When a positive integer p is divided by 3, what is the remainder? 1) W

Question

When a positive integer p is divided by 3, what is the remainder?

1) When p^2 is divided by 3, the remainder is 1 
2) When p is divided by 2, the remainder is 1

niks18 · Answer

Statement 1 : if  p^2=25  when divided by 3 leaves 1 as a remainder, but  p=5  when divided by 3 leaves a remainder 2.

Now if  p^2=49  when divided by 3 leaves 1 as remainder, but  p=7  when divided by 3 leaves a remainder 1.

So we get two remainders for different values of  p^2 . Hence  Insufficient

Statement 2 : This implies that  p  is ODD. but Odd number when divided by 3 can leave 1 & 2 as remainders. Hence  Insufficient

Combining 1 & 2. both the statements are not sufficient to lead to the value of p and as is clear from the illustrations there can be two different remainders. Hence insufficient

Option  E

MathRevolution · Answer

=>

Condition 1) & 2)
The remainder of p = 5 is 2, when it is divided by 3.
The remainder of p = 7 is 2, when it is divided by 1.

Ans: E

LeoN88 · Answer

statement 2 is easy.
p = 2K + 1
3 = 2*1 + 1
7 = 2*3 + 1. In both the cases p/3 gives different remainders. Insufficient.

statement 1
p^2 - 1 = 3K = (p+1)(p-1)
When p=2 remainder->0
When p=3 remainder->2. Insufficient
When p=4 remainder-> 1

1+2,
3,4 can substitute p in both the cases and gives us different remainders. so, insufficient.

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When a positive integer p is divided by 3, what is the remainder? 1) W

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