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07 May 2018, 02:35
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:35) correct
47%
(02:01)
wrong
based on 134
sessions
History
Date
Time
Result
Not Attempted Yet
07 May 2018, 02:49
Kudos
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Bunuel
To answer the question, we need to know if |x| < |y|.
We'll look for an answer that gives us this information, a Logical approach.
(1) Tells us nothing about which of the two is larger.
Insufficient.
(2) Since y - x = 7 then y = x + 7 meaning y > x. However, we do not know if |y| > |x| as both can be negative numbers.
Insufficient.
Combined:
Substituting y = x+7 into the first equation gives us a quadratic equation and without solving it is hard to know if there is one root or two and if both roots gives |y| > |x|. However, if we notice that 169 = 13^2 and recall the Pythagorean triplet (5,12,13) than we know that one solution is y = 12, x = 5 and can guess that the other is x = -12, y = -5. Then we cannot know if |y| > |x|.
Insufficient.
(E) is our answer.
07 May 2018, 03:43
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Bookmarks
Bunuel
OA : E
Is \(x^2 < y^2\) ?
\(x^2-y^2< 0\)
\((x-y)(x+y)< 0\)
Case 1 : \((x-y)< 0 and (x+y)>0\)
Case 2 : \((x-y)> 0 and (x+y)<0\)
Plotting these 2 case , we will get following graph , red area in graph satisfies the condition\(x^2 < y^2\)
Attachment:
question stem.PNG [ 31.35 KiB | Viewed 2541 times ]
Statement 1 : \(x^2 + y^2 = 169\)
Attachment:
statement 1.PNG [ 37.91 KiB | Viewed 2543 times ]
Other points on circumference does not satisfy the condition
So Statement 1 alone is not sufficient to answer Is \(x^2 < y^2\) .
Statement 2 : \(y - x = 7\)
Attachment:
statement 2.PNG [ 34.45 KiB | Viewed 2500 times ]
So Statement 2 alone is not sufficient to answer Is \(x^2 < y^2\) .
Combining 1 and 2,
We get point (-12,-5) and (5,12) , point of intersection of \(x^2 + y^2 = 169\) and \(y - x = 7\)
Attachment:
combining statement 1 and 2.PNG [ 42.47 KiB | Viewed 2491 times ]
So after Combining 1 and 2 also, We are not able to answer Is \(x^2 < y^2\)
