<p>Hello, I was doing some practice for the SATs, and I had a few math questions. If anyone could help me and explain them, I would really appreciate it. </p>
<p>1) if the difference of two numbers is less than the sum of the numbers, which of the following must be true?
(a) neither number is positive
(b) at least one of the numbers is positive
(c) both numbers are positive</p>
<p>The answer for this question is (c), but I'm not sure why. If the numbers were -10 and 1 for example, it would not work.</p>
<p>2) When it is noon EST in New York City, it is 9 am PST in San Francisco. A plane took off from NYC at noon EST and arrived in San Francisco at 4 pm PST on the same day. If as second plane left San Francisco at noon PST and took exactly the same amount of time for the trip, what was the plane's arrival time (EST) in NYC?
(a) 10:00 PM EST
(b) 9:00 PM EST
(c) 7:00 PM EST
(d) 6:00 PM EST
(e) 4:00 PM EST</p>
<p>3) Each term of a sequence is greater than the term before it. The difference between any two consecutive terms in the sequence is always the same number. If the third and sixth terms of the sequence are 17 and 77, respectively, what is the eighth term?</p>
<p>Given:
When it is noon (EST) in New York City, it is 9.00 a.m. (PST) in San Francisco</p>
<p>A plane took off from New York City at noon EST and arrived in San Francisco at 4.00 p.m. on the same day</p>
<p>A second plane left San Francisco at noon PST and took exactly the same amount of time for the trip</p>
<p>To find:
The second planes arrival time (EST) in New York City</p>
<p>Solution:
When it is 9:00 a.m. PST, it is 12:00 noon EST. </p>
<p>The time difference from PST to EST is +3 hours. </p>
<p>A plane took off at 12:00 noon EST and arrived at 4:00 p.m. PST. </p>
<p>4:00 p.m. PST would be 4 + 3 = 7:00 p.m. EST.</p>
<p>The time taken would be from 12:00 noon to 7:00 p.m., which is 7 hours.</p>
<p>A second plane took off at 12:00 noon PST and took the same amount of time as the first plane, which is 7 hours. It would then be arriving at 7:00 p.m. PST. </p>
<p>7:00 p.m. PST would be 7 + 3 = 10.00 p.m. EST</p>
<ol>
<li><p>If a-b < a+b, then -b < b → 0 < 2b → b > 0. You cannot conclude anything about a. The answer is B.</p></li>
<li><p>Sequence is arithmetic with common difference (77-17)/3 = 20. The eighth term is 77+20+20 = 117.</p></li>
</ol>
<p>For the first question, I think it’s just a badly worded sentence. I think what the writers meant by “difference” was the larger number subtracted by the smaller number.</p>
<p>Actually I just realized, it’s not badly worded at all. It doesn’t matter whether the “difference” is the larger # minus the smaller #, or vice versa. That’s why it says “at least one of the numbers is positive.”</p>