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Units Digit!

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by Neo Anderson » Sun Apr 15, 2012 4:22 am
Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A)3
B)6
C)7
D)9
E)CAN'T BE DETERMINED

OA after some discussion

I stand corrected! its P^3 and P^2
Last edited by Neo Anderson on Sun Apr 15, 2012 5:24 am, edited 1 time in total.
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by Abhishek009 » Sun Apr 15, 2012 5:00 am
Neo Anderson wrote:Given that p is a positive even integer with a positive units digit, if the units digit of p3 minus the units digit of p2 is equal to 0, what is the units digit of p + 3?

A)3
B)6
C)7
D)9
E)CAN'T BE DETERMINED

OA after some discussion
If P3 and P2 means P^3 and P^2 then we can reach a conclusion quickly...


Even +ve units digit can be -

2 , 4 , 6 , 8

Now we find that -

P^3 - P^2 = 0 as units digit ..

This means that the units digit of the cube and square of the number must be same.

Which is only possible if the units digit is 6.


Now the unit's digit of P + 3 = 6 + 3 => 9....
Abhishek
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by sam2304 » Sun Apr 15, 2012 5:08 am
Please check if the question is right. What is supposed to be understood by p2 and p3 ? ?
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by Neo Anderson » Sun Apr 15, 2012 5:27 am
Abhishek009 wrote:
Neo Anderson wrote:Given that p is a positive even integer with a positive units digit, if the units digit of p3 minus the units digit of p2 is equal to 0, what is the units digit of p + 3?

A)3
B)6
C)7
D)9
E)CAN'T BE DETERMINED

OA after some discussion
If P3 and P2 means P^3 and P^2 then we can reach a conclusion quickly...


Even +ve units digit can be -

2 , 4 , 6 , 8

Now we find that -

P^3 - P^2 = 0 as units digit ..

This means that the units digit of the cube and square of the number must be same.

Which is only possible if the units digit is 6.


Now the unit's digit of P + 3 = 6 + 3 => 9....
Thanks for such a simple approach! was bogged-down by the OE!!
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by Abhijeet03 » Fri May 04, 2012 7:57 am
p^3 and p^2 unit digit is 0
that implies P is such type of number which has same unit digit as
p*p*p or p*p

that implies case are 5 and 6
for 5^2 and 5^3, unit digit is same

Same case with 6
however option 5 is not there , so the answer is 6
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by tomada » Fri May 04, 2012 8:06 am
What do you mean by "positive units digit"?

Neo Anderson wrote:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A)3
B)6
C)7
D)9
E)CAN'T BE DETERMINED

OA after some discussion

I stand corrected! its P^3 and P^2
I'm really old, but I'll never be too old to become more educated.
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by tomada » Fri May 04, 2012 8:14 am
Be careful. The units digit of 'p' is determined to be '6', but that's not the answer.
We're being asked for the units digit of p + 3. So, if you had selected (B)on a test, you'd be incorrect.

Abhijeet03 wrote:p^3 and p^2 unit digit is 0
that implies P is such type of number which has same unit digit as
p*p*p or p*p

that implies case are 5 and 6
for 5^2 and 5^3, unit digit is same

Same case with 6
however option 5 is not there , so the answer is 6
I'm really old, but I'll never be too old to become more educated.
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