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# If x+2/y = 3, is xy an integer?

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If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 00:45
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If $$x+\frac{2}{y}= 3$$,is xy an integer?

(1) x is an integer less than 3
(2) x >-1

Kudos for correct solution.Question made by me.
[Reveal] Spoiler: OA

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Last edited by mau5 on 19 May 2013, 07:50, edited 3 times in total.
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Re: If x+1/y = 3, is xy an integer? [#permalink]

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07 May 2013, 00:55
2
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If $$x+\frac{2}{y}= 3$$,is xy an integer?

I. x is an integer less than 3
x=-1 y=0.5
-1+4=3 xy = -0.5 no integer
x=2 y=2
2+1=3 xy=4 integer
Not sufficient

II. x >-1
Clearly not sufficient. x can be any decimal value >-1

I and II) x is an integer between -1 and 3 ( not included) so x is 0,1 or 2
Case x=0 xy is an integer
Case x=1 so y=1 xy integer
Case x=2 so y=2 xy integer.
Sufficient C
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 02:22
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vinaymimani wrote:
If $$x+\frac{2}{y}= 3$$,is xy an integer?

(1) x is an integer less than 3
(2) x >-1

Kudos for correct solution

The answer is C for me as well......

as you can find out the value of 1 variable x or y if you have the value of one variable on hand. ..& then you can find out whether xy is an integer or not.

stmt 1... is clearly insufficient as it says that x<3.. & from this the value of xy can be non-integer or integer. Therefore, Insufficient
stmt 2... is clearly insufficient as it says that x>-13..& from this as well the value of xy can be non-integer or integer. Therefore, Insufficient.

From 1+2 ...... we have a a definite range I,e.; $$-1<x<3$$. & for all the value of x in this range the solution of xy must be integer as well. Therefore, C is sufficient.
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Last edited by manishuol on 07 May 2013, 02:46, edited 1 time in total.
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 02:30
manishuol wrote:

The answer is C for me as well......

as you can find out the value of 1 variable x or y if you have the value of one variable on hand. ..& then you can find out whether xy is an integer or not.

stmt 1... is clearly insufficient as it says that x<3.. & from this the value of xy can be non-integer or integer. Therefore, Insufficient
stmt 2... is clearly insufficient as it says that x>-13..& from this as well the value of xy can be non-integer or integer. Therefore, Insufficient.

From 1+2 ...... we have a a definite range I,e.; $$-1<x<3$$. & for all the value of x in this range the value of y must be integer as well. & as we know Integer * Integer = Integer. Therefore, C is sufficient.

Statement 1 says that x is an integer, read carefully

From 1+2 it not true that we have int*int. If x=0 then y is not an integer. xy is an integer because x is 0.

Hope this clarifies
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 02:33
manishuol wrote:
vinaymimani wrote:
If $$x+\frac{2}{y}= 3$$,is xy an integer?

From 1+2 ...... we have a a definite range I,e.; $$-1<x<3$$. & for all the value of x in this range the value of y must be integer as well. & as we know Integer * Integer = Integer. Therefore, C is sufficient.

Was about to post the same thing as Zarrolou has already mentioned above.No need now.
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 02:44
Zarrolou wrote:
manishuol wrote:

The answer is C for me as well......

as you can find out the value of 1 variable x or y if you have the value of one variable on hand. ..& then you can find out whether xy is an integer or not.

stmt 1... is clearly insufficient as it says that x<3.. & from this the value of xy can be non-integer or integer. Therefore, Insufficient
stmt 2... is clearly insufficient as it says that x>-13..& from this as well the value of xy can be non-integer or integer. Therefore, Insufficient.

From 1+2 ...... we have a a definite range I,e.; $$-1<x<3$$. & for all the value of x in this range the value of y must be integer as well. & as we know Integer * Integer = Integer. Therefore, C is sufficient.

Statement 1 says that x is an integer, read carefully

From 1+2 it not true that we have int*int. If x=0 then y is not an integer. xy is an integer because x is 0.

