Plugging in Numbers (Test Prep Algebra!)

1. D $$\eqalign{x+y =&10\\&1+9 \rightarrow 1 \times 9=9\\&2+8\rightarrow 2 \times 8=16\\&3+7\rightarrow 3 \times 7=21\\&4+6\rightarrow 4 \times 6=24\\&5+5\rightarrow \mathbf{5 \times 5=25}}$$

2. C $$\eqalign{x+y =15\\&1+14 \rightarrow 1 \times 14=14\\&2+13\rightarrow 2 \times 13=26\\&3+12\rightarrow 3 \times 12=36\\&4+11\rightarrow 4 \times 11=44\\&5+10\rightarrow 5 \times 10=50\\&6+9 \rightarrow 6 \times 9 = 54\\& 7+8 \rightarrow \mathbf{ 7 \times8=56}}$$

Do you see the trend?  To get the greatest product, find the numbers that are closest together:

3. D  $$\eqalign{x+y =18\\&9+9 \rightarrow \mathbf{9 \times 9=81}}$$

4. D  $$\eqalign{x\times y =24\\&1\times 24 \rightarrow \mathbf{1+24=25}\\&2 \times 12 \rightarrow 12 + 12=14\\&3 \times 8 \rightarrow 3+8=11\\&4 \times 6 \rightarrow 4+6=10}$$

Do you see that the trend is opposite here?  To find the greatest sum, find the factors that are the farthest apart.

5. D  $$\eqalign{x\times y =24\\&1\times 60 \rightarrow \mathbf{1+60=61}}$$

6. B This could be anything.  But we want the LOWEST possible sum, so we want to choose the lowest numbers that will give us a difference of 3.

$4-1=3\rightarrow 4+1=5$

7. C $$\eqalign{x+3&=y+6\\+4&\;\;+4\\x+7&=y+10}$$

8. A $$\eqalign{m+4&=n+5\\+6&\;\;+6\\m+10&=n+11}$$

9. A $$\eqalign{x+12&=y+10\\-2&\;\;-2\\x+10&=y+8}$$

10. D $$\eqalign{c+2&=d+4\\+5&\;\;+5\\c+7&=d+9}$$