If P, Q, R are integers greater 1, have P and R common factors other

Question

If P, Q, R are integers greater 1, have P and R common factors other than 1?

(1) P and Q have common factors other than 1
(2) Q and R have common factors other than 1

gmatophobia · Answer

The statements are individually not sufficient as each of the statements considers only one variable, either P or R.

Combined

Let's take two cases

Case 1 :

P = 7
 
 Q = 2 * 7
 
 R = 2

In this case, P and R do not share any common factor other than 1. Hence the answer to the question "P and R common factors other than 1" -- No

Case 2 :

P = 7 * 2
 
 Q = 2 * 7
 
 R = 2

In this case, P and R do not share a common factor 2. Hence the answer to the question "P and R common factors other than 1" -- Yes

The statements combined are insufficient.

Option E

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