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# If 5x = y +7, is (x – y) > 0?

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Manager
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If 5x = y +7, is (x – y) > 0? [#permalink]

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04 Dec 2013, 16:23
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If 5x = y +7, is (x – y) > 0?

(1) xy = 6
(2) x and y are consecutive integers with the same sign

D01-43
[Reveal] Spoiler: OA

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Manager
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Re: If 5x = y +7, is (x – y) > 0? 1) xy = 6 2) x and y are conse [#permalink]

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04 Dec 2013, 16:24
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This is my version of explanation, please correct my concept if there is any. Many Thanks in advance.

If 5x = y +7, is (x – y) > 0?
1) xy = 6
2) x and y are consecutive integers with the same sign

Statement 1:
Because the given statement xy = 6, and 5x = y + 7; we know that there will be 2 answer since xy = 6 is non-linear.
Therefore, statement 1 is not sufficient.

Statement 2:
Since x and y are consecutive integers of the same sign, we can assign them x = x, y = x+1.
Therefore by plugging into the equation: we get -1<0, which means that (x-y) NOT > 0.
Thus, statement 2 is sufficient.

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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18 Aug 2014, 10:54
I think 5x-y-7 = 0. xy=6, so it may be any of the following: 2*3=6, -2*-3=6, 1*6=6, -1*-6=6, but Here only 2 and 3 will make it the equation 0. Statement 2 is definitely sufficient. Answer is D. Correct me if I am wrong. Thanks.

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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18 Aug 2014, 11:13
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I think 5x-y-7 = 0. xy=6, so it may be any of the following: 2*3=6, -2*-3=6, 1*6=6, -1*-6=6, but Here only 2 and 3 will make it the equation 0. Statement 2 is definitely sufficient. Answer is D. Correct me if I am wrong. Thanks.

Yes, you are wrong.

We are not told that x and y are integers, so there exist other solutions. For example, y=-10 and x=-3/5.
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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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19 Aug 2014, 03:51
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smartyman wrote:
If 5x = y +7, is (x – y) > 0?

(1) xy = 6
(2) x and y are consecutive integers with the same sign

D01-43

The given question can be reduced to

5x=y+7 so $$x=\frac{y+7}{5}$$ ----->$$\frac{y+7}{5}-y>0$$

$$\frac{7-4y}{5}$$>0 or $$7-4y>0$$-----> Is y<1.75 ??

St 1 says xy=6...we have multiple case x=2,y=3 (Ans to question is Y) but if y=1,x=6 then Ans to Q. is no

St 2 says x,y are consecutive integers. Let x=y+1 so we have
5y+5=y+7 or 4y=2 or y=1/2 and x=3/2------> But x and y are fractions here so this case is not possible

Consider y=x+1 so we have 5x=x+1+7 or 5x=x+8 or 4x=8 x=2, y=3...Answer to the question is Y.

Ans is B
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If 5x = y +7, is (x – y) > 0? [#permalink]

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19 Aug 2014, 06:09
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5x=y+7... given

statement 1:
xy=6
x=6/y
substitute above value in given

5*6/y=y+7
30=y^2+7y
y^2+7y-30=0
(y+10)(y-3)=0
y=-10 or y=3
Therefore
x=-6/10 or x=2

for x=-6/10 and y=-10
(x-y)>0 ?
(-6/10+10)>0.... true

for x=2= and y=3
(x-y)>0 ?
2-3>0... false

statement insufficient

statement 2:
x and y are consecutive integers with the same sign
There are two possibilities
x>y or y>x
If x>y, then x=y+1
substitute in given
5(y+1)=y+7
4y=2
y=1/2.. not an integer... possibility discarded

Therefore, y>x
y=x+1
substitute in given
5x=x+8
x=2
y=3
we can answer definitely (x-y)>0 ?

statement sufficient

Ans - B

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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24 Feb 2017, 03:47
How can it be B? Even in B, the two numbers could be x, x+1 or y+1,y

Posted from my mobile device

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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25 Feb 2017, 05:05
OreoShake wrote:
How can it be B? Even in B, the two numbers could be x, x+1 or y+1,y

Posted from my mobile device

Hmm i guess in B, the only way to have two integers is by taking y = x+1. Hence is B is sufficient.

