Math problems

Test Preparation SAT Preparation
1

<ol>
<li>What are all values of x for which the absolute value of (x-8) is greater than 6.
The correct answer is x is less than 2 or x is greater than 14</li>
</ol>

<p>Set A =(1,2,3,4,5,6)
Two numbers from set A are selected at arandom without replacement and their sum recorded. How many different sums are possible?
The answer is nine.</p>

<p>pq +rs+ tu
The expression above represents an odd integer. At most, how many of the integers p,q,r,s,t and u could be even.
The correct answer is 4.</p>

<p>The remainder when n is divided by 8 is 5. What is the remainder if 2n is divided by 8.
The answer is 2.</p>

<p>On a blueprint of a building, o.5inches represents 5 feet. If the area of a square room in this building is 100 square feet, what is the room’s area, in square inches, as represented on the blueprint?</p>

<p>I would like to know how to work these problems</p>

2

<ol>
<li>|x-8|>6. To solve this, you need to know how to split the inequality. This is what is becomes after you split:</li>
</ol>

<p>x-8>6
AND
x-8<-6</p>

<p>One inequality remains the same (though without absolute value signs), and the other is flipped around, with the number (on the right) multiplied by -1.</p>

3

<p>For the remainder question, pick an arbitrary n.</p>

<p>You know n/8 has a remainder of 5. Pick n=13, because 13/8 has a remainder of 5. Then, divide 2n (2*13) by 8. 26/8 is 3, remainder 2.</p>

4

<p>

</p>

<p>5 feet is represented by 0.5 inches
So, 1 feet is represented by 5/0.5 or 0.1 inches</p>

<p>The building is 100 square feet, which we can write as 10ft<em>10ft
Now convert 10ft to inches 10</em>0.1inches = 1 inch</p>

<p>So 100 squareft= 10ft<em>10ft = 1inch</em>1inch = 1 square inch on the blue print</p>

5

<p>For the Set A question:</p>

<p>1+2 = 3</p>

<p>3+2 = 5</p>

<p>4+3 = 7</p>

<p>5+4 = 9</p>

<p>5+6 = 11</p>

<p>1+5 = 6</p>

<p>2+6 = 8</p>

<p>3+1 = 4</p>

<p>6+4 = 10</p>

<p>There are total of 9 different sums.</p>

6

<p>For the second question, think of it like this. What are the two situations in which the sum or product of two numbers is odd? This first situation is that odd=even+odd and the second situation would be that odd=odd*odd. </p>

<p>Keeping this is mind, let’s try and make all 6, (pqrstu), equal even.
Thus, pq=e<em>e(even</em>even)–>even
rs=e<em>e–>even
tu=e</em>e–>even, now, pq+rs+tu=(e+e)+e=e+e=e. Since, the question says the final sum is odd(o), 6 cannot be right. </p>

<p>Now, let’s move on to 5 even numbers and one odd number(assume that this sole odd number is p). Then you would have</p>

<p>pq=o<em>e–>e
rs=e</em>e–>e
tu=e*e–>e</p>

<p>Now, pq+rs+tu=(e+e)+e as before and so the final result is e+e–>e. Again, since the final sum is odd, 5 cannot be the right answer. Now on to 4 even numbers and 2 odd numbers(we will assume p and q to be odd).</p>

<p>pq=o<em>o–>o (in accordance to the very first forumula I stated).
rs=e</em>e–>e
tu=e*e–>e</p>

<p>Now, pq+rs+tu= (o+e)+e–>o+e=odd. Thus, 4 even numbers is the right answer.</p>

<p>As for the remainder question, a simple plug-in method would be efficient. However, it is still necessary to know the algebra beyond it for potentially harder questions.</p>

<p>The first sentence of the question can be represented as follows–> n=8x+5. Now, its asking what is the remainder when 2n is divided by 8? So, simply multiply n by 2 on both sides of the equations as follows–> 2n=16x+10. Then, since 16x+10 is divided by 8, the following equation can be formed–> 16x+10=8y+r where r is the remainder(which is unknown know) and 8y is any multiple of 8. Now, do the following</p>

<p>16x+10=8y+r
8(x+1)+2=8y+r. Thus, x+1=y and 2 is equal to the remainder. Hope I helped.</p>

7

<p>Thank you all so much for your assistance.</p>