Inspiring Questions from the Sea of Examinations——题海拾贝

Bob, Fred, and Vi play a game in which a card numbered 2,3,4,5,6,7,or 8 is stuck to each of their foreheads. Each player can see the other two players＇ numbers but not his or her own. An observ er tells the three players that the three numbers are not all different and that their product is a perfect square（安全平方数）, how many of them can deduce the number on their foreheads？     

Inspiring Questions from the Sea of Examinations（题海拾贝）

Suppose（假设） that a,b,c,d, and e arenumbers that satisfy this system of three equations. { 13a ＋ 26b＋ 2c＋13d ＋ 3e=18, 6a＋12b＋c＋6d＋e=7,5a＋10 b＋c＋5d＋e=6} 译文：已知方程组： {13a＋ 26b＋ 2c＋13d＋ 3e=18, 6a＋12b＋c＋6d＋e= 7 , 5a＋ 10b＋c＋5d＋e=6.}求e的值．     

Inspiring Questions from the Sea of Examinations （题海拾贝）

七枚外表相同的硬币中,有五枚分量相同,有两枚稍重一些,使用天平的两个托盘,在没有砝码的前提下,至少需要多少次,可以找出那两枚稍重的硬币？     

Inspiring Questions from the Sea of Examinations（题海拾贝）

In the figure（图形）,∠ABC and ∠BDA are both right angles.If v＋w=35and x＋y=37,what is the value of y？     

Inspiring Questions from the Sea of Examinations（题海拾贝）

在一次狗展上，狮子狗的数量至少是猎兔犬数量的1/5，至多是牧羊犬数量的1/6；而且狮子狗和猎兔犬的数量至少有23只．请问在这次狗展上的牧羊犬至少有多少只？     

Inspiring Questions from the Sea of Examinations （题海拾贝）

已知正方形ABCD内接于一个半径为r的圆,P是圆上任意一点,求AP^2＋BP^2＋CP^2＋DP^2．     

Inspiring Questions from the Sea of Examinations （题海拾贝）

译文：四个朋友去钓鱼，一共钓到11条鱼．如果每人至少钓到一条鱼，下面选项中哪个是正确的？（a）一定有人钓到两条鱼；（b）一定有人钓到三条鱼；（c）一定有人钓的鱼少于三条；（d）一定有人钓的鱼超过三条；（e）有两个人每人钓到的鱼超过一条．     

Inspiring Questions from the Sea of Examinations(题海拾贝)

1 Al, Bee, Cecil, andDihave ＄16, ＄24,＄32, ＄48, respectively. Their father proposedthat Al and Bee share their wealth equally, and thenBee and Cecil to do likewise, and then Cecil and Di.Their mother's plan is the same except that Di andCecil begin by sharing equally, then Cecil and Bee,and then Bee and A1. determine the number of chil-dren who end up with more money under theirfather's plan than under their mother's plan.Al、Bee、Cecil 和 Di 分别有16,24,32和48美元.爸爸建议 Al 和 Bee 均分财富,然后 Bee 再和 Cecil     

Inspiring Questions from the Sea of Examinations——题海拾贝

1 Without using a calculator or computer,determine which is larger,2~(3000) or 3~(2000).不使用计算器、计算机,比较2~(3000)和3~(2000)的大小.Solution;3~(2000)=(3~2)~(1000)=9~(1000) is greater than2~(3000)=(2~3)~(1000)=8~(1000).2 How many ordered triples of positiveintegers(x,y,z)satisfy (x~y)~z=64?有多少三个有序整数组(x,y,z)满足(x~y)~z=64?     

Inspiring Questions from the Sea of Examinations——题海拾贝

1 A dozen(12个)Ping-Pong balls are num-bered from 1 to 12.Tom separated the balls into twogroups and noticed that the sum of the numbers onthe balls in the first group equaled the sum of thenumbers on the balls in the second group.What isthe common sum(依次求这两组乒乓球上的数字和)?有12个乒乓球,每个乒乓球上分别标有从1到12的一个数字.汤姆把这些乒乓球分成两组,发现两组乒乓球上的数字和相等,求这两组乒乓球上的数字和是多少?     

