Math Q's

Test Preparation SAT Preparation
1

<p>1) If x is a positive number, which of the following
expressions could have a negative value?
(A) (x + 2)(x + 2)
(B) (x + l)(x + 2)
<a href="C">b</a> (x-2)(x-2)<a href="D">/b</a> x(x + 2)
(E) x(x-2)</p>

<hr>

<p>2) The five digits 1,2,3,4, and 5 are used to form
five-digit numbers in which no digit is repeated. How
many such five-digit numbers greater than 40,000 are
possible?
**I got the right answer but I am looking for a quick way to do this?<a href="A">/b</a> 24
<a href="B">b</a> 48<a href="C">/b</a> 64
(D) 96
(E) 120</p>

<hr>

<p>3) 3,5,7,10,x
A number will be chosen at random from the five
numbers listed above.The probability is —that the
number chosen will be an even number that is a
multiple of 5. Which of the-following could be the
value of x ?
<a href="A">b</a> 15<a href="B">/b</a> 20
(C) 30
(D) 40
(E) 130</p>

<hr>

<ol>
<li>The surface of a 3-dimensional solid consists of faces,
each of which has the shape of a polygon. What is the
least number of such faces that the solid can have?
(A) 2
(B) 3
<a href="C">b</a> 4<a href="D">/b</a> 5
(E) 6</li>
</ol>

<hr>

<ol>
<li>At a party, there was one pizza for every 3 people,
one salad for every 6 people, and one cake for every
8 people. If the total number of pizzas, salads, and
cakes was n, then, in terms of n, how many people
were at the party?
<a href="A">B</a> (8/5)n<a href="B">/B</a> (3/2)n
(C) (7/4)n
(D) 2n
(E) (9/4)n</li>
</ol>

<hr>

<ol>
<li>(x - a)^5 = (x - a)k^4</li>
<li>In the equation above, x and k are positive numbers
and 0 < a < x. Which of the following must be
equal to x ?
(A) k
(B) k - a
<a href="C">b</a> k + a<a href="D">/b</a> a^4
(E) k^4 +a</li>
</ol>

<hr>

<ol>
<li>
DIAGRAM: <a href="http://i44.tinypic.com/10dcxnm.jpg%5B/url%5D"&gt;http://i44.tinypic.com/10dcxnm.jpg&lt;/a>
The pattern above is formed by four tiles measuring
2 inches by 1 inch and one square tile with side 1 inch.
If a rectangular section of floor measuring 24 inches
by 15 inches is to be covered with this pattern and no
extra space is needed for adhesive material, how many
tiles will be used?
(A) 40
(B) 80
(C) 160
<a href="D">b</a> 200<a href="E">/b</a> 240</li>
</ol>

<hr>

<p>Please explain these to me and some tips on solving them quicker would also be very helpful!!</p>

2

<h2>Some more</h2>

<p>If |x| + |y|=6, what is the least value possible
for x + y ?
(A) -6
(B) -3
<a href=“C”>B</a> 0<a href=“D”>/B</a> 2
(E) 6</p>

<hr>

<p>Gift certificates were sold by an ice-cream parlor in the
month of July. Each gift certificate was worth either
$2, $3,or $5.Twice as many $2 gift certificates were
sold as $3 gift certificates, and twice as many $3gift
certificates were sold as$5 gift certificates. The total
value of all the gift certificates sold was $57. How
many $3 gift certificates were sold in July?
Answer is 6</p>

<hr>

<p>If (a - 10b)^2 = a2 100b^2, what is the value
of a^2*b^4.
Answer is 0</p>

3

<p>For no.1 i would skim through the answer choices and look for minus signs. Choices narrowed down to C and E. I would choose a positive number that’s really small since subtraction is involved in both of the narrowed down choices. So if i choose 0.5 I get C-positive and E-negative. So the answer is E. </p>

<p>For no. 2 since the combination has to bigger than 40000, it has to begin with either 4 or 5 as the beginning digit. Also we know that it will be a 5 digit figure like xxxxx. The quick way to do this is to notice that without the first digit, we will have 4 remaining digits to deal with. So to find the number of all combinations beginning with a “5” do a 4! (a 4 factorial is 4<em>3</em>2<em>1). Okay, now to find the number of combinations beginning with a “4” repeat the same step. okay so now you have 2 factorials of four. Add them, because you want the total number of combinations you can make out of rearraging the 5 digits with “4” or “5” in the beginning. so 2</em>(4!)=48</p>

<p>I don’t understand the 3rd question…</p>

<p>For no. 4… Figure out what the smallest possible polygon is…a triangle. Okay now, picture a few triangles in your mind and think how many triangles you could use at minimum to make an ENCLOSED (solid) figure. You’d probably think about a pyramid and it’s 5 faces including the bottom. But the pyramid could do without a face and still be a solid figure. You need to do this in your head. </p>

<p>I can’t do 5 or 6. </p>

<p>For no. 7… Find the area of the floor (24<em>15=360 square inches). Area of figure given. It’s a square so just square a side ([3^2]=9 square inches). Okay, now find out how many 9 square inches you can fit into a 360 square inch area (360/9=40). You know that in each 9 square inch area you have 5 tiles- the question already tell you that. You can fit 40 of those patterns in the entire floor and since each of the 40 patterns consist of 5 tiles, multiply 40 by 5 to find the total number of tiles required (40</em>5=200).</p>

