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Bunuel
If z is an integer, what is the units digit of z^3?

(1) z is a multiple of 5.
(2) \(\sqrt{z}\) is an integer.


Statement 1

Let us take 2 values of z which is a multiple of 5, 5 & 10. Cube of 5 will result in 5 as units digit and cube of 10 will give us a 0 as units digit.
Thus statement 1 is insufficient.

Statement 2

Let us again take 2 values, 25 & 100, which have their respective square roots as 5 & 10. This will again give us the scenario in eg. discussed in previous statement.
Thus statement 2 is also insufficient.


Combining both statements, we have again no unique values as seen in examples for statements 1 & 2.


Hence the answer is E.
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Vardan95
If z is an integer, what is the units' digit of \(z^3\)?

(1) z is a multiple of 5
(2) \(\sqrt{z}\) is an integer

Solution:

Statement 1: Z can either be 25 or 100. Insufficient.

Statement 2: Z can either be 25 or 100. Insufficient.

Combining St1 and St2,
We still have 2 choices, so its E.
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Vardan95
If z is an integer, what is the units' digit of \(z^3\)?

(1) z is a multiple of 5
(2) \(\sqrt{z}\) is an integer

St 1

Z is a multiple of 5- but what is Z? 5..10 or maybe 100? Insufficient

St 2

\(\sqrt{z}\)

This just means Z is a perfect square- obviously in suff

St 1 and St 2

Insuff- we could have 100 which is a perfect square and multiple of 5 or 25 which is a perfect square and multiple of 5

E
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Vardan95
If z is an integer, what is the units' digit of \(z^3\)?

(1) z is a multiple of 5
(2) \(\sqrt{z}\) is an integer


We need to determine the units digit of z^3.

Statement One Alone:

z is a multiple of 5.

Statement one is not enough information. If z = 5, then the units digit of z^3 = 5, and if z = 10, then the units digit of z^3 = 0.

Statement Two Alone:

z√z is an integer.

The information in statement two is not sufficient. For instance, if z = 25, then the units digit of 25^3 = 5; however, if z = 100, then the units digit of 100^3 = 0.

Statements One and Two Together:

Using the statements together, we still do not have enough information. Again, if z = 25, then the units digit of 25^3 = 5; however, if z = 100, then the units digit of 100^3 = 0.

Answer: E
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