The figure above represents the floor plan of an art gallery that has a lobby and 18 rooms. If Lisa goes from the lobby into room A at the same time that Paul goes from the 10bby into room R and each goes through all of the rooms in succession, entering by one door and exiting by the other, which room will they be in at the same time ?()
(1)Lisa spends 2x minutes in each room and Paul spends 3x minutes in each room.
(2)Lisa spends 10 minutes less time in each room than Paul does.
A.条件(1)充分,但条件(2)不充分.
B.条件(2)充分,但条件(1)不充分.
C.条件(1)和(2)单独都不充分,但条件(1)和条件(2)联合起来充分.
D.条件(1)充分,条件(2)也充分.
E.条件(1)和条件(2)单独都不充分,条件(1)和条件(2)联合起来也不充分.
参考答案:A
解析:
由图可知,L和P两个人经过房间的次序是一定的,设他们两人在L到达第n个房间时相遇,则由(1)可得方程:
2xn=3x(18-n)
而由(2)可得到方程:
x·n=(18-n)(x+10)
在第一个方程中,两边可同时消掉x解出n,所以(1)单独能够充分地回答问题;而第二个方程却存在两个未知数,所以无法定出n的值。