Re: [計量] CAT計量問題請教(II)

看板GRE (GRE入學考試)作者wearytolove (奪真書生A.W.)時間16年前 (2009/08/05 23:41)推噓5(5推 0噓 6→)

留言11則, 4人參與討論串3/3 (看更多)

※ 引述《think12381 ()》之銘言： : 不好意思~麻煩各位了 : 謝謝各位的幫助 : CAT 18 : 8. : a wooden cube with edges of 4 inches is painted red. : the cube is then cut into 64 small cubes with edges of 1 inch. : COL A the number of small cubes that have exactly three red faces : COL B the number of small cubes that have no red faces : A B 分別如何算 : ans C A=有三邊有顏色的就是8個角落 B=中間的8塊,2x2x2 因此A=B : 11. : which of the following express the area of a circle in terms of C, : its circumference? : ans c^2/4pi c是指週長嘛,所以半徑就是c/2pi,因此面積就是pi*(c/2pi)^2=c^2/4pi : 24 : a shool group charters three identical buses and occpuies 4/5 of seats. : after 1/4 of the passengers leave,the remaining passengers : use only two of the bues. : COL A the fraction of the seats on the two buses that are occupied : COL B 9/10 : ans C 假設每台車載5人,原本3台每台各4人共12人,後來變每台3人共9人. 變兩台車,因此每台變坐4.5人,因此是4.5/5=9/10 : 26 : in a group of 100 students, there are more students on the fencing team than : in the french club. if 70 are in the club and 20 are in neither on the team : nor in the club, what is minimum number of students who : could be both on the team and in the club. : a 61 b 60 c 50 d 49 e 10 : ans 61 兩邊都不參加有20人,剩80人都至少參加1個團體,又club有70人,因此team至少71人此時80人中,一邊有70人,一邊有71人,至少有70+71-80=61人重覆 : 28 : one side of a triangle has length 6 and a second side has length 7. : which of the folling could be the area : I.13 : II 21 : III 24 : ans I and II 一邊邊長6一邊是7,面積最大為直角三角形=21,因此比21小都有可能 a*b*sin日*1/2<=a*b*1/2 : CAT19 : 17. : the first term of a sequence is 1, and each of the following terms is 1 : less than than 3 times preceding term. : COL A the smaller number that is greater than 100 in the sequence : COL B 120 : ans A 第一個是1,第二個是1x3-1=2,第三個是2x3-1=5,再來是14,41,122, 他問是說第一個比100大的最小的數跟120比誰大,所以是A : 26. : An obtuse triangle has sides of lengths of 11, 15, and k, : where k is an integer. : COL A the number of K values of K : COL B 13 : ans C 是鈍角嘛,所以考慮兩種情況-->K是最大邊orK是最小邊最大邊 (11^2+15^2)^1/2=18 <K<11+15 ,一共有19,20,21,22,23,24,25共7個最小邊 15<K+11<(15^2-11^2)^1/2 ,一共有5,6,7,8,9,10共6個 : CAT 20 : 6 : 圖是一個方形裡面有兩個半圓長這樣 ")(" 有相切問的是不是圓的部份 : the shaded region above is bounded by two semicircles and : two sides of square abcd.the perimeter of the shaded region is 4+2pi. : COL A the area of the shaded region : COL B 1 : ans B 邊長是4+2pi,代表圓的半徑=1,也代表正方形邊長為2 因此不是圓的部份=4-pi=4-3.14<1 : 17 : 圖是一個圓裡面有兩個互相垂直的直徑這兩條直徑成這個形狀 "+" : in the circle with center O show above,AB and CD are diameters : perpendicular to each other and chord DF intersects AB at point E. : if DE = 6 an EF = 2, the area the area of the circle O is : ans 24pi 這題我算法比較麻煩,應該有更簡單的,我是假設OE=a,BE=b,則AO=半徑=a+b 由三角形ODE可知6=√(a^2+(a+b)^2) 又因為三角形ADE與三角形EFB是相似,因此可以得到2a+b:2=6:b,可得12=b^2+2ab 將這值代入第一式,可得a=√12,再代回第二式可得b=-√12+√24,因此a+b=半徑=√24 因此面積=24pi : 23 : if E(n) represents the sum of even digits of n for example, : E(5681) = 6 + 8 = 14, then E(1) + E(2) + E(3) +.....E(100) is : ans 400 (2+4+6+8)*10+2*10+4*10+6*10+8*10=400 : 26. : if a is greater than c by 50%, and b is greater than c by 25%, : then a is greater than b by what percent : ans 20 順便問一下 by 50%是什麼意思比c多50%,假設C是10,則a=15,b=12.5,因此a比b多20% : 28. the two-digit integers N ans N' are positive and have the same digits, : but in reversed ordered. how many integers N are there : if the sum of N and N' is a percect square?? : ans 8 是說perfect square嗎= =? 10*a+b+10*b+a=11(a+b),因此一定是11的倍數,又規定是要平方和因此只有可能是11*11=121,即兩數相加=121 因為都只有2位,加起來不可能超過200 因此a+b=11,可能的(a,b)=(2,9),(3,8),(4,7),(5,6),(6,5),(7.4).(8.3).(9.2) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.5.19