Difference between revisions of "2014 CEMC Gauss (Grade 8) Problems/Problem 6"
(I hate doing problems like this, but yea) |
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<math>y = \boxed {\textbf {(A) } 45}</math> | <math>y = \boxed {\textbf {(A) } 45}</math> | ||
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| + | ~anabel.disher | ||
| + | ==Solution 3 (answer choices)== | ||
| + | We can notice that <math>5y - 100 = 125 > 0</math>. This means the answer for <math>y</math> cannot be less than <math>0</math>, eliminating choices D and E. | ||
| + | |||
| + | We can now try <math>45</math> since it is the median of the answer choices (excluding the eliminated choices) and then check whether or not the value found for <math>5y - 100</math> is too large, too small, or is correct. This gives: | ||
| + | |||
| + | <math>5 \times 45 - 100 = 225 - 100 = 125</math> | ||
| + | |||
| + | This is equal to <math>125</math>. Thus, the answer is <math>\boxed {\textbf {(A) } 45}</math>. | ||
~anabel.disher | ~anabel.disher | ||
Latest revision as of 14:30, 29 April 2025
Problem
The value of 
that satisfies the equation 
is
Solution 1
Adding 
to both sides, we get:
~anabel.disher
Solution 2
All of the terms as well as the coefficient of is divisible by 
. Dividing both sides by , we get:
~anabel.disher
Solution 3 (answer choices)
We can notice that 
. This means the answer for cannot be less than 
, eliminating choices D and E.
We can now try 
since it is the median of the answer choices (excluding the eliminated choices) and then check whether or not the value found for 
is too large, too small, or is correct. This gives:
This is equal to 
. Thus, the answer is 
.
~anabel.disher
