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705-805 (Hard)|   Exponents|   Remainders|      
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chetan2u
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What is the remainder when x^2y is divided by 10? 28 Jul 2018, 00:34
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What is the remainder when \(x^{2y}\) is divided by 10?

(1) x=9
(2) y=2

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chetan2u
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What is the remainder when x^2y is divided by 10? 28 Jul 2018, 01:02
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axmanX
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

Answer: A
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you missed out y as fraction..

\(x^2y\) divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified
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What is the remainder when x^2y is divided by 10? 28 Jul 2018, 00:57
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(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

We can see a pattern forming here, for all positive values of y, even powers of 9 will leave a remainder = 1, when divided by 10.
So, statement 1 is SUFFICIENT

(Statement 2) y=2
knowing just y without x is not sufficient for us to even find out the unit digit of the resulting value, statement 2 is thus INSUFFICIENT.


Answer: A
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What is the remainder when x^2y is divided by 10? 28 Jul 2018, 16:00
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chetan2u
axmanX
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

Answer: A

you missed out y as fraction..

\(x^2y\) divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified
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Makes sense. Thanks for correcting me!
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What is the remainder when x^2y is divided by 10? 31 Jul 2018, 06:55
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Statement 1:

The Pattern is:
When the exponent is odd the unit digit is 9, when it is even the unit digit is 1. As we don't know whether Y is an integer or even whether if Y > 0, then inssuficient.

Statement 2:
We need to know the value of X. Not Sufficient.

1) & 2) As we know now that Y is an integer greater than zero the remainder will be 1. Sufficient.

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What is the remainder when x^2y is divided by 10? 13 Jun 2020, 21:57
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chetan2u
What is the remainder when \(x^{2y}\) is divided by 10?

(1) x=9
(2) y=2

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Since odd power raised to 9 gives you 9 as unit digit while even power gives you 1 as unit digit.
here if y=1/2 as nothing is mentioned about y
9^1/10
Remainder is 9
while
9^2/10
Remainder is 1
Y alone does not decide here the unit digit of x^(2y)
Combining both the given conditions we can say that
X^2Y is 9^4
even power- 1 as unit digit
Remainder is 1
C:)
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What is the remainder when x^2y is divided by 10? 03 Feb 2023, 10:05
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