Hope this clarifies

Thanks !! but I know this ... & that's how I reached the solution .... oderwise I would have not get the answer .... Anyways thanks for pointing out my typo...... Appreciate that. Thanks !!
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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07 May 2013, 02:46
Zarrolou wrote:
manishuol wrote:

The answer is C for me as well......

as you can find out the value of 1 variable x or y if you have the value of one variable on hand. ..& then you can find out whether xy is an integer or not.

stmt 1... is clearly insufficient as it says that x<3.. & from this the value of xy can be non-integer or integer. Therefore, Insufficient
stmt 2... is clearly insufficient as it says that x>-13..& from this as well the value of xy can be non-integer or integer. Therefore, Insufficient.

From 1+2 ...... we have a a definite range I,e.; $$-1<x<3$$. & for all the value of x in this range the value of y must be integer as well. & as we know Integer * Integer = Integer. Therefore, C is sufficient.

Statement 1 says that x is an integer, read carefully

From 1+2 it not true that we have int*int. If x=0 then y is not an integer. xy is an integer because x is 0.

Hope this clarifies

Thanks !! Typo Edited !!..............
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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11 Mar 2014, 05:42
we can re-write the equation as:
x = 3 - (2/y)

1) x is an integer less than 3: So (2/y)>0. The answer is Yes when y = 2, 1/3 and answer is no when y = 1/4, 1/8. Satisfies both Yes & No. Insufficient.
2) x > -1: (2/y) < 4. Since nothing has been mentioned about x, it can be either integer or non integer. Answer is yes y<(-1/2), y>(1/2) and answer is no for all other values of (-1/2)<y<(1/2) except zero. Insufficient.

combining: Answer is yes when it satisfies both[y = 2, 1/3 & y<(-1/2), y>(1/2) ] Only value satisfying is y = 2 when x = 2. Sufficient.

Tried to attempt somewhat different method. Kindly comment.
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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17 Apr 2014, 08:51
I really understand this, why my method doesn't solve this problem

x + 2/y = 3
so, xy + 2 =3y
so, xy= 3y - 2

We need to know if xy is integer.

(1) x is an integer less than 3
xy = 3y -2
So, this depends upon value of y,
y=0.1, xy= -1.7 ( Not an integer)
y=1, xy=1 (Integer)
Not sufficient
(2) x >-1
xy = 3y -2
So, this depends upon value of y,
y=0.1, xy= -1.7 ( Not an integer)
y=1, xy=1 (Integer)
Not sufficient

(1)+(2) give the same solution. E is my answer.

Please let me know what is wrong with my method.
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Re: If x+2/y = 3, is xy an integer? [#permalink]

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17 Apr 2014, 08:59
Expert's post
umeshpatil wrote:
If $$x+\frac{2}{y}= 3$$,is xy an integer?

(1) x is an integer less than 3
(2) x >-1

I really understand this, why my method doesn't solve this problem

x + 2/y = 3
so, xy + 2 =3y
so, xy= 3y - 2

We need to know if xy is integer.

(1) x is an integer less than 3
xy = 3y -2
So, this depends upon value of y,
y=0.1, xy= -1.7 ( Not an integer)
y=1, xy=1 (Integer)
Not sufficient
(2) x >-1
xy = 3y -2
So, this depends upon value of y,
y=0.1, xy= -1.7 ( Not an integer)
y=1, xy=1 (Integer)
Not sufficient

(1)+(2) give the same solution. E is my answer.

Please let me know what is wrong with my method.

The point is that the first statement says that x is an integer. So, you cannot randomly pick a value for y substitute into xy= 3y - 2 and check. You must ensure that x will be an integer for y you choose.

Also, notice that when we consider both statements together x can only be 0, 1, or 2. For each of those values xy will be an integer.

Hope it's clear.
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Re: If x+2/y = 3, is xy an integer?   [#permalink] 17 Apr 2014, 08:59
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