Solution:

Total Number of Matches: 63
Explanation:
32+16+8+4+2+1 = 63

Solution:

9+8+7+65+4+3+2+1+0

Solution:

The only number is 2592. 2^5 is 32 and 9^2 is 81. 32*81 is 2592.

Solution:

3:36 PM.
The clock loses 10 minutes each hour,
so it loses 5 minutes every half-hour,
and it loses 1 minute very 6 minutes.

It is 12:50 PM at 1:00 o'clock.
It is 1:40 PM at 2:00 o'clock.
It is 2:30 PM at 3:00 o'clock.
It is 2:55 PM at 3:30 o'clock.
It is 3:00 PM at 3:36 o'clock.

Solution:

The grocer offered her sixteen eggs for twelve cents, which would be at the rate of nine cents a dozen.

She made him throw in two eggs extra, so that she got eighteen eggs for the twelve cents, which is at the rate of eight cents a dozen, or one cent a dozen less than the first price asked.

Solution:

11 / .11

Solution:

In one hour,

Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.

Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.


Soln 2:
Let V be the total volume of the tank. From equation (1),

Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.

Substituting in equation (2),

Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).

Using the above result in equation (1),

Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].

Note that V cancels out on simplifying the above expression.

Fraction of the tank that will be filled in 0.64 hours =

0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.

Solution:

10%

100 - [ (100-85)+(100-80)+(100-75) +(100-70)]
=100-(15+20+25+30)
=100-90

Solution:

12

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

Solution:

47 + 53 + 59 + 61 = 220