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Is x > y ? (1) x + y < 0 (2) x + |y| < -1

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Director
Joined: 02 Oct 2017
Posts: 729
Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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01 Jul 2018, 09:13
10
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:42) correct 49% (02:14) wrong based on 162 sessions

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Is x > y ?

(1) x + y < 0

(2) x + |y| < -1

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Joined: 09 Jun 2018
Posts: 190
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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01 Jul 2018, 20:14
2
1
IMO Option B

Here's my take.

Stmt 1: x < -y
If y > 0 then x has to be -ve since x is less than a negative number, then Answer to question stem is No.
If y < 0 then x can be positive or negative and answer to question stem will depend on sign of x, hence answer is Maybe.
Hence insufficient. So cross out A,D.

Stmt 2: If y > 0, then inequality becomes x + y < -1 which gives x < -y -1. Also if y > 0, then y > -1 or 0> -y-1 which gives:
x<-y-1<0. Hence x<0. Now answer to question stem then is NO.

If y< 0, then inequality becomes x - y < -1 which gives x < y - 1. If x < y-1 then x has to be less than y as well. Hence answer to question stem is NO.

As we get definite answers in Case of Stmt 2, it is Sufficient!

Hence Option B.

Anything I'm missing?

Now, I also took quite some time to answer this. Does anyone else have a better approach?
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Intern
Joined: 23 Apr 2018
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Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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29 Sep 2018, 08:36
nkin wrote:
IMO Option B

Here's my take.

Stmt 1: x < -y
If y > 0 then x has to be -ve since x is less than a negative number, then Answer to question stem is No.
If y < 0 then x can be positive or negative and answer to question stem will depend on sign of x, hence answer is Maybe.
Hence insufficient. So cross out A,D.

Stmt 2: If y > 0, then inequality becomes x + y < -1 which gives x < -y -1. Also if y > 0, then y > -1 or 0> -y-1 which gives:
x<-y-1<0. Hence x<0. Now answer to question stem then is NO.

If y< 0, then inequality becomes x - y < -1 which gives x < y - 1. If x < y-1 then x has to be less than y as well. Hence answer to question stem is NO.

As we get definite answers in Case of Stmt 2, it is Sufficient!

Hence Option B.

Anything I'm missing?

Now, I also took quite some time to answer this. Does anyone else have a better approach?

I don't understand statement 1 here, as x will always be smaller than y, I feel, can you clear my doubt with better examples ?

And in Statement 2, I took numbers, they satisfy the statement, to no..

Posted from my mobile device
Intern
Joined: 26 Sep 2018
Posts: 2
Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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01 Oct 2018, 23:57
Statement1: x+y<0
This means only one possibility:
X Y X+Y
a) -ve -ve always -ve, even if x>y, or y>x eg: -2-3 = -5<0 (x>y), -3-2=-5<0 (y>x)

Hence Insufficient

Statement2: x + |y| < -1
Here, |y| > 0, +ve
for x + |y| to be less than -1,
1. x must be negative and it cannot be equal to |y|
and 2. X must be greater than |Y|
Which implies x NE y, x NE 0 and x>y for value of -x to be greater than |y|

-x + (+ve value ) <-1 => -x must be atleast -(y+1)

eg. x = 1, y = 2 never satifies the equation
x = 2, y = 1 holds the statement true
Hence Sufficient.
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Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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07 Oct 2018, 23:45
push12345 wrote:
Is x > y ?

(1) x + y < 0

(2) x + |y| < -1

I am using simple logic of integer substitution:
Statement1: x+y is less than 0.
Possibilities:
A.x=-2 ,y=0 ....x+y=-2+0 =-2 ...which is less than 0
B.Also x=-2 ,y=-4 ....x+y=-2-4=-6...which is less than 0

So insufficient

Statement2: x + |y| < -1
Possibilities:
A.x=-2 ,y=0 ....x + |y|=-2+0 = -2 ...which is less than -1
B.Also x=-2 ,y=-4 ....x + |y|=-2+4=2...which is greater than -1
So sufficient,since when x>y ,the second statement will hold true
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Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1  [#permalink]

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08 Oct 2018, 00:40
Shrey9 wrote:
nkin wrote:
IMO Option B

Here's my take.

Stmt 1: x < -y
If y > 0 then x has to be -ve since x is less than a negative number, then Answer to question stem is No.
If y < 0 then x can be positive or negative and answer to question stem will depend on sign of x, hence answer is Maybe.
Hence insufficient. So cross out A,D.

Stmt 2: If y > 0, then inequality becomes x + y < -1 which gives x < -y -1. Also if y > 0, then y > -1 or 0> -y-1 which gives:
x<-y-1<0. Hence x<0. Now answer to question stem then is NO.

If y< 0, then inequality becomes x - y < -1 which gives x < y - 1. If x < y-1 then x has to be less than y as well. Hence answer to question stem is NO.

As we get definite answers in Case of Stmt 2, it is Sufficient!

Hence Option B.

Anything I'm missing?

Now, I also took quite some time to answer this. Does anyone else have a better approach?

I don't understand statement 1 here, as x will always be smaller than y, I feel, can you clear my doubt with better examples ?

And in Statement 2, I took numbers, they satisfy the statement, to no..

Posted from my mobile device

In statement 1: the sum of x and y is negative, that means, either x or y is a larger negative number or both are negative numbers. therefor you have 3 options,
Either y is the larger negative number, and x is a positive number, and the answer is negative (eg: y= -5, and x= 2, then x+y= -3)
Either x is the larger negative number, and y is a positive number, and the answer is negative (eg. x= -5, and y= 3, then x+y=-2)
Both x and y are negative numbers, and their sum will be negative, but it would not tell us if x is greater than y.
Hence, this statement is not sufficient.

The second statement is x+|y|<-1.... enough to explain that x is infact farther than the absolute distance from 0 to y, and is a larger negative number. Hence sufficient to answer yes or no to the question of x>y
Re: Is x > y ? (1) x + y < 0 (2) x + |y| < -1   [#permalink] 08 Oct 2018, 00:40
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