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02 Apr 2018, 04:54
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D
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Difficulty:
95%
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Question Stats:
40% (02:14) correct
60%
(01:51)
wrong
based on 87
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What is the remainder when y^2 is divided by 6?
(1) y is a prime number greater than 10.
(2) y is a positive odd number which is NOT divisible by 3.
(1) y is a prime number greater than 10.
(2) y is a positive odd number which is NOT divisible by 3.
Updated on: 02 Apr 2018, 17:53
Originally posted by GMATBusters on 02 Apr 2018, 06:28.
Last edited by GMATBusters on 02 Apr 2018, 17:53, edited 1 time in total.
Last edited by GMATBusters on 02 Apr 2018, 17:53, edited 1 time in total.
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Statement 1 : y is a prime number greater than 10.
Any prime no greater than 3 can be represented by 6n+1 or 6n-1
Now \(y ^2 = (6n+1)^2 or (6n-1)^2\)
\(y^2 = (36n^2+12n+1) or (36n^2-12n+1)\)
Hence remainder when y ^2 divisible by 6 = 1
Sufficient.
Statement 2: y is a positive odd number which is NOT divisible by 3.
y can be 7 : y ^2 = 49. remainder when divided by 6 =1
y can be 11: y^2 = 121, remainder when divided by 6 = 1
It will always be 1.
sufficient.
Answer D
Any prime no greater than 3 can be represented by 6n+1 or 6n-1
Now \(y ^2 = (6n+1)^2 or (6n-1)^2\)
\(y^2 = (36n^2+12n+1) or (36n^2-12n+1)\)
Hence remainder when y ^2 divisible by 6 = 1
Sufficient.
Statement 2: y is a positive odd number which is NOT divisible by 3.
y can be 7 : y ^2 = 49. remainder when divided by 6 =1
y can be 11: y^2 = 121, remainder when divided by 6 = 1
It will always be 1.
sufficient.
Answer D
Updated on: 02 Apr 2018, 20:06
Originally posted by kunalcvrce on 02 Apr 2018, 08:44.
Last edited by kunalcvrce on 02 Apr 2018, 20:06, edited 1 time in total.
Last edited by kunalcvrce on 02 Apr 2018, 20:06, edited 1 time in total.
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amanvermagmat
Statement 1 : y is a prime number greater than 10.
Any prime no greater than 3 can be represented by 6n+1 or 6n-1
By remainder theorem the remainder of y ^2 will product of individual remainders.
for 6n+1 =rem(1) when divided by 6 so ,actual remainder for y ^2 =1*1=1
6n-1 = rem(-1) when divided by 6 so ,actual remainder for y ^2=-1*-1=1
Hence remainder when y ^2 divisible by 6 = 1
Sufficient.
Statement 2: y is a positive odd number which is NOT divisible by 3.
y can be 7 : remainder when divided by 6 =1
y can be 11: when divided by 6 = 1
sufficient.
Answer D
