For prime number y, y3. Which of the following could be the remainder

Question

For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?

A. 2
B. 3
C. 4
D. 5
E. 6

vitaliyGMAT · Accepted Answer

Prime number greater than 3 can be expressed as  6k + 1  or  6k -1 .

\frac{(6k ± 1)^3}{12} = \frac{6^3k^3 ± 3*6^2k^2 + 3*6k ± 1}{12} = \frac{0 + 0 + 18k ± 1}{12} = \frac{6k ± 1}{12}

Let’s check first case  6k + 1

k=1 (7/12) rem=7
k=2 (13/12) rem =1
k=3 (19/12) rem = 7
k =4 (25/12) rem = 1

we have cycle of remainders  7  and  1 .

Next  6k – 1

k=1 (5/12) rem=5
k=2 (11/12) rem =11
k=3 (17/12) rem = 5
k =4 (23/12) rem = 11

again cycle of only two remainders  5  and  11 .

The only remainders after division by 12 cube of prime number  y > 3  can have are  1 ,  5 ,  7  and  11 .

Checking our options.

Answer D.

GMATinsight · Answer

Checking with prime numbers greater than 3 @y=5, Rem (y^3 / 12) = Rem (5^3 / 12) = 5 (BINGO) :-D

Answer: Option D

Abhishek009 · Answer

y = { 5 , 7 , 11............ }

Plug in a number and check -

5^3/12 = Remainder 5

Thats in the given option , hit it...

Answer will be (D)

JeffTargetTestPrep · Answer

Let’s test the first prime number greater than 3, which is 5.

5^3 = 125

125/12 = 10 remainder 5

Answer: D

saurabhsavant · Answer

I have a doubt here please....prime numbers graeter than 3 can be expressed as 6k+1..putting k=4 we get 25, which is not a prime num,ber....am I missing something here?

Bunuel · Answer

Any prime number  p>3  when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case  p  would be even and remainder can not be 3 as in this case  p  would be divisible by 3).

So any prime number  p>3  could be expressed as  p=6n+1  or p=6n+5  or  p=6n-1 , where n is an integer >1.

But: 
 Not all number which yield a remainder of 1 or 5 upon division by 6 are prime , so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.

Hope it's clear.

praveenmittal95605 · Answer

prime number 5 , 5^3 /12 = 25*5 /12 => 1*5/12 ( since 25/12 will give rem as 1) => 5 is rem

Option D is answer

swapnils10 · Answer

We can check it by plugging prime numbers greater than 3.

For Ex. Take prime number 5. Y^3 = 125 and divide by 12 then remainder become 5. Hence, Answer is D

Hope it helps !

bumpbot · Answer

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For prime number y, y>3. Which of the following could be the remainder

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