What is the units digit of even integer n ?

Question

What is the units digit of even integer n?

(1) n^2 and n^4 have the same units digit.

(2) n^1 and n^3 have the same units digit.

GMATinsight · Answer

Question  : Unit digit of even Integer n = ?

Statement 1 : n^2 and n^4 have the same units digit.

i.e. Unit digit of n may be 0, 1, 5, 6 4 or 9

NOT SUFFICIENT

Statement 2 : n^1 and n^3 have the same units digit.

i.e. Unit digit of n may be 0, 1, 5, 6 4 or 9

NOT SUFFICIENT

Combining the two statements

i.e. Unit digit of n may be 0, 1, 5, 6, 4 or 9

NOT SUFFICIENT

Answer: Option E

LevanKhukhunashvili · Answer

As the stem says "even" integer, exclude all odd integers from your examples
1 stm: n may have 0, 4, 6 units digit
2 stm: n may have 0, 6 units digit
1 and 2 stm: 0 or 6 stays and we cant say for sure which one

mrinalsharma1990 · Answer

While the answer mentioned above is correct, just one minor error in the solution above. The question states that n is an even integer and hence cannot have 1,5 or 9 as the units digit.

globaldesi · Answer

You are told that n
 is an even integer and are asked to find its units digit. Remember for any data sufficiency question - especially one where you may need to plug in a few small numbers to prove a rule - you want to make sure to play devil's advocate and try to anticipate the assumption you're making that might lead you into a trap.

Statement (1) tells you that n2
 and n4
 have the same units digit. To test for possible values for n
's unit digit, you may want to list out the units digit of the first four powers of each of the even units digits. However, consider - are there any digits that, when raised to a power, always give the same units digit?

For 6, 
61
 has a units digit of 6. 
62
 has a units digit of 6... 
As does 63
 and 64
. Since all positive integer powers of 6
 will have a units digit of 6, this could be your answer.

However, is there another value for the units digit of n
 that would satisfy statement (1)? What if the units digit of n
 was 0? Then all powers of n
 would have a units digit of 0
. Since you can therefore have two different possible units digits for n
, you must conclude that statement (1) is insufficient.

Statement (2) states that n1
 and n3
 have the same units digit. You should recognize from your work on statement (1) that this is insufficient since both 6 and 0 will always give you the same value for any power of n
.

Even when taken together the two statements are not sufficient - units digits of 6 and 0 satisfy both statements. And since that means that the statements do not yield a consistent answer, you must conclude that they are not sufficient even when taken together and choose (E).

BARUAH · Answer

What is the units digit of even integer n?

(1) n^2 and n^4 have the same units digit.

(2) n^1 and n^3 have the same units digit.

1st : n may be 0,4,6 as unit digit. so Not sufficient.
2nd : n may be 0, 4,6 as unit digit. so not sufficient.
Combining 1 & 2 > n may be 0,4,6 . Answer E

cabpri28 · Answer

chetan2u , I would like to clarify my reasoning. I looked at the data in s1 and s2. Based on the cyclicity of the even numbers only numbers with units digits of 4,6 or 0 would be ideal. Is picking numbers based on their cyclicity fine here?

chetan2u · Answer

Yes, that would be the perfect way to tackle a question like the one given.

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What is the units digit of even integer n ?

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GMAT Data Sufficiency (DS) Questions

What is the units digit of even integer n ?

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