If p is an odd prime number, and if 5 is a factor of p + p^2, which of

Question

If p is an odd prime number, and if 5 is a factor of  p + p^2 , which of the following might be the remainder when p is divided by 5?

I. 0
II. 3
III. 4

A. I only
B. II only
C. III only
D. I and III only
E. I, II, III

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chetan2u · Answer

p+p^2=p(p+1) 
p(p+1) is multiple of 5.

Two cases
1) p is multiple of 5, so p will have units digit as 0 or 5. Since p is odd, only possibility is 5.
2) p+1 is multiple of 5, so p+1 will have units digit as 0 or 5, meaning p will have units digit as 9 or 4. Since p is odd, only possibility is 9.

Units digit 0 and 9 will give 0 and 4 as remainder.

D

GMATinsight · Answer

5 is a factor of  p + p^2 
i.e. 5 is a factor of  p(1 + p) 
i.e. either p is a multiple of 5 OR p+1 is a multiple of 5

case 1: p is a multiple of 5
let, p = 5
i.e, when p is divided by 5  remainder is 0

case 2: p+1 is a multiple of 5
let, p+1 = 5
i.e. p = 4
i.e, when p is divided by 5  remainder is 4

Answer: Option D

federica.sgarzani · Answer

P is an odd prime number, how could p be equal to 4?

i think the correct answer is A (i.e. 0). Am I wrong?

ifyouknowyouknow · Answer

We are given that  p  is odd prime number  i.e p can never be 2. . And we write  p + p^2  as  (p)*(p+1) .We are given that  p + p^2  is multiple of 5. Since we know that p is an odd prime number. Value of p+1 will always be even. Only when p=5 satisfy the given conditions. Therefore the remainder will be 0.

In my opinion A is the correct answer.

chetan2u · Answer

Hi
4 is not p but the remainder when p is divided by 5. 
If you divide 19, an odd prime number, by 5, the remainder will be 4.

If p is an odd prime number, and if 5 is a factor of p + p^2, which of

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GMAT Problem Solving (PS) Questions

If p is an odd prime number, and if 5 is a factor of p + p^2, which of

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