If 5x = y +7, is (x y) 0?

Question

If 5x = y +7, is (x – y) > 0?

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

D01-43

WoundedTiger · Accepted Answer

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

smartyman · Answer

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.

Answer: B

sunaimshadmani · Answer

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.

Bunuel · Answer

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.

desaichinmay22 · Answer

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

OreoShake · Answer

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

OreoShake · Answer

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

kivalo · Answer

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

broall · Answer

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.

The answer is B.

subsauce · Answer

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.

Bunuel · Answer

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.

tejas0999 · Answer

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?

ncs58 · Answer

Is there a reason that x = -1 y = -2 would not also be a suitable pair for the second statement.

5x = y + 7 would become 5*-1 = -2 + 7 and (x - y) > 0

Using x = 2, y = 3, we get 5*2 = 3 + 7 and (x - y) < 0.

Wouldn't these two pairs make statement 2 insufficient and require both statements for sufficiency? Thanks!

Antreev · Answer

-1 and -2 doesnt satisfy the equation.
5x=y+7
5(-1)= -2+7
-5=5 which is no possible, this we cannot use -1,-2

Posted from my mobile device

blitzkriegxX · Answer

I think  most of us are making the same mistake  in eliminating statement 1. I did the same mistake too.
 You   cannot   test values for y=1 and x=6 and just dismiss statement 1. 
You have to check with the main equation.  5x=y+7  
So if u take y=1 and x=6 then main equation is  5(6) = 1 + 7 . 
The above is NOT possible. You cannot just take any value. It has to satisfy the main equation.

Solution :

Statement 1  :  xy = 6 
 y = 6/x

Substitute above in main equation  - 
 5x=y+7  
 \frac{30}{y} = y + 7 
 30 = y^2 + 7y 
 y^2 + 7y - 30 = 0 
Solving we get y = 3 and y = -10 
You can stop here because we are getting two different values of y so obviously we have different values of x. 
Hence statement 1 is insufficient.

Raxit85 · Answer

Can anyone please explain how the highlighted part derived?
Thanks

PriyamRathor · Answer

Statement 1 is INSUFFICIENT - AGREED

Statement 2 is also INSUFFICIENT.
Give x and y are two consecutive integer.
In that case x can be 2 and y can be 3. whereas x can be -2 and y can be -3.

In case 1 x- y is less than 0(2-3=-1) . whereas in 2nd case x-y is greater than 0 ( -2 +3=1)

Any views ?

Varane · Answer

if x is -2 and y is -3 then x-y is 1
but if x is -3 and y is -2 then x-y is -1

how can B be right?

mrd1761 · Answer

I have the same doubt as you.

If 5x = y +7, is (x y) > 0?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions