = 3 then x=1, y 2 = cannot satisfy 14. If x+y=5, x=4, y=1 cannot satisfy 14. x=2 and y=3 ..ruled out x+y=6 = I got the answer I liked the equation approach as its clean. Although I could solve it in less than a minute
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]
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23 Jul 2015, 23:31
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3 B. 5 C. 6 D. 8 E. 9 Easiest way to solve this question seems substitution because the values can't be too big as the multiplication of those two Positive Integers x and y must be less than 15 as per the given expression 1 + x + y + xy = 15Values of x and y have to be less than 3 and 5 as 3*5=15 Let's try with 2 and 3 1+2+3+2*3 = 12 i.e. One of the numbers must be a little bigger Let's try with 2 and 4 1+2+4+2*4 = 15 BINGO!!!i.e. x+y = 2+4 = 6 Answer: option C
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]
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08 Nov 2017, 17:41
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3 B. 5 C. 6 D. 8 E. 9 Note that the expression y + xy can be factored as y(1 + x). Let’s simplify the given equation: 1 + x + y(1 + x) = 15 (1 + x) + y(1 + x) = 15 The two terms on the left side of the equation have (1 + x) in common, so we can factor it out: (1 + x)(1 + y) = 15 Since x and y are positive integers, so are (1 + x) and (1 + y). We should investigate the different ways of writing 15 as a product of positive integers. Note that 15 can be expressed as a product of positive integers in two ways: 1 x 15 (scenario one) or 3 x 5 (scenario two). For scenario one, we have either 1 + x = 1 and 1 + y = 15 OR 1 + x = 15 and 1 + y = 1. Note that in either case, one of x or y equals 0; since x and y are given as positive, this scenario is ruled out. For scenario two, we have either 1 + x = 3 and 1 + y = 5, which means x = 2 and y = 4 OR 1 + x = 5 and 1 + y = 3, meaning x = 4 and y = 2. In either case, x + y = 6. Answer: C
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]
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24 Dec 2017, 15:53
Can someone show me the details of this step?
1+x + y(x+1)=15
(1+x)(1+y)=15



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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]
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24 Dec 2017, 17:55
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Quote: Can someone show me the details of this step?
1+x + y(x+1)=15
(1+x)(1+y)=15 xlgoh1992 , sure. 1) 1+x + y(x + 1) = 15 Factor out (1 + x) from the first two terms (because 1 + x is identical to x + 1 by which y is multiplied) 2) 1 (1 + x) + y(x+1) Notice that if you multiplied 1(1 + x) you would be back to: 1 + x 3) Note that (1 + x) has already been factored out in this term: y(x + 1)1 (1 + x) + y (x + 1)4) Combine what factoring out (1 + x) left: 1 and + y (1 + x) (1 + y) = 15 Hope that helps.
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
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