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These kinds of questions are discussed in our free video: https://www.gmatprepnow.com/module/gmat- ... ts?id=1031[email protected] wrote: If n = (33)^43 + (43)^33, what is the units digit of n ?
(A) 0
(B) 2
(0 4
(D) 6
(E) 8
To begin, look for a pattern.
33^1 = 33 (units digit is 3)
33^2 = --9 (units digit is 9)
Aside: we need only determine the units digit, so don't worry about the other digits
33^3 = --7 (units digit is 7)
33^4 = --1 (units digit is 1)
33^5 = --3 (units digit is 3)
33^6 = --9 (units digit is 9)
33^7 = --7 (units digit is 7)
33^8 = --1 (units digit is 1)
etc.
As you can see, the pattern repeats every 4 exponents.
So, we say the pattern has a cycle of 4.
Also notice that 33^4 has units digit 1, 33^8 has units digit 1, 33^12 has units digit 1, etc.
So, 33^40 will have units digit 1. Continuing with the pattern...
33^41 has units digit 3
33^42 has units digit 9
33^43 has units digit 7
We can apply the same technique to see that 43^33 has units digit 3
So, (33)^43 + (43)^33 will have units digit 0, since 7 + 3 = 10 [spoiler](units digit 0)[/spoiler]
Answer: A
Cheers,
Brent
