SAT math questions!?

Question

can somebody explain how to solve these two questions?

5.101001000100001

1.The decimal number above consists of only 1's and 0's to
the right of the decimal point. The first 1 is followed by one 0, the second 1 is followed by two 0's, the third 1 is followed by three 0's, and so on. What is the total number of 0's between the 98th and the 101st 1 in this decimal number?
(A) 288
(B) 291
(C) 294
(D) 297
(E) 300

2.During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x - z dollars. Which of the following represents the customer's cost, in dollars, for n shirts bought during this sale?

(A) x+ (n-1)(x-z)
(B) x + n(x - z)
(C) n(x-z)

Answer 1

Question 1.
The pattern is follows:

1st one - 1 zero follows
2nd one - 2 zeroes follow
3rd one - 3 zeroes follow
...
98th one - 98 zeroes follow
99th one - 99 zeroes follow
100th one - 100 zeroes follow
....

So between the 98th and 101st one, you have 98, 99 and 100 zeroes respectively. (You don't count any more because the other zeros are after the 101st one).

Adding:
98 + 99 + 100 = 297

D) 297

Question 2:

Shirt 1 costs x dollars
Shirt 2 costs x-z dollars
Shirt 3 costs x-z dollars
Shirt ... x-z dollars.

So you have 1 shirt at x dollars and n-1 shirts (all remaining) at x-z dollars.

First shirt: x dollars
Remaining shirts: (n-1) shirts at (x-z) dollars

Adding these together, the total cost for n shirts is:
A) x + (n-1)(x-z)

Answer 2

the answer to the first question is D. if there are as many zeros as the numbered position of each '1', then you would add 98, 99 and 100 together (the number of zeros that fall after the 98th '1' and before the 101st '1'). You'll get 297.

my answer for the second question is A. say the first shirt cost $30 and each additional was $20. if you bought 4 shirts, the total would be $90 (30+20+20+20). Knowing that, if you substituted the numbers for the variables, the equation would read:
30 + (4-1)(30-10). Break that down to 30+(3*20). Already you can see that this works.

take time to fully read and understand what the question is asking and apply logic.

Answer 3

The first question is easy. After the 98th one is 98 zeros, and before the 101st one is 100 zeros. So, 98+99+100 (counting all the broups of zeros in between) = 297, or (D).

2. If the customer buys n shirts, the total cost is x + (x-z) + (x-2z)... + (x-(n-1)z). So, The total cost would nx - n(n-1)z. Expanding, we get nx - n^2z + nz,, or n(x-nz+z). I don't think any of the above are correct...

EDIT: Oh, I thought each shirt cost z dollars than the previous shirt... In this case the answer is A) x + (n-1)(x-z).

Answer 4

1. In the first question you have to add the following
i. 98 ceros after the 98th "1"
ii. 99 ceros after the 99th "1"
iii. 100 ceros after the 100th "1"
You do this really fast by doing this:
300 -1 - 2 = 297 ... Correct answer (D)

2. You just have to add the cost of all the shirts:
i. First shirt costs = $x
ii What do the additional shirts cost?
First of all, how many additional shirts are there?
Amount of additional shirts = n - 1 (Note 1 represents the first shirt)
Cost of each additional shirt = x-z
Multiply Amount x Cost = (n-1)(x-z)
iii TOTAL COST = x+(n-1)(x-z) Correct Answer (A)

Please contact me if you have further doubts.

Answer 5

1.D
98+99+100=297

2.A

If x = the cost of the 1st Shirt
z= the amount of the discount
therefore the cost of the addl shirts = x-y
n=the number of shirts bought
But remember the fisrt shirt 's cost is x, (no discount)

Example
If x=$10.00
z= $2.00
the cost w/b of the additional shirts w/b $8.00
the cost of the first shirt is $10.00
n=3

10+ (3-1)(10-2)
10+ 2(8)
10+16
Answer $26.00

Answer 6

98
+99
+100=297

C

2) A because x is represented by itself and (n-1) because Z is only affected by when 2 shirts+ are bought. (x-z) then represents the cost of the extra shirts

Answer 7

Number 1 - D

Number 2 - aaa

Answer 8

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Answer 9

what kind of doctor should i go to?

Answer 10

HEY !!!!! I'M TOBY KEITH ... I 'm too rich to be bothered with numbers !!!!!!!!!!!!!!!!!!!!