Inspiring Questions from the Sea of Examinations(题海拾贝)

1 If x,y,and z are.positive intergers,howmany integers are between xy(z-1) and xyz?已知 x,y,z 是三个正整数,问在 yx(z-1)和xyz 之间存在多少个整数.Solution:xy-1.The number of integers between xy(z-1) and xyzmay be found by finding the difference between the twoproducts and subtracting 1.Thus this difference can be     

Inspiring Questions from the Sea of Examinations(题海拾贝)

弗朗西斯科从5开始得到一个数列,其中第二项是5的二倍,第三项是5的二倍加一,第四项是前一项的二倍,第五项比前一项多一,按此模式依次类推.弗恩也从5开始得到一个数列,其中第二项是5加1,第三项是前一项的二倍,第四项比前一项多1,第五项是前一项的二倍,按此模式依次类推.每人都进行了8次计算,问两个数列最后一项的差是多少?     

Inspiring Questions from the Sea of Examinations(题海拾贝)

1 There are four cottages on a straight road.The distance between Ted's and Alice's cottages is3 km.Both Bob's and Carol's cottages are twice asfar from Alice's as they are from Ted's.Find thedistance between Bob's and Carol's cottages in kilo-meters,在笔直的公路边有四幢房子,它们分别是 Ted、Alice、Bob 和 Carol 的家.已知 Ted 和 Alice 的家相距3千米,Bob 和 Carol 的家到 Alice 家的距离都是到Ted 家距离的二倍.问 Bob 和 Carol 的家相距多少千米.     

Inspiring Questions from the Sea of Examinations(题海拾贝)

译文:如图所示,正方形 WXYZ 的面积是25平方厘米,四个小正方形的边长为1厘米.在△ABC 中,AB=AC,当△ABC 沿 BC 边折叠时,A 点与正方形WXYZ 的中心 O 重合,求△ABC 的面积.     

Inspiring Questions from the Sea of Examinations(题海拾贝)

1 In the figure(图形),∠ABC and ∠BDAare both right angles.If v+w=35 and x+y=37,what is the value of y?译文:如图所示,已知∠ABC 和∠BDA 为直角,且 v+w=35;x+y=37.求 y 的值.Solutions:1 2.Observe that by the Pythagoreantheorem(勾股定理),v~2+w~2=x~2.Also,vw=xy,as each of these expressions is equal to twice the areaof △ABC.Hence,35~2=(v+w)~2=v~2+2vw+w~2=     

Inspiring Questions from the Sea of Examinations(题海拾贝)

1 A store buys televisions from a factory for$87.89 each.The store normally sells one of thesetelevisions for 225 percent of the factory cost,but astore coupon(优惠券)gives 25 percent off this sellingprice.Without tax,how much does a customer(顾客)with this coupon pay for the television?商店从厂家购进电视机每台$87.89,通常每台电视机的售出价是购进价的225%,但使用优惠券可以优惠25%,请问使用优惠券的顾客买一台电视需要     

Inspiring Questions the Sea of Examinations (题海拾贝)

译文:四个朋友去钓鱼,一共钓到11条鱼,如果每人至少钓到一条鱼,下面选项中哪个是正确的?(a)一定有人钓到两条鱼;(b)一定有人钓到三条鱼;(c)一定有人钓的鱼少于三条;(d)一定有人钓的鱼超过三条;(e)有两个人每人钓到的鱼超过一条.     

Inspiring Questions from the Sea of Examination(题海拾贝)

在一次狗展上,狮子狗的数量至少是猎兔犬数量的1/5,至多是牧羊犬数量的1/6;而且狮子狗和猎兔犬的数量至少有23只.请问在这次狗展上的牧羊犬至少有多少只?