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04 Sep 2022, 09:48
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If |y| > |x|, is x – y < 0?
(1) |x| + |y| > |x - y|
(2) x + y < 0
(1) |x| + |y| > |x - y|
(2) x + y < 0
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04 Sep 2022, 18:17
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If |y| > |x|, is x – y < 0?
This tells us that the numerical value of y is greater than that of x.
Thus, if y>0, then y>x and if y<0, then y<x.
We require to know whether y is positive or negative.
(1) |x| + |y| > |x - y|
Square two sides
\(|x|^2+|y|^2+2|x||y|>x^2+y^2-2xy…..2|x||y|>-2xy……..|x||y|>-xy\)
So surely xy is positive, that is both x and y have same sign.
y could be positive or negative.
Insufficient
(2) x + y < 0
\(|y|>|x|……|y|^2>|x|^2……y^2-x^2>0……(y-x)(y+x)>0\)
Since x+y<0, we can say y-x<0.
Answer is NO for ‘Is x-y<0?’
Sufficient
B
This tells us that the numerical value of y is greater than that of x.
Thus, if y>0, then y>x and if y<0, then y<x.
We require to know whether y is positive or negative.
(1) |x| + |y| > |x - y|
Square two sides
\(|x|^2+|y|^2+2|x||y|>x^2+y^2-2xy…..2|x||y|>-2xy……..|x||y|>-xy\)
So surely xy is positive, that is both x and y have same sign.
y could be positive or negative.
Insufficient
(2) x + y < 0
\(|y|>|x|……|y|^2>|x|^2……y^2-x^2>0……(y-x)(y+x)>0\)
Since x+y<0, we can say y-x<0.
Answer is NO for ‘Is x-y<0?’
Sufficient
B
General Discussion
04 Sep 2022, 22:42
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I am big fan of number line 
, hence will use number line to solve this question.
Given
The distance of y from zero is greater than the distance of x from 0.
Alright ! So we can either have both x and y on the same side of zero (i.e. both x and y can either be positive or both can be negative), or have x and y on opposite side of 0 (i.e. either x is positive and y is negative or vice versa).
Let's plot the above observations on a number line (shown below) -
Screenshot 2022-09-05 105510.jpg [ 67.42 KiB | Viewed 3489 times ]
Now, the questions ask us if x - y < 0.
So, from the cases above, x - y < 0 for Case 1(A) or for Case 2(B). Therefore our goal is to find out if Case 1(A) or Case 2(B) can be uniquely obtained from the given statements.
Having done some pre-analysis, let's delve into the statements -
Statement 1
|x| + |y| > |x-y|
This expression translates to
The sum of the distance between 0 and x and 0 and y is greater than the distance between x and y.
When we look at the plotted cases, we see that both sub cases of case 1 satisfies the given statement.
So is the statement sufficient to answer the question x-y < 0 ? No !
Hence we can eliminate A and D
Screenshot 2022-09-05 110412.jpg [ 77.34 KiB | Viewed 3359 times ]
Statement 2
x + y < 0
The sum of x and y is less than 0.
We can see the cases that satisfy our condition are Case 1(B) and Case 2(A) and in both of these cases we see that x-y is not less than 0.
As we have a definite answer, the statement is sufficient.
Screenshot 2022-09-05 111043.jpg [ 75.83 KiB | Viewed 3290 times ]
Answer B
, hence will use number line to solve this question.Given
The distance of y from zero is greater than the distance of x from 0.
Alright ! So we can either have both x and y on the same side of zero (i.e. both x and y can either be positive or both can be negative), or have x and y on opposite side of 0 (i.e. either x is positive and y is negative or vice versa).
Let's plot the above observations on a number line (shown below) -
Attachment:
Screenshot 2022-09-05 105510.jpg [ 67.42 KiB | Viewed 3489 times ]
Now, the questions ask us if x - y < 0.
So, from the cases above, x - y < 0 for Case 1(A) or for Case 2(B). Therefore our goal is to find out if Case 1(A) or Case 2(B) can be uniquely obtained from the given statements.
Having done some pre-analysis, let's delve into the statements -
Statement 1
|x| + |y| > |x-y|
This expression translates to
The sum of the distance between 0 and x and 0 and y is greater than the distance between x and y.
When we look at the plotted cases, we see that both sub cases of case 1 satisfies the given statement.
So is the statement sufficient to answer the question x-y < 0 ? No !
Hence we can eliminate A and D
Attachment:
Screenshot 2022-09-05 110412.jpg [ 77.34 KiB | Viewed 3359 times ]
Statement 2
x + y < 0
The sum of x and y is less than 0.
We can see the cases that satisfy our condition are Case 1(B) and Case 2(A) and in both of these cases we see that x-y is not less than 0.
As we have a definite answer, the statement is sufficient.
Attachment:
Screenshot 2022-09-05 111043.jpg [ 75.83 KiB | Viewed 3290 times ]
Answer B
