What is the units digit of the non-negative integer y?

Question

Tough and Tricky questions: Number Properties.

(1) y is a multiple of 8.
(2) The units’ digit of y^2 is the same as the units’ digit of y^3.

Kudos for a correct  solution .

Source: Chili Hot GMAT

Ankur9 · Answer

Since y is a non-negative integer therefore y>=0
(1) y is a multiple of 8.
as per the cyclicity of 8 , unit digit of y can be 8 , 6 ,4 , 2 , 0
not sufficient
(2) The units’ digit of y^2 is the same as the units’ digit of y^3.
y can take 0 , 5 or 6 only
5^2 = 25
5^3 = 125
6^2 = 36
6^3 = 216
0^2 = 0^3
thus not sufficient
combining (1) and (2) also does not give any solution for y thus (E)

intheend14 · Answer

Statement 1 says that y is an even number: 0, 8, 16... Insufficient.
Statement 2 says that y must end in 0, 1, 5, 6... Insufficient.

Combining, the answer could be 0 or 6 as 1 and 5 are odd and won't be multiples of 8. Insufficient to combine
E

taleesh · Answer

E - as y can have unit digit 0 ,1 and 6 i m not considering 5 bz if unit digit would be 5 it cannot be divisible by 8 but 0,1 and 6 are the number which give same unit digit on any power- as it has two ans its E

vietnammba · Answer

Its E.

Each Statement alone is cleary insufficient.
Combine two statements still insuff because the unit digit can be 0 or 6.

kinghyts · Answer

1. y is a multiple of 8. 
Here is the unit digits of a possible multiple of 8

{8, 6, 4 , 0 } . Clearly insufficient

2. The units’ digit of y^2 is the same as the units’ digit of y^3.
Clearly insufficient

Combining 1 and 2,

we can say the number could an multiple of 8 having the unit digits of either 0 or 6. Hence insufficient

E) should be the answer

amitshri15 · Answer

Answer is E.

Statement 1: Unit digit can be 2,4,6,8,0: Insufficient
Statement 2: Unit digit can be 0,5,6 : Insufficient
Statement 1&2: Unit digit can be 0,6 : Insufficient

harshaiit · Answer

y is a multiple of 8 - patter - 0, 8, 6, 4, 2, 0, etc.....NOT sufficient
y^2 & y^3 have same units digits - y = 0, 5, 6......Not sufficient

1+2 - common 0 & 6 - Now...it may seem dual answers here. But it is stated that y > 0 and it doesn't say if y has 1 digit or 2 or 3....Y>0 is the only condition.

If we assume y is single digit number...then 0 doesn't fit. 6 is the answer.
If we assume y is double digit number....then 0 & 6 fit the answer.
If we assume y is triple digit number....again 0 & 6 fit the answer.

I think I'll go with E?
OA?

82vkgmat · Answer

Another vote for E!
1) Not sufficient data.
2) This narrows down to the units digit of y to 5, 6 or 0 since only that means y^2 and y^3 have same units digit. So not sufficient.

Combining the two, the units digit may still be 6 or 0 (16 and 40 both satisfy both conditions). So cannot determine unit digit of y.
Answer = E.

Bunuel · Answer

The correct answer is E.

AlexGenkins1234 · Answer

(1) Statment 1 
- y=8a (a is a non negative int).
- case 1: y=24
- case 2 y=32
-> not suff.

(2) statment 2
- case 1: 5^2=25 and 5^3=125
- case 2: 10^2=100 and 10^3=1000
-> not suff.

(1)+(2) | Stm. 1 + Stm 2
- notice the followings for y=8*a
a=0 y=0= 0*2^3 
a=1 y=8= 1*2^3
a=2 y=16= 2*2^3
a=3 y=24= 3*2^3
a=4 y=32= 4*2^3
a=5 y=40= 5*2^3
a=6 y=48= 6*2^3
a=7 y=56= 7*2^3
a=8 y=64= 8*2^3
a=9 y=72= 9*2^3
a=10 y=80= 10*2^3
- so from the pattern of: a*2^3, it is cleaer we can have many cases.
- for example, look at the values of y for a=0,5,10...
- since their last digit is 0, it is clear that statment 2 hold, and we have endless values for y that holds true for 1+2.
-> not suff.

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.

What is the units digit of the non-negative integer y?

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