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2, 3, 5, x, 2x creates the largest median no matter what. x can be any integer you want it to be, but the median will always be 5.

It is always much easier to list the combinations first and convert them to permutations:

{A, A, B, B} | {A, A, B, C} | {A, A, B, D} | {A, A, C, C} | {A, A, C, D} | {A, A, D, D} | {A, B, B, C} | {A, B, B, D} | {A, B, C, C} | {A, B, C, D} | {A, B, D, D} | {A, C, C, D} | {A, C, D, D} | {B, B, C, C} | {B, B, C, D} | {B, B, D, D} | {B, C, C, D} | {B, C, D, D} | {C, C, D, D} = 19 combinations.

Their permutations =[6 x 6] + [12 x 12] + 24 =36  +  144 +  24 =204 permutations, or number of possible codes

I get the following:

There are 6 possible rolls   1 through 6      only TWO are perfect squares   1  and  4      so  2 out of 6 =  2/6 = 1/3

reg child =   a - 9       on sale     value     =   (4) 1/2(a-9)

One adult ticket        on sale      value =   1(1/2)a                    summed = 132

4 (1/2)(a-9)   +  1/2  a   = 132

2.5 a  - 18 = 132

a = $  60      adult regular price                child is   a-9    =  $ 51

Not POSITIVE of these answers

Possible 4 card hands out of a 52 card deck

     52 c 4  =  52! / ( 48! 4!) = 270725

there are TWO sets red cards each set is 13 cards    a flush is  4 cards of the SAME SUIT ...not just 'red'

    13 c 4   + 13 c 4  = 1430 flushes  ( 4 hearts  or  4  diamonds)

1430 possible 'red' flushes out of 270725 possible hands =   ............

r = sqrt(22)

When a list of numbers is sorted in sequence, the median is the number in the center of the list.  In other words, there are the same amount of numbers less than the median as the amount of numbers more than the median.  

Example:  In the list  1  2  3  15  100  200  300  the median number is 15.   

Note particularly that the median is not synonymous with the average. 

So in the list in the above problem, sorted from lowest to highest, is  2  3  5  x  2x    

The largest possible median is 5.  The value of x can be anything larger than 5. 

_.

I think it is more an example of the power of suggestion .....   

   I do not think either answer is 'dumb'......just incorrect because of a mistake....

The easy one first     Tan A = opp / adj =  24/ 36 = 2/3       so it is eather answer  A  or D

Now find the hypotenuse length by pythagorean theorem

24²  + 36² = h²

h = sqrt 1872  =  12 sqrt 13

Sin A = opp/ hyp =   24 / (12 sqrt13) =  2 / sqrt13  = 2 sqrt13/13      so the answer is A

    as a check, see if you can calculate the cosine A = adj/hyp   to see if it matches the answer !  

Unit conversion.....pay attention to the units and how they should 'cancel out' to get your desired answer units:

54 mile / hr   *   1 hr / 60 min  *  5280 ft / mile    =  ..........     ft/min

See how the things 'cancel out' ?   It defines how you divide or multiply to get you final answer desired units.....

When you have questions ...such as this one....pay attention to the units....note how they 'cancel out' in this exampe and you are left with only 'gm' in your answer..... this is an important way to figure out a LOT of problems ...AND check your answers too ! :

1 gm / ml     *   10 ml  = ..........   gm

What have you done?!

MN + LM = LN

3x + 2x + 7 = 4x + 9

x = 2  

Find the lengths of side x, y, and z.

Hint:    z = √13.5 

7/9  -   4/9  + 2/9  = .........

 Factors of 24    

   1 2 3 4 6 8 12 24

8 out of 24             1/3

I only find one sequence that comes close to satisfying your conditions and it begins with:

36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.......etc.

The ratio of the difference between the 8th and the 4th terms and the 15th term is:

[43 - 39] / 50 =4 / 50 and NOT 4 / 15. The difference between the squares of the 4th term and the 1st term is:

39^2 - 36^2 =225.

If the above is correct, then 2015 will be the 1980th term.

The sum of the DIGITS of all numbers from 1 to 100 =1+2+3+4+5+6+7+8+9+1+0+1+1+1+2+1+3+1+4+1+5+1+6+1+7+1+8+1+9+2+0......etc=901 including 100.

1-100

(1+100) (2+99) (3+98)... (50+51)

(101 x 50) = 5050

(4x + 9) - (2x + 7) = 2x + 16, x = 16.

2(16) + 7 = 39

Agree with Alan..... I made the same mistake Asinus did

v = v_o  - at        where   v = 0     v₀ = initial velocity      a = 9.81 m/s^2       t = 4/5 sec        (there is no 1/2 in the equation!!)

Oops !    THANX , Alan !