Problem Solving

1. At a certain theater, the cost of each adults ticket is $5 and cost of each childs ticket is $2. What was the average(arthematic mean) of all the adults and childrens ticket sold at the theatre yeaterday:
(1) yesterday the ratio of the number of childrens ticket sold at the theater to number of adults ticket sold was 3 to 2.
(2) Yesterday 80 adult tickets were sold.


Guys the gmat prep is showing the ans that each statement alone is sufficient to answer the question. How its possible. Ithink Both are required together to arrive at the solution. Is gmat prep wrong?

Well..My answer wold be A..Because A gives the ratio of the tickets of the adults to the tickets of the children..Try plugging in any value for that ratio and you will find that the answer to be the same..

Satement 2 alone cannot be sufficient because it does not mention anything about the number of tickets sold for children..

The infinite sequence a1, a2,…, an,… is such that a1 = 3, a2 = -1, a3 = 6, a4 = -2, and an = an-4 for n > 4. What is the sum of the first 83 terms of the sequence?

A. 120
B. 124
C. 128
D. 132
E. 136

any thought on this ?

a1,a2,a3,a4 are given
As per the infinite sequence formula an = an-4
a5,a6,a7,a8 are a1,a2,a3,a4 respectively.
So the sequence keeps repeating every four numbers.

Let's first get the sum of a1 + a2 + a3 + a4 = 6
No we have to get the sum of 83 terms.
We know to get to 80 terms a1,a2,a3,a4 get repeated 20 times (80 = 4 * 20)
20 * 6 + a81 + a82 + a83.
a81,a82 and a83 are nothing but a1,a2,a3
So the answer is 120 + 3 - 1 + 6 = 128 (C)

Hi,
Thx for the reply
Only one more thing :

How do u know that a1,a2,a3,a4 are the only different numbers and that they start repeating themselves after a4?
I hope I understood u correctly,

How do u know that a1 is equal to a81
and a2 to a 82
ans so on ...

Thx !

and one more thing :

at the end instead of 20* 4

u wrote 20 *6 + ...

Why is that ?

If u had to define to a 18 year old what a ""infinite sequence formula "" is
What would you guys say ?

:roll:

ROXANA PROCA wrote:u wrote 20 *6 + ...

Why is that ?

because 6 is the sum of a1 to a4!

Let's write it down a bit
a1 + a2 + a3 + a4 = 6
Now let's use an = an-4 for the other terms
a5 + a6 + a7 + a8 = a1 + a2 + a3 + a4 = 6
a9 + a10 + a11 + a12 = a5 + a6 + a7 + a8 = 6

So every 4 terms you repeat the same pattern.
a1 + a2 + a3 +a4 + (a1 + a2 + a3 + a4) + ....so on

So you repeat the same to get the sum of a1 ......a80.
We repeat the four terms 20 times and so you multiply
the number of times you repeat(20) with the sum(6)

Now to figure out how a81 corresponds to a1 you just divide 81 by 4 and the remainder is '1'. Similarly 82/4 gives 2 meaning it is a2 and so on.

Remember the infinite sequence could be different for each series.
In this question it is an = an-4, you could have an = an-1 or an = 1 + an-2 and so on.

The infinite sequence is a series of numbers that repeat for ever when you substitute n with 1,2,3,......infinity

I hope this helps

I Recommend sck159 s advice to everyone.
Very "skilfully"and calmly explained !
Thx u SCK159 !

Grace has 16 jellybeans in her pocket.
She has 8 red ones, 4 green ones, and 4 blue ones.
What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
4
8
12
13
16

PS- how long till your Gmat exam sck159 ?

13.

In the worst case, she could take out all the 8 reds and 4 greens in a row (or 8 reds and 4 blues in a row). So, for each color to show up, she needs 13.

@ Roxana .. welcome to BTG ...

.... roxana for every new question start a seperate thread by clicking on the "new topic" button ... plz do not post problems on exisitng threads ... thank u ..