When the positive integer d is divided by 12, the remainder is 5. What

Question

When the positive integer d is divided by 12, the remainder is 5. What is the remainder when d^2 is divided by 8 ?

A. 1
B. 3
C. 5
D. 6
E. 7

CareerGeek · Answer

When the positive integer d is divided by 12, the remainder is 5
--> d = 12k + 5, for any non-negative integer k
-->  d^2 = (12k + 5)^2  
-->  d^2 = 144k^2 + 120k + 25  
-->  d^2 = 8(18k^2 + 15k + 3) + 1 
-->  d^2 = 8m + 1 , for any positive integer m

--> Remainder = 1

IMO Option A

Mohammadmo · Answer

d=12a+5
d²=144a²+120a+25
=(144a²+120a +24)+1=8n+1
Option A

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Archit3110 · Answer

least integer value of d = 5
so d^2 = 25 remainder 1 when divided by 8
IMO A

J2S2019 · Answer

Remainder is 1.

d=12K+5
d^2=144K^2+120K+25

144K^2+120K is divisible by 8, hence 25/8, remainder is 1

Abhishek009 · Answer

Least possible value of d = 5

d^2 = 25

25/8 = Remainder 1 , Answer must be (A) 1

VINO2493 · Answer

To solve this question , let us remember this property when trying to find a remainder :

When a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller
integer.

Therefore,when the quotient is 0 , smaller integer is divided by larger integer the remainder is the smaller integer.

In our case ,

d = 12(Q) + 5

5 = 12(0) + 5

So d = 5.

d^2 = 25.

d^2 / 8 = 25/8 = 1.

Remainder is 1.

Thanks. This is my first post. Hope it is useful and easy to understand.

CrackverbalGMAT · Answer

When the positive integer d is divided by 12, let the quotient be an integer k and the remainder be 5. Using the division algorithm, we can write the following equation:

d = 12k + 5.

Therefore,  d^2  =  (12k + 5)^2  . Simplifying, we have   d^2  = 144 k^2  + 120k + 25.

When this expression is divided by 8, the first and the second terms are fully divisible and hence yield a remainder of 0. The remainder when 25 is divided by 8 is 1.
Therefore, final remainder when  d^2  is divided by 8 = 0 + 0 + 1 = 1.

The correct answer option is A.

Hope that helps!
Aravind BT

bumpbot · Answer

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When the positive integer d is divided by 12, the remainder is 5. What

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When the positive integer d is divided by 12, the remainder is 5. What

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