求助求助~~四道GWD上的数学题求解~~

茵琳小派 · 发表于 2010-10-6 13:05:39

GWD9-2
GWD9-26
GWD10-10
GWD11-5

茵琳小派 · 发表于 2010-10-6 13:23:25

啊啊啊忘记把题给贴上来了拜托各位了哈
贴题~~~
Q2:
Guy’s net income equals his gross income minus his deductions. By what percent did Guy’s net income change on January 1, 1989, when both his gross income and his deductions increased?
(1)    Guy’s gross income increased by 4 percent on January 1, 1989.
(2)    Guy’s deductions increased by 15 percent on January 1, 1989.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Q26:
In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1)    16x is an integer.
(2)    8x is an integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Q10:
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

A.   20
B.   36
C.   48
D.   60
E.   84

The sides of a square region, measured to the nearest centimeters, are 6 centimeters long. The least possible value of the actual area of the square region is

A.   36.00 sq cm
B.   35.00 sq cm
C.   33.75 sq cm
D.   30.25 sq cm
E.   25.00 sq cm

谢谢各位牛牛鸟~~拜过拜过~~

alfxu · 发表于 2010-10-7 23:48:48

第二题题目都看不懂.....含泪飘过.

milon123 · 发表于 2010-10-8 00:39:25

Q2:
Guy’s net income equals his gross income minus his deductions. By what percent did Guy’s net income change on January 1, 1989, when both his gross income and his deductions increased?
(1) Guy’s gross income increased by 4 percent on January 1, 1989.
(2) Guy’s deductions increased by 15 percent on January 1, 1989.

SOLUTION.
Suppose n=g-d, then under (1) & (2), get g'=1.04g, d'=1.15d, (n'-n)/n=(g'-d'-n)/n=(0.04g-0.15d)/(g-d)
Since the proportion of g to d is unknown, (1) + (2) not sufficient so the answer is E.

milon123 · 发表于 2010-10-8 00:46:20

Q26:
In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

SOLUTION.
The smallest integer will be 1.
1/16=0.0625, 1/8=0.125

so, (1) when x=0.0625,16x=1 which is an integer, but the tenths digit of 0.0625 is zero. (1)not sufficient.
(2) 8x is an integer,at least x=0.125, the tenths digit of number which is greater than 0.125 but smaller than 1 will not be 0. (2) is sufficient.

Hence the key is B

milon123 · 发表于 2010-10-8 00:55:42

Q10:
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

A. 20
B. 36
C. 48
D. 60
E. 84

SOLUTION.
The key is the sentence saying " R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60".
R6=S30
R24=S60

Since both are related linearly, then ΔR=kΔS, where k is a constant.
hence we get, 18 on R equals to 30 on S.
i.e. 1 on R equals to 5/3 on S, so k=3/5.

S100-S60=ΔS=40, ΔR=kΔS=40*(3/5)=24

S100=S60+ΔS=R24+24=R48,the answer is C

milon123 · 发表于 2010-10-8 01:02:22

The sides of a square region, measured to the nearest centimeters, are 6 centimeters long. The least possible value of the actual area of the square region is

A. 36.00 sq cm
B. 35.00 sq cm
C. 33.75 sq cm
D. 30.25 sq cm
E. 25.00 sq cm

SOLUTION.

The length of the square will be AT LEAST 5.5 which satisfies " ***measured to the nearest centimeters, are 6 centimeters long".
So the area will be AT LEAST 5.5^2=30.25, so 25.00 is not a possible value.

The answer is E.

hints: This type of question has an answer either A or E one of which must be a extremely large or extremely small number.

owen870930 · 发表于 2010-10-8 01:02:44

Q2.
个人感觉应该选E吧，因为虽然两个条件告诉了总收入和支出各增长了多少但是之前的收入比例没告诉所以没法判断，
Q26.选B
16X is an integer，举例当这个整数是1，X=0.0625 the tenths digit if x是0，当16X是2时X=0.125所以条件1不充分
8X is an integer，举例当这个整数是1，X=0.125。根据0 < x < 1，8X肯定大于0，而大于零的最小的整数是1得出the tenths digit if x是大于0的，所以条件2充分。

milon123 · 发表于 2010-10-8 01:08:39

The difficulty：

Q10 >> Q26>Q2> the last Question.

Q10 must be very tough and time-consuming if misunderstood!!!

茵琳小派 · 发表于 2010-10-8 08:57:17

milon123你太给力了！！！我赞美你！！！

求助求助四道GWD上的数学题求解

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