Data Sufficiency

Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

B) (x - 4)/(y - 3) = 1 -> x-y=1
your 3 scenarios are incorrect.
y=-0.5 and x=1+y = 0.5
xy = -.25

revised, choice c is correct.

Solving this question from more of a algebraic perspective:

A) x^2 - x < 0 ---> Not enough
B) (x-4) / (y-3) = 1
So x-4 = y-3 --> y = x-1 ----> Not enough

Combining A) and B)

put the value of x-1 as y in A)

x^2 - x < 0 ---> x(x-1) < 0 ---> xy < 0 ---> Enough

So IMO C

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

revised, choice c is correct.

Hi Pemdas,
How did you assum 0 < x <2 , this is only one part of the solution to first equation , How can you ignore the other one.

Regards
Mukesh

pemdas wrote:to be precise with combined statements (1&2)

we know that x is positive as such 0<x<2, hence 0<y+1<2 and -1<y<1

SO we are legitimate in setting xy with the given equation x=y+1 as following

1) y=0.5 and x=1.5, xy is positive
2) y=-0.5 and x=0.5, xy is negative
3) y=0 and x=1, xy is non-negative and non-positive

the answer must be e

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C

Hi neeraj,
if we have x = 0.5 and y = -0.5 then x - y =1 , You didn't considered this scenario in 2). It is not mentioned in the problem that x and y are Integers!!

Hope this helps.

neerajkumar1_1 wrote:

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C

exactly my point mukgera...
i have not assumed x and y are integers..

pls read the question..

for any value of x... y will be negative in the given conditions
and the product of xy will be -ve...

we get a consistent answer...

Hope this helps..

mukgera wrote:Hi neeraj,
if we have x = 0.5 and y = -0.5 then x - y =1 , You didn't considered this scenario in 2). It is not mentioned in the problem that x and y are Integers!!

Hope this helps.

neerajkumar1_1 wrote:

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C

What I had posted earlier is to prove a scenario in which x is +ve and y is -ve and still we are getting x - y =1 and xy < 0 which according to ur post is not possible.

what you considered :

1. x and y --> +ve
2. x and y --> -ve
3. either x or y is 0 and the other is 1 / -1

You said that x - y = 1 only in these three scenario. and xy > 0 in these three cases.
However the fourth scenario in which x - y = 1 is
x = 0.25 and y = -0.75
and in this case xy < 0 which is conflicting to your assumption.

Please let me know in case I am missing something here.

Regards
Mukesh

neerajkumar1_1 wrote:exactly my point mukgera...
i have not assumed x and y are integers..

pls read the question..

for any value of x... y will be negative in the given conditions
and the product of xy will be -ve...

we get a consistent answer...

Hope this helps..

mukgera wrote:Hi neeraj,
if we have x = 0.5 and y = -0.5 then x - y =1 , You didn't considered this scenario in 2). It is not mentioned in the problem that x and y are Integers!!

Hope this helps.

neerajkumar1_1 wrote:

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C

I suppose mukgera u r highly confused...
Please check the solution...

I am replying to a post..

Please read carefully..

mukgera wrote:What I had posted earlier is to prove a scenario in which x is +ve and y is -ve and still we are getting x - y =1 and xy < 0 which according to ur post is not possible.

what you considered :

1. x and y --> +ve
2. x and y --> -ve
3. either x or y is 0 and the other is 1 / -1

You said that x - y = 1 only in these three scenario. and xy > 0 in these three cases.
However the fourth scenario in which x - y = 1 is
x = 0.25 and y = -0.75
and in this case xy < 0 which is conflicting to your assumption.

Please let me know in case I am missing something here.

Regards
Mukesh

neerajkumar1_1 wrote:exactly my point mukgera...
i have not assumed x and y are integers..

pls read the question..

for any value of x... y will be negative in the given conditions
and the product of xy will be -ve...

we get a consistent answer...

Hope this helps..

mukgera wrote:Hi neeraj,
if we have x = 0.5 and y = -0.5 then x - y =1 , You didn't considered this scenario in 2). It is not mentioned in the problem that x and y are Integers!!

Hope this helps.

neerajkumar1_1 wrote:

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C

My bad

neerajkumar1_1 wrote:I suppose mukgera u r highly confused...
Please check the solution...

I am replying to a post..

Please read carefully..

mukgera wrote:What I had posted earlier is to prove a scenario in which x is +ve and y is -ve and still we are getting x - y =1 and xy < 0 which according to ur post is not possible.

what you considered :

1. x and y --> +ve
2. x and y --> -ve
3. either x or y is 0 and the other is 1 / -1

You said that x - y = 1 only in these three scenario. and xy > 0 in these three cases.
However the fourth scenario in which x - y = 1 is
x = 0.25 and y = -0.75
and in this case xy < 0 which is conflicting to your assumption.

Please let me know in case I am missing something here.

Regards
Mukesh

neerajkumar1_1 wrote:exactly my point mukgera...
i have not assumed x and y are integers..

pls read the question..

for any value of x... y will be negative in the given conditions
and the product of xy will be -ve...

we get a consistent answer...

Hope this helps..

mukgera wrote:Hi neeraj,
if we have x = 0.5 and y = -0.5 then x - y =1 , You didn't considered this scenario in 2). It is not mentioned in the problem that x and y are Integers!!

Hope this helps.

neerajkumar1_1 wrote:

vipin85 wrote:Please can someone shed light on the answer for this DS question.

Is the product xy negative?

(1) x^2 - x < 0
(2) (x - 4)/(y- 3) = 1

The Manhattan explanation says the answer is (C). However, I think the answer is (B). Following is my reasoning.

Statement (1): This statement does not tell us anything about 'y'. Hence, cannot be sufficient.

Statement (2): (x - 4)/(y - 3) = 1 works out to x - y = 1.
This can be true only in the following 3 scenarios:
i) x and y are -ve
ii) x and y are +ve
iii)either x or y is 0 and the other is 1 / -1

In each of these scenarios, the product 'xy' will not be -ve. It will be either +ve or zero.
Hence, Statement B is SUFFICIENT to answer that the product of x and y is not negative.

Hi Vipin,
ur assumptions for statement 2 are wrong..
if x-y=1 or x = y +1 ....
x and y can both be positive or negative or so on so forth...

statement 1 is for obvious reasons insufficient..
statement 2 as i explained above is not sufficient..

combine the two statements

statemet 1 says
x^2<x
by simple number properties knowledge... u know this is possible only in region 0<x<1
that means x is +ve and less than 1
statement 2 says
x = y + 1
or y = x -1

now for any value of x between 0 to 1... y will be negative...
hence the product will xy will always be negative...

IMO: C