<p>By the way, where are these questions from?</p>

4

<p>What book is this from?</p>

5

<p>Thanks packrat.</p>

6

<p>And whoops, I labeled the wrong answer in #1, it is E.</p>

7

<p>

</p>

<p>(C) is clearly not the answer. If (x-2) is negative, (x-2)(x-2) is positive. If (x-2) is positive, (x-2)(x-2) is positive. Thus, (x-2)(x-2) could not be negative.</p>

<p>The answer is (E). If X=1, X<em>(X-2) is (1)</em>(-1) = -1.</p>

<p>

</p>

<p>The digits cannot be repeated, so you can just multiply the amount of choices you have as you gradually go from the first number to the last number:</p>

<p>2 * 4 * 3 * 2 * 1 = 48
The first digit is 2 because it can only be 4 and 5; anything less would yield a number smaller than 40,000 (e.g., 35,421). In other words, you only have 2 numbers to choose from for your first digit. The second digit can be any of the 4 remaining numbers. The third digit can be any of the 3 remaining numbers. And so on.</p>

<p>

</p>

<p>You typed this question incorrectly. What is the probability? If it is 1/5, then X must NOT be a multiple of 5, which would mean that there is only 1 out of the 5 numbers that is an even number that is a multiple of 5. Every other answer choice is an even number that is a multiple of 5. </p>

<p>

</p>

<p>First of all, ALL of these questions are not accurate SAT questions. Do you really expect this type of problem to be on the test? Anyway, the 3D solid with the least amount of faces is a tetrahedron. Google it. The 2D polygon with the least amount of sides is a triangle, which has 3 sides, so a 3D solid cannot have 3 or fewer sides.</p>

<p>

</p>

<p>Find a common denominator:
3, 6, 9, 12, 15, 18, 21, 24
6, 12, 18, 24
8, 16, 24</p>

<p>One pizza for every 3 people -> 8 pizzas for every 24 people
One salad for every 6 people -> 4 salads for every 24 people
One cake for every 8 people -> 3 cakes for every 24 people</p>

<p>A total of 8+4+3=15 food items for every 24 people
Thus, the ratio of the number of food items to the number of people is 15:24.
If the number of food items is n, then the number of people must be 24/15=8/5</p>

<p>

</p>

<p>(x-a)^5 = (x-a)k^4
(x-a)(x-a)^4 = (x-a)k^4
(x-a)^4 = k^4
x-a = k
x = a + k</p>

<p>The information given is irrelevant. Just solve for x.</p>

8

<p>Wow thanks bandit you’re awesome!</p>

<p>As for the questions, YES they are SAT questions.
These questions are coming from 2005 PSAT Saturday version.</p>

9

<p>Wow. Maybe the PSAT is different, then? I don’t remember.</p>

10

<h2>Can someone explain these?</h2>

<p>If |x| + |y|=6, what is the least value possible
for x + y ?
(A) -6
(B) -3
<a href=“C”>b</a> 0<a href=“D”>/b</a> 2
(E) 6</p>

<hr>

<p>Gift certificates were sold by an ice-cream parlor in the
month of July. Each gift certificate was worth either
$2, $3,or $5.Twice as many $2 gift certificates were
sold as $3 gift certificates, and twice as many $3gift
certificates were sold as$5 gift certificates. The total
value of all the gift certificates sold was $57. How
many $3 gift certificates were sold in July?
Answer is 6</p>

<hr>

<p>If (a - 10b)^2 = a2 100b^2, what is the value
of a^2*b^4.
Answer is 0</p>

11

<p>If |x| + |y|=6, what is the least value possible
for x + y ?
(A) -6
(B) -3
(C) 0
(D) 2
(E) 6</p>

<p>I think the answer should be A. </p>

<p>because x can be -6 and y can be 0. or vice versa</p>

12

<p>aha! I copied the wrong answer again hah, i had it right originally, whoops.</p>

13

<h1>6 is trying to get you to plug in numbers.</h1>

<p>(x - a)^5 = (x - a)k^4
In the equation above, x and k are positive numbers
and 0 < a < x. Which of the following must be
equal to x ?
(A) k
(B) k - a
(C) k + a
(D) a^4
(E) k^4 +a</p>

<p>if 0 < a < x, then:
let a = 1
let x = 2</p>

<p>(x - a)^5 = (x - a)k^4
(2 - 1)^5 = (2 - 1)k^4
(1)^5 = (1)k^4
1 = k^4
k = 1</p>

<p>2 = 1 + 1
x = k + a</p>

<p>*on second thought, this would mean that the question would have to be more specific than “0 < a < x”</p>

14

<p>There are x numbers of $5 certificates, 2x numbers of $3 ones, and 4x number of $2 certificates- simply using the information given in the line “Twice as many $2 gift…$5 gift certificates” in reverse order. Total value= $57, therefore, ($5<em>x)+($3</em>2x)+($2*4x)=$57 … x=3 … so 2x=6</p>

<p>For the modulus question… I don’t get why the answer isn’t (A) :expressionless:
x, y pairs such as (-2, -4), (-3, -3), (-1, -5) etc satisfy the equation. If you added any one x,y pair you would get -6.
Edit: typo again?..lol</p>

15

<p>yea, packrat read up there ^^.</p>

<p>thanks for doing the other one though :)</p>