karthikpandian19 wrote:If m and n are positive integers and mn = p + 1, is m + n = p ?
Both m and n are prime numbers.
p + 1 and m are both even.
How to deal with this problem - odd&even method OR algebraic method?
It is given that mn = p + 1.
Thus, if m+n = p, then mn = m+n + 1.
In other words, then the PRODUCT of m and n is one more than the SUM of m and n.
Question rephrased: Is the product of m and n one more than their sum?
Statement 1: m and n are prime.
Statement 2: p+1 (which is equal to the product of m and n) and m are even.
If m=2 and n=3, both statements are satisfied.
Here, the answer is YES: the product (2*3=6) is one more than the sum (2+3=5).
If m=2 and n=5, both statements are satisfied.
Here, the answer is NO: the product (2*5=10) is not one more than the sum (2+5=7).
Since the answer can be YES or NO, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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