I need help with a few problems...

Test Preparation SAT Preparation
1

<li>The sum of eleven different integeres is zero. What is the least number of these integers that MUST be positive?</li>
</ol>

<p>(A) None
(B) One
(C) Five
(D) Six
(E) Ten</p>

<p>For this q, I have no idea what the answer is…</p>

<li>In a certain game, each token has one of three possible values: 1 point, 5 points, or 10 points. How many different combinations of these token values are worth a total of 17 points?</li>
</ol>

<p>(A) Two
(B) Three
(C) Four
(D) Five
(E) Six</p>

<p>The answer is (E). It’s so vexing that I’m getting combination questions wrong, but how is this Q approached? Do I do the nCr thing? For all questions like this, which ask for diff. combinations, what do I do?</p>

<li>2, -4, 8,…</li>
</ol>

<p>The first term of the sequence above is 2, and every term after he first term is -2 times the preceding term. How many of the first 50 terms of this sequence are less than 100?</p>

<p>(A) 22
(B) 25
(C) 28
(D) 30
(E) 37</p>

<p>Isn’t there a formula for this Q?</p>

<li>A cube with volume 8 cubic centimeters is inscribed in a sphere sothat each vertex of the cube touches the sphere. What is the length of the diamter, in centimeters, of the sphere?</li>
</ol>

<p>(A) 2
(B) SQRT 6 (appox. 2.45)
(C) 2.5
(D) 2 SQRT 3 (approx. 3.46)
(E) 4</p>

<p>???</p>

<hr>

<li>In the novel, Jane Eyre must make many difficult choices, like when she forces herself to leave the house of Mr. Rochester, the man she loves.</li>
</ol>

<p>(A) like when she forces
(B) and as an example, when she forces
(C) for example, by forcing
(D) as exemplified by when she forces
(E) including forcing</p>

<p>I knew the answer was E, because I’ve seen this type of Q several times. But why not C or D? Why is E grammatically correct?</p>

<li>Nicknamed the supergrain of the future, quinoa is a complete protein, one that contains all the necessary amino acids and is high in fiber.</li>
</ol>

<p>(A) protein, one that contains all the necessary amino acids and is
(B) protein, it contains all the necessary amino acids and is
(C) protein, and containing all the necessary amino acids in addition to being
(D) protein, that contained all the necessary amino acids and also is
(E) protein; thus containing all the necessary amino acids and being also</p>

<p>I narrowed in down to (A) and (E), and the answer was A, I believe. Why?</p>

<p>Thanks a ton.</p>

2

<p>..........................</p>

3

<p>
[quote]
12. The sum of eleven different integeres is zero. What is the least number of these integers that MUST be positive?</p>

<p>(A) None
(B) One
(C) Five
(D) Six
(E) Ten

[/quote]
</p>

<p>i am pretty sure the answer is five. you have to remember that zero is an integer. so if you add -5+-4+-3+-2+-1+0+1+2+3+4+5, then it equals 0, and there are five positive numbers.</p>

<p>
[quote]
13. In a certain game, each token has one of three possible values: 1 point, 5 points, or 10 points. How many different combinations of these token values are worth a total of 17 points?</p>

<p>(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

[/quote]
</p>

<p>no, you dont have to do the ncr thing. when i do stuff like this, i just write it out.</p>

<p>:10 + 5 + 1 + 1
:5 + 5 + 5 + 1 + 1
:10 + 7 1s
:17 1s
:5 + 12 1s
:5 + 5 + 7 1s</p>

<p>and thats six.</p>

<p>
[quote]
15. 2, -4, 8,...</p>

<p>The first term of the sequence above is 2, and every term after the first term is -2 times the preceding term. How many of the first 50 terms of this sequence are less than 100?</p>

<p>(A) 22
(B) 25
(C) 28
(D) 30
(E) 37

[/quote]
</p>

<p>ok, when i do these, i always extend the chain of numbers out to about ten terms so that i can clearly see a pattern. so 2, -4, 8, -16, 32, -64, 128, -256, 512, -1024. so you can see that the even terms (second, fourth, sixth, eighth, and so on) are all negative. so they are less than 100. how many terms out of 50 are negative? 25, because half are odd and half are even. so you can eliminate A and B because your answer has to be more than 25. your answer is the 25 negative terms, plus 2, 8, and 32. so the answer is C, 28.</p>

<p>
[quote]

  1. In the novel, Jane Eyre must make many difficult choices, like when she forces herself to leave the house of Mr. Rochester, the man she loves.</p>

<p>(A) like when she forces
(B) and as an example, when she forces
(C) for example, by forcing
(D) as exemplified by when she forces
(E) including forcing

[/quote]
</p>

<p>yeah, e would be correct. a lot of times the most concise answer is correct on the sat.</p>

<p>
[quote]

  1. Nicknamed the supergrain of the future, quinoa is a complete protein, one that contains all the necessary amino acids and is high in fiber.</p>

<p>(A) protein, one that contains all the necessary amino acids and is
(B) protein, it contains all the necessary amino acids and is
(C) protein, and containing all the necessary amino acids in addition to being
(D) protein, that contained all the necessary amino acids and also is
(E) protein; thus containing all the necessary amino acids and being also

[/quote]
</p>

<p>A is correct. the "thus" and the "being also" in E is wrong. only a few choices with "being" will be correct on the sat.</p>

<p>hope this helps.</p>

4

<p>ok for the one that says: The sum of eleven different integers is Zero. What is the least number of these integers that must be positive? </p>

<p>THe answer is B) One because even though you can have all negatives, -4,-5,-1,-2, you can cancel it out with one bigger but positive number +12 to get 0</p>

5

<p>oh, i read that as consecutive integers. oops.</p>

6

<ol>
<li>A cube with volume 8 cubic centimeters is inscribed in a sphere sothat each vertex of the cube touches the sphere. What is the length of the diamter, in centimeters, of the sphere?</li>
</ol>

<p>(A) 2
(B) SQRT 6 (appox. 2.45)
(C) 2.5
(D) 2 SQRT 3 (approx. 3.46)
(E) 4</p>

<p>The answer is D-you just need to recognize that the diameter of the sphere is equal to the diagonal of the cube. The diameter of a sphere is the longest line segment that can be drawn between two points on the surface; likewise, the longest distance between two points on a cube is the diagonal from one corner to the opposite.</p>

<p>To find the length of the diagonal of the cube (which is also the diameter of the sphere)-inscribed means that the cube touches the cube only 8 times-one for each vertex.</p>

<p>The volume of the cube is 8, and the volume formula for a cube is V=s^3, where s is the side. So, you know that s=2.</p>

<p>Draw a triangle, using 2 as one side and the diagonal as another and connect the base. The base is simply the diagonal of a square, which is 2root2.</p>

<p>The triangle formed is a right triangle-meaning you can use the pythagorian theorem to solve for x. This yields 2root3, which is your answer.</p>