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题库 / GMATAdvanced-DS-69
If m and n are positive integers, is n even?
(1)m(m+2)+1=mn
(2)m(m+n)is odd.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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(1) m(m+2)+1=mn-->mn=(m+1)*(m+1)-->n=(m+1)*(m+1)/m
因为m和m+1互质，n又是整数，两个互质的数相除是个整数，被除数只能是1，所以这个条件的解只有一个：m=1，n=4
m+2+(1/m) = n
As n is a positive integer, 1/m must be an integer.
It's only possible if m is 1.
Hence m+2+(1/m) = n and m is 1
n is 4.
Sufficient.
m(m+n) is odd
Hence m and m+n are both odd.
Hence n must be even
Sufficient.
2: m(m+n)=odd m只能是odd-m是even的话这个条件就不成立。 m=odd. odd*n=odd-odd^2=even even/odd=even. 所以n是even。