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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10 May 2017, 13:36
On gmat, when we are told that x and y are consecutive integers, does it always mean that they are ordered exactly as given (x, y=x+1)? I don't know why I am confused about this

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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10 May 2017, 20:19
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smartyman wrote:
If 5x = y +7, is (x – y) > 0?

(1) xy = 6
(2) x and y are consecutive integers with the same sign

D01-43

Solution.

From given condition, we have $$y=5x-7$$

(1) $$xy=6 \implies x(5x-7)=6 \implies 5x^2-7x-6=0 \\ \implies 5x^2-10x+3x-6=0 \implies 5x(x-2)+3(x-2)=0 \\ \implies (x-2)(5x-3)=0 \implies x=2 \,\,\, \text{or} \,\,\, x=\frac{3}{5}$$

If $$x=2 \implies y=3 \implies x-y=-1 <0$$
If $$x=\frac{3}{5} \implies y=-4 \implies x-y=\frac{23}{5} >0$$

Hence insufficient.

(2) $$x$$ and $$y$$ are consecutive integers.

If $$y=x+1 \implies 5x=(x+1)+7 \implies x=2 \implies y=3$$.
In this case, we have $$x-y=-1 <0$$

If $$y=x-1 \implies 5x=(x-1)+7 \implies x=\frac{3}{2}$$. Eliminate this case because $$x$$ must be integer.

Hence, in (2), we only have $$x-y<0$$. Sufficient.

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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14 Oct 2017, 14:29
kivalo wrote:
On gmat, when we are told that x and y are consecutive integers, does it always mean that they are ordered exactly as given (x, y=x+1)? I don't know why I am confused about this

No one seems to have discussed this yet. I am unsure whether when the GMAT says X and Y are consecutive integers that always means X = X and Y = X + 1

BUT

In this problem,

You can plug Consecutive integers X, X+1 into the given equation.

5X = Y + 7
X = X and Y = X+1
-----------------------
5x = y +7
5X = (X+1) + 7
5X = X + 8
4X = 8
X = 2, X+1 = 3

Now if you plug X=X and Y= X-1 into the equation:

5X = (X-1) + 7
4X = 6
X = 6/4

Note this is not an integer, so this solution does not work. Thus only X, X+1 should be considered.

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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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15 Oct 2017, 00:32
subsauce wrote:
kivalo wrote:
On gmat, when we are told that x and y are consecutive integers, does it always mean that they are ordered exactly as given (x, y=x+1)? I don't know why I am confused about this

No one seems to have discussed this yet. I am unsure whether when the GMAT says X and Y are consecutive integers that always means X = X and Y = X + 1

BUT

In this problem,

You can plug Consecutive integers X, X+1 into the given equation.

5X = Y + 7
X = X and Y = X+1
-----------------------
5x = y +7
5X = (X+1) + 7
5X = X + 8
4X = 8
X = 2, X+1 = 3

Now if you plug X=X and Y= X-1 into the equation:

5X = (X-1) + 7
4X = 6
X = 6/4

Note this is not an integer, so this solution does not work. Thus only X, X+1 should be considered.

x and y are consecutive integers does not necessarily mean that y = x + 1, it could be that x = y + 1. But yes you are right 5x = y +7 and x = y + 1 does not give integer solution for x and y, so this case is not possible while 5x = y +7 and x = y - 1 give x = 2 and y = 3. So, the answer is B.
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Re: If 5x = y +7, is (x – y) > 0? [#permalink]

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15 Oct 2017, 07:07
Question stem: 5x - y = 7 - (I)
Statement 1: Insufficient since xy could be fractions

Statement 2: either x-y = 1 - (II) or y-x = 1 - (III) (note that the signs of x and y do not matter) and we are told that x and y are integers. Now subtracting II from I we get x = 6/4 which is not possible since x is an integer. Adding I with II we get x as 2 and y as 3. Hence statement 2 is sufficient.

Ans - B

Does this make sense?

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Re: If 5x = y +7, is (x – y) > 0?   [#permalink] 15 Oct 2017, 07:07
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