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20 Apr 2020, 04:12
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E
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Difficulty:
45%
(medium)
Question Stats:
62% (01:56) correct
38%
(01:48)
wrong
based on 152
sessions
History
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Time
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Not Attempted Yet
Is \(m > n\) ?
(1) \(m^2 + n^2 > 2mn\)
(2) \(|m|n = m|n|\)
Are You Up For the Challenge: 700 Level Questions
(1) \(m^2 + n^2 > 2mn\)
(2) \(|m|n = m|n|\)
Are You Up For the Challenge: 700 Level Questions
20 Apr 2020, 04:41
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We are to determine whether \(m>n?\)
Statement 1: \(m^2+n^2>2mn\)
Statement 1 basically says \((m-n)^2>0\) or \(|m-n|>0\)
\(m-n>0\) or \(m-n<0\) both satisfy statement 1 above. Hence insufficient.
Statement 2: |m|n=|n|m
Statement 2 basically says that m=-n or m=n When m=n, the answer is No. When m=-n, the answer is Yes and No. For example, let m=-1 hence n=1 The answer is No. However when m=1 and n=-1, then the answer is Yes.
Statement 2 is insufficient.
1+2
(m-n)<0 or m-n>0 implies that m≠n
But m=-n and when we will still end up with Yes and No. For example when n=1 and m=-1 m-n=-2<0 The answer is No. However when n=-1 and m=1 then m-n=2>0 and the answer is Yes.
Hence both statements even when combined are not sufficient.
E is the answer.
Statement 1: \(m^2+n^2>2mn\)
Statement 1 basically says \((m-n)^2>0\) or \(|m-n|>0\)
\(m-n>0\) or \(m-n<0\) both satisfy statement 1 above. Hence insufficient.
Statement 2: |m|n=|n|m
Statement 2 basically says that m=-n or m=n When m=n, the answer is No. When m=-n, the answer is Yes and No. For example, let m=-1 hence n=1 The answer is No. However when m=1 and n=-1, then the answer is Yes.
Statement 2 is insufficient.
1+2
(m-n)<0 or m-n>0 implies that m≠n
But m=-n and when we will still end up with Yes and No. For example when n=1 and m=-1 m-n=-2<0 The answer is No. However when n=-1 and m=1 then m-n=2>0 and the answer is Yes.
Hence both statements even when combined are not sufficient.
E is the answer.
20 Apr 2020, 04:53
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Statement 1 -
\(m^2 + n^2 > 2mn\)
\((m-n)^2 >0\) or \(|m-n|>0\)
Only thing we can infer is m and n are not equal. But we can't compare m and n
Insufficient
Statement 2-
\(|m|n = m|n|\)
We get mn≥0. We can't compare m or n
Combining both equations won't give us anything new to compare m and n.
Insufficient
OR
Statement 1
Case 1- m=4; n= 2; (m-n)^2=4>0
m>n (yes)
Case 2- m=2; n= 4; (m-n)^2=4>0
m<n (no)
Insufficient
Statement 2-
Case 1- m=4; n= 2; \(|m|n = m|n|\) = 8
m>n (yes)
Case 2- m=2; n= 4; \(|m|n = m|n|\)=8
m<n (no)
Insufficient
Same 2 cases shows both statements are insufficient.
E
\(m^2 + n^2 > 2mn\)
\((m-n)^2 >0\) or \(|m-n|>0\)
Only thing we can infer is m and n are not equal. But we can't compare m and n
Insufficient
Statement 2-
\(|m|n = m|n|\)
We get mn≥0. We can't compare m or n
Combining both equations won't give us anything new to compare m and n.
Insufficient
OR
Statement 1
Case 1- m=4; n= 2; (m-n)^2=4>0
m>n (yes)
Case 2- m=2; n= 4; (m-n)^2=4>0
m<n (no)
Insufficient
Statement 2-
Case 1- m=4; n= 2; \(|m|n = m|n|\) = 8
m>n (yes)
Case 2- m=2; n= 4; \(|m|n = m|n|\)=8
m<n (no)
Insufficient
Same 2 cases shows both statements are insufficient.
E
Bunuel
