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21 Aug 2023, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:24) correct
40%
(01:39)
wrong
based on 48
sessions
History
Date
Time
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Not Attempted Yet
If m, x and y are non-zero integers, is x + y even?
(1) m^x*m^y = 1
(2) m ≠ 1
(1) m^x*m^y = 1
(2) m ≠ 1
Updated on: 21 Aug 2023, 21:59
Originally posted by AryaSwagat on 21 Aug 2023, 03:37.
Last edited by AryaSwagat on 21 Aug 2023, 21:59, edited 2 times in total.
Last edited by AryaSwagat on 21 Aug 2023, 21:59, edited 2 times in total.
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m,x,y are non-zero integers.
1)m^x*m^y = m^(x+y)= 1
So here if m=1 then for any value of x+y the expression will be 1.
So not sufficient alone.
2) m≠ 1 doesn't give us any clue. Not sufficient alone.
Now combining both the statements
if x+y =0 then for any value of m the expression will be 1.
In another case if m=(-1) and (x+y)=2 then the expression will be 1.
these two cases are the only instances for which the expression m^(x+y) can be 1, in both these cases a+b is even.
So IMO C(Corrected)
1)m^x*m^y = m^(x+y)= 1
So here if m=1 then for any value of x+y the expression will be 1.
So not sufficient alone.
2) m≠ 1 doesn't give us any clue. Not sufficient alone.
Now combining both the statements
if x+y =0 then for any value of m the expression will be 1.
In another case if m=(-1) and (x+y)=2 then the expression will be 1.
these two cases are the only instances for which the expression m^(x+y) can be 1, in both these cases a+b is even.
So IMO C(Corrected)
21 Aug 2023, 12:44
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Bunuel
Statement 1: \( m^x*m^y = 1\)
Simplifying : \( m^{x+y} = 1\)
here if m=1, x+y can be anything, Not sufficient
Statement 2: m ≠ 1
Not Sufficient on its own
Statement 1 + 2 :
if m ≠ 1, then we can simplify \( m^{x+y} = 1\) that it can only result to 1 if power is equal to 0, hence x+y=0, ie. even
Therefore, Answer : C
AryaSwagat
FYI:
Options in the Question for Data Sufficiency
(A) Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
(B) Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are not sufficient.
AryaSwagat, According to your solution, the correct answer is C not D
