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Updated on: 03 Nov 2019, 19:13
Originally posted by Anasayaydah on 02 Nov 2019, 06:43.
Last edited by chetan2u on 03 Nov 2019, 19:13, edited 1 time in total.
Last edited by chetan2u on 03 Nov 2019, 19:13, edited 1 time in total.
Corrected the OA
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:
75%
(hard)
Question Stats:
49% (01:57) correct
51%
(02:15)
wrong
based on 103
sessions
History
Date
Time
Result
Not Attempted Yet
Is 3x+7y an integer?
(1) (x+y)^3 is an even integer.
(2) (x-y)^3 is an even integer
(1) (x+y)^3 is an even integer.
(2) (x-y)^3 is an even integer
02 Nov 2019, 08:17
Kudos
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Statement 1-
Case 1- x=3 and y=1
\((x+y)^3= 4^3=64\)
3x+7y= 16{integer}
Case 2-
\(x=3*[2]^{1/3}\) and \(y=2*[2]^{1/3}\)
\((x+y)^3= [5*[2]^{1/3}]^3\) =250
\(3x+7y=23*[2]^{1/3}\) { not an integer}
Insufficient
Statement 2-
Case 1- x=3 and y=1
\((x-y)^3= 2^3=8\)
3x+7y= 16{integer}
Case 2-
\(x=3*[2]^{1/3}\) and \(y=2*[2]^{1/3}\)
\((x-y)^3= [[2]^{1/3}]^3\) =2
\(3x+7y=23*[2]^{1/3}\) { not an integer}
Insufficient
Combining both equations
We can take same 2 cases
Insufficient
IMO E
Case 1- x=3 and y=1
\((x+y)^3= 4^3=64\)
3x+7y= 16{integer}
Case 2-
\(x=3*[2]^{1/3}\) and \(y=2*[2]^{1/3}\)
\((x+y)^3= [5*[2]^{1/3}]^3\) =250
\(3x+7y=23*[2]^{1/3}\) { not an integer}
Insufficient
Statement 2-
Case 1- x=3 and y=1
\((x-y)^3= 2^3=8\)
3x+7y= 16{integer}
Case 2-
\(x=3*[2]^{1/3}\) and \(y=2*[2]^{1/3}\)
\((x-y)^3= [[2]^{1/3}]^3\) =2
\(3x+7y=23*[2]^{1/3}\) { not an integer}
Insufficient
Combining both equations
We can take same 2 cases
Insufficient
IMO E
Anasayaydah
02 Nov 2019, 09:19
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Anasayaydah
Case 1
(x+y)^3 is an even integer.
Take x=1.6 and y = 0.4 x+y = 2 but 3x+7y = 3*1.6 +7*0.4= 4.8 + 2.8 = 7.6 False
Take x = 2 and y = 4, x + y = 6 3x+7y = 3*2 + 7*4 = 6+28=34 True
Insufficient
Case 2
(x-y)^3 is an even integer
Take x = 5 and y = 3 , x-y =2 , 3x+7y = 3*5 +7*3 = 36 True
Take x = 2.4 y = 0.4 x-y = 2 but 3x+7y = 3*2.4 +7*0.4 = 10 true
But take x = 2*2^1/3 and y = 22^1/3 x-y = 2^1/3 (x-y)^3 = (2^1/3)^3 = 2 , 3x+7y =3*2*2^1/3 + 7*2^1/3 = -2^1/3 False
Together also they are insufficient
hence E
