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neokeynesian
10-15-2004, 04:05 AM
1)If 55% of a group of people have brown hair & 80% of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?

a)1/4 b)4/11 c)4/9 d)5/9 e)4/5

2)Which of the following could be the sum of 2 positive integers such that one of them is time the other?
a)450 b)560 c)640 d)750 e)800

3)If x=-4 & y=-2, what is the value of -l-xl - l-yl?
a)-6 b)-2 c)2 d)6 e)8

4)Working indepentdently, Jing takes x hours to mow a certain large lawn & Bill takes twice as long as Jing to mow the lawn
Col A
The number of hours it takes Jing & Bill working together at thier own rates to mow the lawn

Col B
3x/4

5) Col A
The average (arithmetic mean) of x+y
Col B
The average (arithmetic mean) x/2 & 2y

6) n=(28)^3
Col A
The units digit of n
Col B
4

7)x & y each represent single digits in the decimal 4.3xy8. When the decimal is rounded to the nearest hundredth, the result is 4.36
Col A
x
Col B
5

8)If a^3 = b^2, which of the following inequalities must be true?
1)a >= 0 2)b>=0 3)a>=b 4)b>=a 5)ab>=0

Answers: 1)c 2)a 3)a 4)b 5)d 6)b 7)d 8)a

Can someone show how to solve the above questions ?
thanks

lmtuan
10-15-2004, 07:26 AM
1)If 55% of a group of people have brown hair & 80% of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?
-----> 45% of the group do not have brown hair; and 20% of the group have red hair. Thus, fraction of those who do not have brown hair have red hair is (20%)/(45%)=4/9.

2)Which of the following could be the sum of 2 positive integers such that one of them is time the other?
-----> I do not understand this question!:) My english is very bad! :(
a)450 b)560 c)640 d)750 e)800

3)If x=-4 & y=-2, what is the value of -l-xl - l-yl?
-----> -|-x| - |-y| = -|2| - |4| = -2 - 4 = -6

8)If a^3 = b^2, which of the following inequalities must be true?
1)a >= 0 2)b>=0 3)a>=b 4)b>=a 5)ab>=0
-----> since b^2>=0 then we have a^3>=0. Thus, a>=0. Answer: 1) a>=0.

Econ
10-15-2004, 07:56 AM
(1) 20/45 = 4/9
(2) ... the one is time (???) the other? How many times? If it was 2 times the other then you are looking for sums that are divided by 3, e.g. 450 is, i.e. 150+300=450 (but also 750=500+250). I do not understand the question.
(3) -6.
(4) J takes x hours and B takes 2x for one job, i.e. J takes 1 hour to complete 1/x jobs and B takes 1 hour to complete 1/2x jobs, i.e. (1/x) + (1/2x) = (1/t) , where t is the time when J and B work together at their individual rates. Thus, t=(2/3x)<(3/4x)
(5) Take x=y=0 then (A)=(B) and x=y=1 then (A)<(B), i.e. choose (D).
(6) n^3= ....(something) that ends in 2 (8X8 ends in 4 and 4X8 ends in 2), thus (B).
(7) (D). Reason: 4.35_8 and y>=5 yields 4.36. But also 4.36_8 with y<5 yields 4.36.
(8) (A).

neokeynesian
10-16-2004, 01:28 AM
Many thanks, Econ for the help.

neokeynesian
10-16-2004, 10:49 AM
To Econ:
The question no.2 sounds correct. No typo

Dingus
10-16-2004, 05:25 PM
To Econ:
The question no.2 sounds correct. No typo

Eh? Would ye mind elaborating?

gre_nidhi
10-21-2004, 10:13 PM
8)If a^3 = b^2, which of the following inequalities must be true?
1)a >= 0 2)b>=0 3)a>=b 4)b>=a 5)ab>=0
-----> since b^2>=0 then we have a^3>=0. Thus, a>=0. Answer: 1) a>=0.
Why not choice 5)ab>=0 bcoz if a>=0 and also b>=0 then product of them would also be greater than or equal to zero. Econ plz help.

Econ
10-21-2004, 10:25 PM
For ab >0 (letting alone the = case for easiness) there are two cases:
(1) a>0 and b>0
(2) a<0 and b<0
We have that a^3=b^2--------------> a>0 (or zero) because b^2 is positive (non-negative) and a is raised to an odd number.

However, b^2 > 0 is not sufficient for b>0, only necessary, that is
b>0 yes then b^2 > 0
b<0 again b^2> 0
b^2 > 0? It does not guarantess neither b>0 not b<0
Since a>o we must have that b>0 so as to choose (E). But we do not have necessarily that b is positive.

test_tkr
11-04-2004, 11:06 PM
8)If a^3 = b^2, which of the following inequalities must be true?
1)a >= 0 2)b>=0 3)a>=b 4)b>=a 5)ab>=0

can any one explain this....
thanks

calm_J
11-05-2004, 02:29 AM
hi
(econ ) u proceeded right in ques. 4 but ur answer is wrong as 1/x + 1/2x = 3/2x which is greater than 3/4x as x is time so it's always positive.

also ques. 2 is not quite identified i thought time means ( 2) but found more than one answer
also i thought it to be ( factorial but found no answer)
another guess for times is ( multiplication but hence we will have to variables with one eqn.) Please NEOKEY identify the ques. more precisely.

calm_J
11-05-2004, 02:37 AM
question (5)

col A is greater than col B ...... Please NEOKEY give feedback if this answer is right

col A is assumed to be one No. not 2 No. as col B because he wrote in col A (+) and in Col B & so this means

col A arithmetic mean = X+Y
col B arithmetic mean = (X/2+ 2Y ) /2 = X/4 + Y which is less than col A

calm_J
11-05-2004, 02:46 AM
ques. 7
so x compared to 5 this means equal not which goes for "C" not "D"
aslo it doesn't go the same if y < 5 it only goes like that if Y = 4 not any thing else.
coz 3.5_8 when rounded to thousandths will add up only 1 to the No. in the thousandths digit not more than that.

Econ
11-05-2004, 09:47 AM
Hi calm J: For (4) please notice that 3/2x is equal to the reciprocal of t, i.e. 3/2x=1/t, i.e. t=2/3x.

neokeynesian
11-05-2004, 10:23 AM
How about Q2? any explanation for it?

thanx

calm_J
11-05-2004, 11:44 AM
NEOKEY,
ques. 2 is not a well stated question. i need to know what (TIME) means to answer the ques. but if this type of ques is not in PP so it may have two answers. as i think
the eqn is x + 2x = sum so this goes for the 450 , 750 that's what i can do.

ECON,
OOOOPSSSSS, sorry i just missed that one

neokeynesian
11-06-2004, 01:35 AM
hi Calm J:
the question is correctly stated & it's from PP.