PP-DS1-4

(1)+(2) - NO!

--------------------------------------------------------------------------------------------------------------------------------------------------------

212. 20491-!-item-!-187;#058&012823

This morning, a certain sugar container was full. Since then some of the sugar from this container was used to make cookies. If no other sugar was removed from or added to the container, by what percent did the amount of sugar in the container decrease?

(1) The amount of sugar in the container after making the cookies would need to be increased by 30 percent to fill the container.

(2) Six cups of sugar from the container were used to make the cookies.

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A 【思路】Full - 100%

(1)+30% → 100%, 70% is the answer - sufficient

(2) Six cups of sugar are quantity, not percentage. - insufficient (1)+(2) - NO!

--------------------------------------------------------------------------------------------------------------------------------------------------------

213. 20735-!-item-!-187;#058&013187

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1 - b). (2) The coordinates of D are (1 - a, b).

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C

【思路】ask the coordinates of the midpoint of line segment CD - use intuition

求兩點的中點座標，關鍵是知道兩點的座標，無所謂這兩點的座標具體是啥，只要有兩點座標就能求出來，其他條件都屬於擾亂思維的，我覺得這個是ets的花招，好多題寫的老長老長的，其實都是廢話，你用數學語言總結出來就是一個簡單的公式，中點就是（1/2,1/2），即兩點的橫縱坐標和分別除以2.所以選擇C

--------------------------------------------------------------------------------------------------------------------------------------------------------

214. 20789-!-item-!-187;#058&013258

The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick?

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick. 4y2x 32xy?

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D 【思路】 根據這題意 :

因為是square, 所以long and width是一樣的.

1. a square slab is proportional to its thickness 假設thickness = T => T * k1

2. also proportional to the square of its length 假設length = L => L * k2 成本C = T * k1 * L^2 * k2^2

=> C = T * L^2 * (k1*k2^2) 由於不管length or thickness怎樣變動, 常數(constant)都不會變, 因為他是成比例的, 因此簡化為 (k1*k2^2) = K => T * L^2 * K

C=cost, k=constant, T=thickness, L =length C= k * T * L^2

so when T=0.1, L=3, C=? (we need to know the value of k)

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick --> C= k * 0.2 * 2^2

the cost of a square slab that is 2 meters long and 0.1 meter thick --> C= k * 0.1 * 2^2

difference of two costs=160 (given) --> (k * 0.2 * 2^2) - (k * 0.1 * 2^2) =160 so you can get the value of k=400 ---> sufficient

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick --> C= k * 0.1 * 3^2

the cost of a square slab that is 2 meters long and 0.1 meter thick --> C= k * 0.1 * 2^2

difference of two costs=200 (given) --> (k * 0.1 * 3^2) - (k * 0.1 * 2^2) =200 so you can get the value of k=400 ---> sufficient

--------------------------------------------------------------------------------------------------------------------------------------------------------

215. 20843-!-item-!-187;#058&013306

If Bob produces 36 or fewer items in a week, he is paid x dollars per item. If Bob produces more than 36 items in a week, he is paid x dollars per item for the first 36 items and 1.5 times that amount for each additional item. How many items did Bob produce last week?

(1) Last week Bob was paid a total of $480 for the items that he produced that week.

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E 【思路】

此題需要把低於36個 或多於36個想進去

(1) Last week Bob was paid a total of $480 for the items that he produced that week.

設last week =y item if y<36 -->xy=480

if y>36-->? 36x+1.5x(y-36)=480

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week. This week =y+2

If y+2<36-->? x(y+2)=510 if y+2>36--> 36x+1.5x(y-34)=510 (1)+(2)

If y<36 combine (1)(2) x=15 y=32 If y>36 combine (1)(2) x=10 y=44

--------------------------------------------------------------------------------------------------------------------------------------------------------

216. 20897-!-item-!-187;#058&013307 Is x < y ? (1) 2x < 3y (2) xy > 0

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E 【思路】intuition (1) insufficient (2) insufficient (1)+(2) - NO!

--------------------------------------------------------------------------------------------------------------------------------------------------------

217. 21093-!-item-!-187;#058&013542

a1 , a2 , a3 , . . . , a15 In the sequence shown, an = an - 1 + k, where

2?n?15 and k is a nonzero

constant. How many of the terms in the sequence are greater than 10 ? (1) a1 = 24 (2) a8 = 10

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B

【思路】In the sequence shown, an = an - 1 + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?

(1) a1 = 24

a2 = a1 + k => a2 = 24 + k a3 = a2 + k => a3 = 24 + 2k a4 = a3 + k => a4 = 24 + 3k

不知到k到底是positive or negative 也不知到 k的大小, 通通會影響>10的個數 insufficient 比方說若k=-15, 那麼全都<10

(2) a8 = 10

a7 = a6 + k => a6 = 10 - 2k a8 = a7 + k => a7 = 10 - k a9 = a8 + k => a9 = 10 + k a10 = a9 + k => a10 = 10 + 2k a11 = a10 + k => a11 = 10 + 3k

由於已知的數據是10, k不管大小, 都會影響10變成大於10或小於10, 可以推論

由此可見假若k>0, 那麼從a9 ~ a15有七個大於10 ; 反之, 假若k<0, a8 ~ a2有七個大於10;充分 --------------------------------------------------------------------------------------------------------------------------------------------------------

218. 21147-!-item-!-187;#058&013552 Is 4z > -6 ? (1) z < 7 (2) z > -1

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B

Z?【思路】

?64

(1) insufficient (2) sufficient (1)+(2) - NO!

--------------------------------------------------