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10 Feb 2017, 09:41
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E
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Difficulty:
45%
(medium)
Question Stats:
64% (01:49) correct
36%
(02:00)
wrong
based on 201
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10 Feb 2017, 10:44
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Bunuel
What is the value of y−x?
(1) 3^y − 3^x is divisible by 10.
(2) y>x
(1) 3^y − 3^x is divisible by 10.
(2) y>x
(1) if y= 4 , x =0 then y-x=4
if y=1 , x=1 then y-x = 0
insuff..
(2) clearly insuff
combining we know y is not equal to x thus
if y= 8 , x= 0 then y-x=8
or
if y= 4 , x =0 then y-x=4
insuff
Ans E
Updated on: 11 Feb 2017, 03:37
Originally posted by Diwakar003 on 11 Feb 2017, 00:57.
Last edited by Diwakar003 on 11 Feb 2017, 03:37, edited 1 time in total.
Last edited by Diwakar003 on 11 Feb 2017, 03:37, edited 1 time in total.
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Bunuel
What is the value of y−x?
(1) 3^y − 3^x is divisible by 10.
(2) y>x
(1) 3^y − 3^x is divisible by 10.
(2) y>x
(1) 3^y − 3^x is divisible by 10
3^y − 3^x = 10k.
3^x(3^(y-x) -1 )=10x.
3^x will not be divisible by 10. So (3^(y-x) -1 ) has to be divisible by 10.
a.One of the cases is x=y, so y-x=o.
b. Other case is when 3^(y-x) has its last digit as 1, so 3^(y-x)-1 will end in 0 thus divisible by 10. For this y-x should be a multiple of 4(Cyclicity of powers of 3). So y-x can be 4,8,12, and so on.
Not sufficient.
(2) y>x - Not sufficient.
(1)+(2) - We can eliminate only case (a) mentioned above as y>x, yet case (b) itself has many values. - Not sufficient.
Answer - E
Cheers!
