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# A certain club has 20 members. What is the ratio of the

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A certain club has 20 members. What is the ratio of the [#permalink]  20 Aug 2007, 20:37
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1. A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

2. If x(x - 5)(x + 2) = 0, is x negative?
(1) x2 – 7x ≠ 0
(2) x2 –2x –15 ≠ 0

3. On Saturday morning, Malachi will begin a camping vacation and he will return home at
the end of the first day on which it rains. If on the first three days of the vacation the
probability of rain on each day is 0.2, what is the probability that Malachi will return
home at the end of the day on the following Monday?
A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

4. If x percent of 40 is y, then 10x equals
A. 4y
B. 10y
C. 25y
D. 100y
E. 400y

5. In the xy-plane, what is the slope of the line with equation 3x + 7y = 9?
A. – 7/3
B. – 3/7
C. 3/7
D. 3
E. 7

6. The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

7. At a certain food stand, the price of each apple is $0.4 and the price of each orange is$0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is$0.52?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

8. Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine M, working along at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

9. 23. (0.8)^-5 / (0.4)^-4=

(A) 3/32
(B) 5/64
(C) 1/2
(D) 1
(E) 2

10. There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
(A) 20
(B) 25
(C) 40
(D) 60
(E) 125

11. A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

(A) 1: 2
(B) 4: 5
(C) 1: 1
(D) 3: 2
(E) 5: 3
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Re: 11 questions [#permalink]  20 Aug 2007, 20:48
Sergey_is_cool wrote:
1. A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

Think this one should be C: 16 to 5.

Basically, it's a 20c5/20c4 where order doesn't matter, right?

While you could perform the calculations in both the numerator and the denominator, you could just set it all up and cancel stuff out:

num = 20 * 19 * 18 * 17 * 16
-------------------------
5 * 4 * 3 * 2 * 1

denom = 20 * 19 * 18 * 17
--------------------
4 * 3 * 2 * 1

now, you can just invert the denominator, multiply and cancel:

20 * 19 * 18 * 17 * 16 4* 3* 2
-------------------------- * --------------------
5 * 4 * 3 * 2 20 * 19 * 18 * 17

Most of it cancels until you arrive at 16/5.
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Re: 11 questions [#permalink]  20 Aug 2007, 20:54
Sergey_is_cool wrote:
2. If x(x - 5)(x + 2) = 0, is x negative?
(1) x2 – 7x ≠ 0
(2) x2 –2x –15 ≠ 0

I think this one should be C. Basically, we're just plugging stuff in.

If we know that x(x - 5)(x + 2) = 0, then we know that x must be either 0, 5, or -2.

Looking at 1) and factoring out an x, we can see that both x and x-7 cannot be equal to zero. We are only concerned with x=0 as a possibilty, so this rules out that as a root.

Looking at 2) and factoring it to (x + 3)(x - 5), we see that x + 3 and x - 5 cannot be equal to zero. Therefore, x cannot equal 5 either.

Having eliminated 0 and 5 as possible roots, we're left with -2, which is negative.
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Re: 11 questions [#permalink]  20 Aug 2007, 20:57
Sergey_is_cool wrote:
1. A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

= 20c5/20c4
= [(20x19x18x17x16x15!) / (15!5!)] [(20x19x18x17x16!)/(16!4!)
= (20x19x18x17x16) (4!) / [(5!) (20x19x18x17)]
= 16/5
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Re: 11 questions [#permalink]  20 Aug 2007, 20:59
Sergey_is_cool wrote:
4. If x percent of 40 is y, then 10x equals
A. 4y
B. 10y
C. 25y
D. 100y
E. 400y

(x/100) (40) = y
10x = 25y
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Re: 11 questions [#permalink]  20 Aug 2007, 21:05
Sergey_is_cool wrote:
3. On Saturday morning, Malachi will begin a camping vacation and he will return home at
the end of the first day on which it rains. If on the first three days of the vacation the
probability of rain on each day is 0.2, what is the probability that Malachi will return
home at the end of the day on the following Monday?
A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

I'm going to go with B on this one. Since we want there to be no rain on Saturday, no rain on Sunday, and rain on Monday:

It's P(no rain) * P(no rain) * P(rain) so = .8 * .8 * .2 = .128
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Re: 11 questions [#permalink]  20 Aug 2007, 21:09
Sergey_is_cool wrote:
5. In the xy-plane, what is the slope of the line with equation 3x + 7y = 9?
A. – 7/3
B. – 3/7
C. 3/7
D. 3
E. 7

Just a little algebra:

3x + 7y = 9
7y = -3x + 9
y = -(3/7)x + 9/7

so the slope = -3/7
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A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

# of 5 member committee = 20C5
# of 4 member committee = 20C4

Ratio = 20C5/20C4 = 16/5 --> Ans C
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2. If x(x - 5)(x + 2) = 0, is x negative?
(1) x2 – 7x ≠ 0
(2) x2 –2x –15 ≠ 0

x(x - 5)(x + 2) = 0 --> x = 0, 5 or -2

St1:
x^2 - 7x = 0
x(x-7) = 0
x = 0 or x = 7

Since valid possibilites are x = 0, 5 or -2, then x must be 0. Sufficient.

St2:
x^2 - 2x - 15 = 0
(x+3)(x-5) = 0
x = -3, 5.

Since valid possibilites are x = 0, 5 or -2, then x must be 5. Sufficient.

Ans D
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On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains.
If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

We need it to rain on Monday. P = (0.8)(0.8)(0.2) = 0.12
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4. If x percent of 40 is y, then 10x equals
A. 4y
B. 10y
C. 25y
D. 100y
E. 400y

x = 0.4y
10x = 4y
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In the xy-plane, what is the slope of the line with equation 3x + 7y = 9?
A. – 7/3
B. – 3/7
C. 3/7
D. 3
E. 7

7y = 9-3x
y = -3x/7 + 9/7

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ywilfred wrote:
2. If x(x - 5)(x + 2) = 0, is x negative?
(1) x2 – 7x ≠ 0
(2) x2 –2x –15 ≠ 0

x(x - 5)(x + 2) = 0 --> x = 0, 5 or -2

St1:
x^2 - 7x = 0
x(x-7) = 0
x = 0 or x = 7

Since valid possibilites are x = 0, 5 or -2, then x must be 0. Sufficient.

St2:
x^2 - 2x - 15 = 0
(x+3)(x-5) = 0
x = -3, 5.

Since valid possibilites are x = 0, 5 or -2, then x must be 5. Sufficient.

Ans D

I don't think this is quite right -- remember, the two statements are not stating equality, they are saying they cannot equal zero.
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Re: 11 questions [#permalink]  20 Aug 2007, 21:41
Sergey_is_cool wrote:
6. The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

I think the answer to this is 80. You want to f(m) to equal 9 * f(v). To this this, we need to examine the function. Since the tens digit is multiplied by three, if we play around with this digit, we should be able to modify the final result by 9.

let's say V = 113 --> f(v) = 2 * 1 * 3 * 1 * 5 * 3 = 90
let's say M = 193 --> f(m) = 2 * 1 * 3 * 9 * 5 * 3 = 810
810 = 90 * 9

so, 193 - 113 = 80
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1.
1) # of combinations of how to form 5 mem. commitee (order does not -> devide by 5!) (20*19*18*17*16) / 5!
2) # of combinations of how to form 4 mem. commitee (order does not -> devide by 4!) (20*19*18*17) / 4!

(20*19*18*17*16) * 4!
---------------------------
5! (20*19*18*17)

Ans: 16/5 or 16:5

2. If x(x - 5)(x + 2) = 0
x=0 or
x= -2 or
x = 5

(1) x^2 – 7x ≠ 0
x ≠ 0 or x ≠ 7 --> we still left with x= -2 or x = 5 --> BCE

(2) x^2 –2x –15 ≠ 0
(x+3)(x-5) ≠ 0
x ≠ -3 or x ≠ 5 --> we still left with x= -2 or x = 0 --> CE

Together: x ≠ 0 or x ≠ 7 or x ≠ -3 or x ≠ 5 eliminate everything, but x = -2

Ans. C

3. The probability of rain = 0.2 ==> the probability that there will be NO rain = 0.8, hence 0.8 * 0.8 * 0.2 = 0,128

Ans. B

4. 40 * x/100 = y
y = 4x/10
x = 10y/4
10x = 100y/4 = 25y

Ans. C

5. 7y = 9 - 3x
y = 9/7 - 3/7x
Eqution of the line: y = kx + b, where k = slope. In our case slope = -3/7

Ans: B

Last edited by Whatever on 20 Aug 2007, 22:35, edited 1 time in total.
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Re: 11 questions [#permalink]  20 Aug 2007, 21:55
Sergey_is_cool wrote:
7. At a certain food stand, the price of each apple is $0.4 and the price of each orange is$0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is$0.52?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

I think the answer is 5. If I saw this one on the test, I might be tempted to just plug in numbers, just remember that if you do, you must subtract the price of the number of oranges from the total ($5.6) and also deduct the number of oranges from the total you're calculating the average on. This helps segue to the algebraic solutions: .52 = (5.6 - .6x) / 10 - x --> "the desired average equals the previous total minus the price of oranges times the number of oranges divided by the old total number of items minus the number of oranges subtracted" 1.12x = .4 .08x = .4 x = 5 Intern Joined: 10 Aug 2007 Posts: 30 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: 11 questions [#permalink] 20 Aug 2007, 22:01 Sergey_is_cool wrote: 8. Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine M, working along at its constant rate, to produce all of the units produced last Friday? (A) 8 (B) 12 (C) 16 (D) 24 (E) 30 I think the answer is 24. Start with our basic rate for machine k: If it took machine k 3 hours to produce 1/4 of the units, then it would take 12 hours to produce all of the units. We can take this information and apply it to the next section: (1/12)(6) + x(6) = 3/4 1/2 + 6x = 3/4 6x = 1/4 x = 1/24 --> hence, in one hour, machine m completes 1/24 of the job, so it would take 24 hours to complete the whole job alone. Manager Joined: 03 Sep 2006 Posts: 233 Followers: 1 Kudos [?]: 10 [0], given: 0 [#permalink] 20 Aug 2007, 22:07 6. don't know 7. At a certain food stand, the price of each apple is$0.4 and the price of each orange is $0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is$0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is \$0.52?

x - applex
y - oranges

(0.4x + 0.6y)/10 = 0.56

0.4x + 0.6y = 5.6
x + y = 10

Solve for x and y

x = 10 - y

0.4*(10 - y) + 0.6y = 5.6
4 - 0.4y + 0.6y = 5.6
0.2y = 1.6
y = 8 --> x = 2

Lets Q - number of oranges Mary keeps (finally we need to know y - Q)

(0.4*2 + Q*0.6) / (2+Q) = 0.52
0.8 + 0.6*Q = 1.04 + 0.52Q
0.08Q = 0.24
Q = 3

Thus y - Q = 8 - 3 = 5

Ans. E
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8.

K = 1/4 units = 3h ==> whole = 12h

(1/12)*6 + (1/M)*6 = 3/4

(1/12)*6 + (1/M) = 3/24

1/M = 3/24 - 1/12 = 1/24 --> M = 24

Ans. D
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10.
_ _ _ _ _ <5> we have 5*4*3*1*1 = 60.

Ans. D

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