Some sat math problems help

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1

<ol>
<li>There is a circular spinner divided into four halves with each halve labeled with 1-4. Let the number of the first spin be p where the arrow stops, and the number of the second spin be q where the arrow stops. If each number has an equal probablility of being the sector on which the arrow stops, what is the probability that the fraction p/q is greater than or equal to 1?</li>
</ol>

<p>a. 1/4
b. 3/16
c. 5/16
d. 1/2 (thats what i got but not sure)
e. 5/8</p>

<ol>
<li>cathy can do a job in 8 hours while Danny can do it in 6 hours. If they work together for three hours, what fraction of the job is left to be finished?</li>
</ol>

<p>a. 1/2
b. 1/8 (Again, what I got but not sure)
c. 1/7
d. 1/6
e. 1/4</p>

<ol>
<li>In a plane, the distance between points X and Y is 10, the distance between the points X and p is 3, and the distance between the points Y and q is 4. Which of the following cannot be the length of pq.</li>
</ol>

<p>a. 2 (I got 2 but unlikely that it is da answer)
b. 3
c. 10
d. 15
e. 17</p>

<ol>
<li>The Maxim telephone company charges k cents for the first t minutes of a call and charges for any additional time at the rate of r cents per minute. If a certain customer pays 10 dollars, which of the following could be the length of the call in minutes.</li>
</ol>

<p>a. 1000/r + rk
b. 1000/r + tk
c. 1000-k-t/r
d. 1000-k/r + t
e. 1000+k/r + kt</p>

<p>I got d but I kinda plugged in and took me a while. Need a faster solution.</p>

<p>Thanks for the help.</p>

2

<ol>
<li>There is a circular spinner divided into four halves with each halve labeled with 1-4. Let the number of the first spin be p where the arrow stops, and the number of the second spin be q where the arrow stops. If each number has an equal probablility of being the sector on which the arrow stops, what is the probability that the fraction p/q is greater than or equal to 1?</li>
</ol>

<p>a. 1/4
b. 3/16
c. 5/16
d. 1/2 (thats what i got but not sure)
e. 5/8</p>

<p>ANSWER: Since the numbers are 1-4 you can just list</p>

<p>So…</p>

<p>If p=1, then q will have to be only 1 (1 number possible)
If p=2, then q can be 2 or 1 (2 numbers possible)
If p=3, then q can be 3, 2, or 1 (3 numbers possible)
If p=4, then q can be 4, 3, 2, or 1 (4 numbers possible)</p>

<p>The total outcomes are: 4*4 = 16
The favorable outcomes are: 4+3+2+1 = 10</p>

<p>Answer = 10/16 = 5/8 (E)</p>

<ol>
<li>cathy can do a job in 8 hours while Danny can do it in 6 hours. If they work together for three hours, what fraction of the job is left to be finished?</li>
</ol>

<p>a. 1/2
b. 1/8 (Again, what I got but not sure)
c. 1/7
d. 1/6
e. 1/4</p>

<p>ANSWER:</p>

<p>How much can cathy do in 1 hour? 1/8 of a job
How much can Danny do in 1 hour? 1/6 of a job</p>

<p>Since they are working together we add their rates…
How much can Danny and Cathy do in 1 hour? (1/8) + (1/6) = 7/24 of a job
How much can Danny and Cathy do in 3 hours? 3(7/24) = 21/24</p>

<p>How much of the job is left? 1 - (21/24) = 3/24 = 1/8</p>

<p>Answer = 1/8
B is correct!</p>

<ol>
<li>In a plane, the distance between points X and Y is 10, the distance between the points X and p is 3, and the distance between the points Y and q is 4. Which of the following cannot be the length of pq.</li>
</ol>

<p>a. 2 (I got 2 but unlikely that it is da answer)
b. 3
c. 10
d. 15
e. 17</p>

<p>I really don’t know a simple way of doing this, sorry! Having a graphing calc is handy</p>

<ol>
<li>The Maxim telephone company charges k cents for the first t minutes of a call and charges for any additional time at the rate of r cents per minute. If a certain customer pays 10 dollars, which of the following could be the length of the call in minutes.</li>
</ol>

<p>a. 1000/r + rk
b. 1000/r + tk
c. 1000-k-t/r
d. 1000-k/r + t
e. 1000+k/r + kt</p>

<p>In this problem the CB is trying to mess you up with Algebra. We know for sure that this equation must have all of the variables k, t, and r. So we can get rid of A. Not sure on this…try plugin if Algebra gets you</p>

3

<ol>
<li>In a plane, the distance between points X and Y is 10, the distance between the points X and p is 3, and the distance between the points Y and q is 4. Which of the following cannot be the length of pq.</li>
</ol>

