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In the two-digit integer RS, R is the tens digit, and S is the units

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In the two-digit integer RS, R is the tens digit, and S is the units  [#permalink]

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New post 03 May 2016, 05:24
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In the two-digit integer RS, R is the tens digit, and S is the units  [#permalink]

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New post 03 May 2016, 20:54
Bunuel wrote:
In the two-digit integer RS, R is the tens digit, and S is the units digit. What is the units digit of S^4?

(1) RS is divisible by 2 but not by 5.
(2) R = 5.


we are looking for units digit of S^4..

It will be important to know the pecularities of 4th power..

1) all ODD numbers except 5 gives 1 as the 4th power
example 3^4 = 81
7^4 = 2401..

2) all EVEN numbers except 0 gives 6 as the 4th power
example 2^4 = 16
4^4 = 256.

3) 4th power of 5 will give 5 as units digit

4) 4th power of 0 will give 0 as units digit


lets see the statements-


(1) RS is divisible by 2 but not by 5.
see the property of all even except 0-- units digit will be 6..
since it is not a multiple of 5, 0 as units digit can be ruled out
ans - 6
Suff

(2) R = 5.
Nothing anout S
Insuff

A
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In the two digit integer RS, R is in the Tens digit,  [#permalink]

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New post 26 Sep 2018, 08:13
In the two digit integer RS, R is in the Tens digit, and S is in the units digit. What is the units digit of S^4?

1. RS is divisible by 2, but not by 5
2. R=5
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Re: In the two digit integer RS, R is in the Tens digit,  [#permalink]

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New post 26 Sep 2018, 08:37
Abhi077 wrote:
In the two digit integer RS, R is in the Tens digit, and S is in the units digit. What is the units digit of S^4?

1. RS is divisible by 2, but not by 5
2. R=5


1. RS is divisible by 2, but not by 5
So S cannot be 0

take RS as 42 => \(2^4\) will give units digit as 6
when RS = 44 => \(4^4\) will give units digit as 6
so will 6 and 8
Sufficient

2. R=5
not sufficient

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Re: In the two digit integer RS, R is in the Tens digit,  [#permalink]

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New post 26 Sep 2018, 08:38
1
We have to decide whether the we can find units digit of S^4 from -
Statement 1- If we take any 2 digit number which is not divisible by 5 and divisible by 2 it will be of the form x2 or x4 or x6 or x8.
In these cases S^4 will be 2^4 or 4^4 or 6^4 or 8^4. Please note that for all these cases we will have units digit as 6.
So statement 1 is sufficient.
From Statement 2 we can have values for units digit of S^4. One is the case we discussed in statement 1 and other will be for numbers of form x0 for which units digit of S^4 will be 0. Since two values are possible this statement is not sufficient.
Hence,A should be the correct choice.
Hope it helps!
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Re: In the two-digit integer RS, R is the tens digit, and S is the units  [#permalink]

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New post 26 Sep 2018, 12:13
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Re: In the two-digit integer RS, R is the tens digit, and S is the units   [#permalink] 26 Sep 2018, 12:13
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