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If 5x = y +7, is (x – y) > 0? [#permalink]
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04 Dec 2013, 17:23
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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 D0143
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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, 17:24
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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 nonlinear. 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 (xy) NOT > 0. Thus, statement 2 is sufficient.
Answer: B



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Re: If 5x = y +7, is (x – y) > 0? [#permalink]
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18 Aug 2014, 11:54
I think 5xy7 = 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, 12:13
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sunaimshadmani wrote: I think 5xy7 = 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, 04:51
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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
D0143 The given question can be reduced to 5x=y+7 so \(x=\frac{y+7}{5}\) >\(\frac{y+7}{5}y>0\) \(\frac{74y}{5}\)>0 or \(74y>0\)> 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, 07:09
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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+7y30=0 (y+10)(y3)=0 y=10 or y=3 Therefore x=6/10 or x=2
for x=6/10 and y=10 (xy)>0 ? (6/10+10)>0.... true
for x=2= and y=3 (xy)>0 ? 23>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 (xy)>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, 04:47
How can it be B? Even in B, the two numbers could be x, x+1 or y+1,y
This would give us both positive and negative answers. Please help.
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, 06:05
OreoShake wrote: How can it be B? Even in B, the two numbers could be x, x+1 or y+1,y
This would give us both positive and negative answers. Please help.
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, 14:36
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, 21:19
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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
D0143 Solution. From given condition, we have \(y=5x7\) (1) \(xy=6 \implies x(5x7)=6 \implies 5x^27x6=0 \\ \implies 5x^210x+3x6=0 \implies 5x(x2)+3(x2)=0 \\ \implies (x2)(5x3)=0 \implies x=2 \,\,\, \text{or} \,\,\, x=\frac{3}{5}\) If \(x=2 \implies y=3 \implies xy=1 <0\) If \(x=\frac{3}{5} \implies y=4 \implies xy=\frac{23}{5} >0\) 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 \(xy=1 <0\) If \(y=x1 \implies 5x=(x1)+7 \implies x=\frac{3}{2}\). Eliminate this case because \(x\) must be integer. Hence, in (2), we only have \(xy<0\). Sufficient. The answer is B.
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Re: If 5x = y +7, is (x – y) > 0? [#permalink]
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14 Oct 2017, 15:29
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= X1 into the equation: 5X = (X1) + 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, 01:32
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= X1 into the equation: 5X = (X1) + 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, 08:07
Question stem: 5x  y = 7  (I) Statement 1: Insufficient since xy could be fractions
Statement 2: either xy = 1  (II) or yx = 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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