<p>a. 2 (I got 2 but unlikely that it is da answer)
b. 3
c. 10
d. 15
e. 17</p>

<p>The easy way to solve this kind of problem is to figure out what the greatest and smallest distance between p and q can be.
For that, we assume that all points X,Y,p and q lie on the same line (in the plane).
In a coordinate system we can visualize the points the easiest if we assume x has coordinates (0,0) and y has the coordinates (10,0). The distance between X and Y is 10. </p>

<p>The distance between X and p is 3 -> p can either be (-3,0) or (3,0)
The distance between Y and q is 4 -> q can either be (6,0) or (14,0)</p>

<p>If p and q are as close as possible they have the coordinates p (3,0) and q (6,0).
Therefore, the smallest distance possible (with the given conditions) is 3.</p>

<p>If p and q are furthest from each other p is (-3,0) and q is (14,0).
Therefore, the greatest possible distance is 17.</p>

<p>If you look at the answer choices, all choices except A) 2 lie in the range of the possible distance between q and p. So your answer is correct.</p>

4

<ol>
<li>The Maxim telephone company charges k cents for the first t minutes of a call and charges for any additional time at the rate of r cents per minute. If a certain customer pays 10 dollars, which of the following could be the length of the call in minutes.</li>
</ol>

<p>a. 1000/r + rk
b. 1000/r + tk
c. 1000-k-t/r
d. 1000-k/r + t
e. 1000+k/r + kt</p>

<p>10 dollars = 1000 cents</p>

<p>k cents – charge for t minutes</p>

<p>(1000-k) – charge for remaining minutes at the rate of r cents/minute</p>

<p>time at r cents/minute = (1000-k)/r
time for k cents = t</p>

<p>Total time = (1000-k)/r + t (choice d)</p>

5

<p>thanks, your explanation helped me visualize it better and I get it now.</p>

6

<p>Hi </p>

<p>@ppathak4
I know this isn’t my post but last question I didn’t not get the explanations of ppathak4.
All I get logically that first calls of the first t minutes should be t*k
then addational should be t2 * r.</p>

<p>so that =
1000 = t2 * r + t * k</p>

<p>shouldn’t it be 1000 / r + t why did we subtracte k from it??</p>

<p>thanks in advance.</p>

7

<p>@GenericMath:
I’ll try to help you by rewording ppathak4’s explanation a bit:</p>

<p>You know the following from the task:

  1. company charges k cents for the first t minutes
  • you do NOT know for how many minutes t there is a fixed charge k
  1. for any additional minutes after minutes t you pay the rate r (cents per minute)
  2. the costumer pays 10 dollars which equal 1000 cents</p>

<p>What do you have to do?
You have to find an abstract equation for the time t in minutes which adhere to all conditions stated above.</p>

<p>1000 cents is what the customer pays. Of these 1000 cents the customer pays a fixed amount of k cents for t minutes.
-> therefore, the final equation has to contain the term “+t” (because you are looking for the total amount of time)</p>

<p>Now you have to find the amount of minutes the customer pays for at a constant rate r.
The overall amount is 1000 cents but you know that the customer already paid k cents of the 1000 cents for t minutes.</p>

<p>What is left over are 1000 cents - k cents. 1000 - k is the amount of cents the customer pays for at a constant rate r.</p>

<p>Cost (cents) = time (minutes) x rate (cents per minute)</p>

<p>-> time = cost/rate</p>

<p>-> time = (1000-k)/r</p>

<p>Now we just add both amounts of time together and we get the final and correct equation:</p>

<p>time = (1000-k)/r + t </p>

<p>Note that 1000-k is only divided by r and not by (r+t)…</p>

<p>Did that help?</p>

8

<p>@Amad3us</p>

<p>Thanks alot Amad3us that made perfect sense thanks for the explanation.</p>

<p>also when u said “Note that 1000-k is only divided by r and not by (r+t)…”
I didn’t understand that at first so it kinda confused me.</p>

<p>Thanks again.</p>

9

<p>For #4, I simply devised an equation that incorporated the variables k, r, and t along with a variable m that stands for total minutes. I then set this equation equal to 1000 cents, then solved for m.</p>

<p>General equation: </p>

<p>k + r(m-t)</p>

<p>k is the amount you must already pay for t minutes, while (m-t) denotes the remaining minutes for which you must pay at a rate r (thus r is multiplied by m-t minutes). </p>

<p>Setting this equation equal to 1000, you can find the total number of minutes m.</p>

<p>k + r(m-t) = 1000
r(m-t) = 1000-k
(m-t) = (1000-k)/r
m = (1000-k)/r + t</p>

<p>So the total number of minutes is (1000-k)/r + t, or choice d.</p>

10

<p>hmmmm i think you guys are probally compounding on an incorrect answer see if it is k cents for firs t minutes that tells me this (1000-k*t)/r + t most of your logic is right but this is just my opnion.
Math:800</p>