Difference between revisions of "2000 CEMC Gauss (Grade 8) Problems/Problem 9"
(Created page with "==Problem== Of the following five statements, how many are correct? <math>\text{(i) } 20\% \text{ of } 40 = 8 \qquad \text{(ii) } 2^{3} = 8 \qquad \text{(iii) } 7 - 3 \time...") |
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We can also use the fact that <math>a^{2} - b^{2} = (a - b)(a + b)</math>, or [[difference of squares]], to verify <math>3^{2} - 1^{2}</math>: | We can also use the fact that <math>a^{2} - b^{2} = (a - b)(a + b)</math>, or [[difference of squares]], to verify <math>3^{2} - 1^{2}</math>: | ||
| − | <math>3^{2} - 1^{2} = (3 | + | <math>3^{2} - 1^{2} = (3 + 1)(3 - 1) = 4 \times 2 = 8</math> |
The answer is <math>\boxed {\textbf {(D) } 4}</math>. | The answer is <math>\boxed {\textbf {(D) } 4}</math>. | ||
~anabel.disher | ~anabel.disher | ||
| + | {{CEMC box|year=2000|competition=Gauss (Grade 8)|num-b=8|num-a=10}} | ||
Latest revision as of 12:51, 20 October 2025
Problem
Of the following five statements, how many are correct?
Solution 1
We can just simply verify whether or not each statement is true, and count how many are true:
, so the first statement is true
, so the second statement is true
, so the third statement is false
, so the fourth statement is true
, so the last statement is true
Four of these are correct. Thus, the answer is 
.
~anabel.disher
Solution 1.5
We can also use the fact that 
, or difference of squares, to verify 
:
The answer is .
~anabel.disher
| 2000 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| CEMC Gauss (Grade 8) | ||
