一大一小两个圆盘,小A把大盘子平均分成100个扇形,其中一半,即50个扇形涂上白色,其余的圆环涂上黑色,小B把小盘子也平均分成100个扇形,并任意的涂上白色或者黑色,(也可以全部涂上白色,或者全部涂成黑色),小C把两个涂完色的圆盘放在一起,小盘子在大盘子上面,分割线重合,而且把两个圆盘的圆心钉在一起,内外相接的两个扇形成为一组扇形,即一共有100组扇形。
小C惊奇的发现一件事,不管小A,小B怎么涂色,小C始终能通过转小盘子找到一个位置,使这100组扇形中颜色一致的数量至少是n,试求n的最大值N是多少?
例如:如果两个盘子都分成两个半圆,那么大盘子的涂色方式只有一种,即一个半圆是黑色,另一个半圆是白色,而小盘子的涂色方式有三种,即(白,白),(黑,黑),(白,黑),则此时共有2组半圆,N的最大值为1。
分析:因为若小盘子涂色方式是(白,白),(黑,黑),那么必然有一组半圆的颜色是一样的;若小盘子也是一黑一白,则有两种情况,即黑白正好交叉,此时颜色相同的扇形为0组,另一种情况,颜色相同的扇形为2组,所以存在一个位置,使颜色相同的扇形至少为1组。
A、参观者在航天博物馆身穿宇航服,置身飞行舱内,体验宇航员高空失重的感觉
B、建筑工程投标时,小王他把设计用电脑表现出来,把业主带来参观,业主感同身受
已知:
1、指针Y和Z只能在1、2、3、4这四个刻度上运转;
2、Y任何时候都不能和Z同指在一个刻度上;
3、可能变动的位置如下所示: 从1到2顺时针或逆时针运转; 从2到3顺时针或逆时针运转; 从3到4顺时针或逆时针运转; 从4到1顺时针或逆时针运转。
4、任何时候,只能一根指针变动位置,每次变动完毕都有一段停留的时间,这时两根指针都保持静止状态。
下列哪组顺序系列位置变化是其中一根指针可能运转的路线?
【专题 GMAT逻辑题】
The heavy traffic in Masana isa growing drain on the city’s economy-the clogging of the streets of thecentral business district alone cost the economy more than$1.2 billion over thepast year. In order to address this problem, officials plan to introducecongestion pricing, by which drivers would pay to enter the city’s most heavilytrafficked areas during the busiest times of the day.Which ofthe following, if true, would most strongly indicate that the plan will be asuccess?
A.Approximately one-fifth of the vehicles in the central business district are intransit from one side of the city to the other.
B.Planners expect that, without congestion pricing, traffic in Masana is likelyto grow by 6 percent in the next five years.
C. Inother urban areas, congestion pricing has strongly encouraged carpooling(sharing of rides by private commuters).
D.Several studies have shown that a reduction in traffic of 15 percent in Masanacould result in 5, 500 or more new jobs.
E. Over30 percent of the vehicles in the city’s center are occupied by more than oneperson.
【专题 GMAT逻辑题】
Which of the following mostlogically completes the argument? Sviatovinis a medieval Moringian text whose author and exact date of composition areunknown. However, the events in the life of Prince Sviatov that the textdescribes occurred in 1165, and in the diagram of Sviatov’s family thataccompanies the text his father, who died in 1167, is identified as stillliving. Thus Sviatovin must have been written between 1165 and 1167, assuringthat.
A. thelife of Prince Sviatov is not the subject of any other medieval Moringian texts
B. theauthor of Sviatovin intended it to provide as accurate a report about PrinceSviatov's exploits as possible
C. thediagram accurately represents the composition of Sviatov's family at thetimeSviatovin was written
D.Sviatovin is the earliest Moringian text whose composition can be dated towithin a few years
E Sviatovin was not written by Sviatov's father himself
有一个神奇的岛,岛上的居民要么总是说真话,要么总是说假话。
在这个岛上有一个数字狂热者俱乐部,有会员40人,他们不是每天都来俱乐部,但是每天至少有4人在。这个俱乐部的会员只用数字回答别人的问题。而且他们回答问题是总是有特殊的癖好:
1.他们只用非负整数来回答问题,且数字永远不会大于当天在场的会员总数。
2.他们对问题有要求,只回答那些正解和被问人无关的问题(举个例子,他们不回答“你多高?”,因为不同人可能不等高,正确答案就和被问人相关了)。
有一天三个当地记者A、B和C来到这个俱乐部,每人问了一个问题,在场的会员都回答了这些问题。
下面是当天A、B和C事后的谈话:
A:我问了在场的会员们他们之中有多少是说实话的。
B:我问了在场的会员们他们之中有多少是不说实话的。
C:上面这两句话不都是实话。
A:对我的问题,这么多回答都不相同。
B:真巧,我的也是呢。
C:对我的问题,这么多回答中至少有两个是不同的。
A:非常有趣的是,对于我的问题,他们的回答加起来正好是个回文数。
B:真巧,我的也是呢。
C:对我的问题,他们的答案加起来不小于在场会员的成员数的平方。
问:那天俱乐部有多少会员?
PS:回文数正读倒读一样,比如1234321,5665,787,99,0等等。