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

Question

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

AdlaT · Answer

Solution:

Statement 1) z is a multiple of 5.

if z=5 , then units digit of z^3 is 5.

if z=10 , then units digit of z^3 is 0.

Hence Insufficient.

Statement 2)  \sqrt{z}  is an integer.

z is an integer then z must be perfect square.

z=4,9,25,or 36... then units digit z^3 is different for different numbers.

Hence Insufficient.

Statement 1) and Statement 2) Together.

z can be 25 or 100 which are perfect squares and are multiples of 5.

units digit of 25^3 and 100^3 is different.

Hence Insufficient.

Ans E.

ashwink · Answer

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.

Bunuel · Answer

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

(1) z is a multiple of 5. The units digit of a multiple of 5 can be 0 or 5, so the units digit of z^3 could be 0 or 5 as well. Not sufficient.

(2)  \sqrt{z}  is an integer --> z = integer^2. Clearly insufficient.

(1)+(2) The units digit of z^3 could still be 0 or 5. For example, consider z = 25 and z = 0. Not sufficient.

Answer: E.

harikrish · Answer

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.

Nunuboy1994 · Answer

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

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards