please help me by solving these problems:part-3

[ahad]

1.Given that the range of 6 consecutive positive numbers is 6.8 and of 7 consecutive numbers is 13.2. If none of these numbers in the two groups are same, what would be the range of the 13 numbers?

2. In a country, the tax paid by a person is 1500 and 6% of the taxable income above 3000. If the total tax paid by a person was 4% of his taxable income, what was that persons taxable income?

3. N = 5^9 + 7^10
Col A: What is the least factor of 'N' greater than 1
Col B:3
4. Two concentric circles were given one inserted in the other, the part between the circles was
shaded.
Col A: The probability of finding a point in the shaded part is
Col B: 3/4.

5. Col A: Least prime factor of (factorial(7) + 7)
Col B: Largest prime factor of factorial(7)

6. In a party of 66 members in a hotel, 40 members like dancing, 23 members like swimming and 6 members like either dancing or swimming or both. Find the number of people who likes only
dancing?

7.If the Arithematic mean of a list of 65 items is 'p' and arithematic mean of a list of 92 items 'n'. When the the two lists are combined the average mean is 84 then what is the value of p/n?( does it make any sense?)

8.Given a solution having 5% salt concentration. To the 500cc of above solution how much amount of a 3.5% salt concentrated solution should be added in order to get 4% salt solution.?

9.There was a survey of 500 persons. Each person was given some questions, and for each question they can answer either "YES" or "NO". If 410 persons from the group answered "YES" for the first question, 220 of the group answered "YES" for the second question and if 'n' is the least number of persons who answered "YES" to both the questions, what is the value of 'n' provided if all the 500 persons answered both the questions?

10.Given that 'm' and 'h' are two positive integers. If 10^50*m+h is divisible by 9, then
Col A: Remainder when 'm+h' is divided by 9 is
Col B: 5

11. 1. 0 < 7/m < m/7
Col A: m
Col B: 7

12.There 20 students in a class, half of the students are boys. If 7 members should be selected out... and of which if 6 are girls find the probability that the 7th member is also a girl?

13. Given a equation of circle x^2 + y^2 = 49 with two points A(4a, 3) and B(0, -b) on the circle
Col A: Distance between points A & B
Col B: 12

14. How many maximum non-overlapping divisions can be made in a rectangular by drawing 3 straight line.

15. Given a right angle triangle ABC, the length of hypoteneous AB is 15 and a point D was given on AB and DB is 5 and other point E was given on AC. Angle c and e are both 90 degree. Find the length of AE?

16.John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit "1" appeared in the last three places and "0" did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16 b) 11/16 c) 11/12 d) 1/2 e) 5/8

[chestnut.cc]

1. D

2.Let x be the taxable income... 0.04x = 1500 + 0.6(x-3000)... 1500 +0.06x - 1800... 0.02x = 300... x = 15,000

3. 5

4. D

5. C

6. AUB cannot be less than A or B...

7. 65p + 92n = (65+92)*84... p/n = [(65+92)*84-92n]/65n...

OR

p+n/2 = 84... p+n = 168... p = 168-n... p/n = 168-n/n

8. 0.05(500) + 0.035x = 0.04(500+x)... 25 + 0.035x = 20 + 0.04x... 0.005x = 5... x = 1000cc...

9. 130

10. please rewrite clearly...

11. A

12. 1/5

13. B

14. 4

15. D... its a 3-4-5 triangle... but since the sides arent specified... the length of AE will vary depending on the selection of base...

[ahad]

12: why is the ans 1/5? i guess it to be 2/7...because...
6 girls already chosen,only 1 post is left, total no. of members left is (10+4) =14, total no. of girls left is 4, so the probability of the 7th member being a girl is =4/14=2/7

[chestnut.cc]

sorry... i forgot to neglect the members already chosen... yes youre correct... 4/14 = 2/7... my bad... :s

[e.cartman]

14. How many maximum non-overlapping divisions can be made in a rectangular by drawing 3 straight line.

I think answer may be 7, not 4. Question says divisions are nonoverlapping. Considering the lines can cross each other, draw a small triangle in center of square. Extrapolate all sides of triangle on all sides. You can get 7 mutually exclusive divisions.

[e.cartman]

I get answer D for 13.
13. Given a equation of circle x^2 + y^2 = 49 with two points A(4a, 3) and B(0, -b) on the circle
Col A: Distance between points A & B
Col B: 12

Center is at origin O. So OA=OB=7.
16a^2+9=49...a= +- 5/2
b= +- 7
A(+-10, 3)
B(0, +-7)
Max distance taking -7 is 10root2 >12
Min distance taking +7 is 2root29 <12

[chestnut.cc]

Now that you mention it yes *respects cartmans authoritah*... the 2 diagonals and a third line through either half...

[chestnut.cc]

Center is at origin O. So OA=OB=7.
16a^2+9=49...a= +- 5/2
b= +- 7
A(+-10, 3)
B(0, +-7)
Max distance taking -7 is 10root2 >12
Min distance taking +7 is 2root29 <12

the max distance can be 14... as the radius of the circle is 7... 10root2 is approx 14.14 > 14... which isnt possible... only the second option is feasible...

[Jeanette]

Originally Posted by chestnut.cc

1. D



8. 0.05(500) + 0.035x = 0.04(500+x)... 25 + 0.035x = 20 + 0.04x... 0.005x = 5... x = 1000cc...

Kaplan's has a different method for dilution problems.

AmountA * (Diff bet. percent A and desired percent) = Amount B * (Difference between Percent B and desired percent).

So in this problem, it would be 500 (.05-.04) = (.04-.035)x, or 500*.01=.005x.

The math checks out in both cases. The way you wrote it out is more intuitive though. I can understand why the equation works. The Kaplan method is quicker but I don't understand exactly why it works.

[chestnut.cc]

If you rearrange the terms in the former eqn... you get the kaplan eqn...