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# What is the units digit of 15^x + 22^y , where x and y are natural num

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What is the units digit of 15^x + 22^y , where x and y are natural num  [#permalink]

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05 Jan 2019, 13:31
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What is the units digit of 15^x + 22^y , where x and y are natural numbers ?

(1) x = 6
(2) y = 18
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Re: What is the units digit of 15^x + 22^y , where x and y are natural num  [#permalink]

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05 Jan 2019, 14:04
Vshal wrote:
What is the units digit of 15^x + 22^y , where x and y are natural numbers ?

(1) x = 6
(2) y = 18

for statement 1: the value of x won't affect the result because the cyclic of '5' unit is always 5 --- "insufficient"

for statement 2: the value of y is required to find out the cyclic of '2' --- "Sufficient"
for details:
As y = 18 and the cyclic of '2' is 4 (2,4,8,6,...), the remainder of $$\frac{18}{4}$$ = 2 which shows that the unit digit of $$22^{18}$$ is 4
At the same time, the unit digit of 15^x is always 5 irrelevant of the value of x as long as x is a positive integer.
so the unit digit of $$15^x$$ + $$22^y$$ = 5 + 4 = 9

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Re: What is the units digit of 15^x + 22^y , where x and y are natural num  [#permalink]

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05 Jan 2019, 21:29
Vshal wrote:
What is the units digit of 15^x + 22^y , where x and y are natural numbers ?

(1) x = 6
(2) y = 18

FYI, to my knowledge the GMAT does not use the term natural numbers. The GMAT will instead say "where x and y are positive integers"

(1) x=6 notice that any power of 5 gives us a units digit = 5, so this statement provides no useful info NS

(2) y = 18. The units digit for powers of 2 follows the following pattern: 2,4,8,6,2,4,8,6. Knowing y tells us which position in the sequence to take for the units digit of 22^y. The units digit of 15^x will always be 5 therefore 2 is suff. B
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Re: What is the units digit of 15^x + 22^y , where x and y are natural num  [#permalink]

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05 Jan 2019, 21:51
simple question:
15^x + 22^y
i depends on value of y since the units digit of 5 remains same for any value of x.
Thus from statement 1: value of 22 ^x can me anything
looking at stmt 2 y =18.
18/4 = remainder 2
hence 2264 unit digit will be 4
thus 5+4 = 9

thus B is sufficient
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Re: What is the units digit of 15^x + 22^y , where x and y are natural num   [#permalink] 05 Jan 2019, 21:51
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