单选题 If x<y<z and y-x>5.where x is an even integer and y and z are odd integers,what is the least possible value of z-x?
【正确答案】 D
【答案解析】Since y - x > 5, it follows that y must be one of the integers x + 6, x + 7, x + 8, x + 9,...Also, because x is even and y is odd, y cannot be an even integer added to x, and thus y must be one of the integersx + 7,x + 9,x+ 11,,x+13,...Since z > y and both y and z are odd integers, it follows that z must be one of the integersy + 2, y + 4, y + 6, y+8, ...Therefore, the least possible value of z - x occurs when y is 7 greater than x and z is 2 greater than y, which implies that z is 7 + 2 = 9 greater than x.The correct answer is D.