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𝟒(𝟐 𝟐 ) + 𝟔(𝟐) + 𝟏 𝟐+𝟐
= 𝟕. 𝟐𝟓 ✓
Which of the following is equivalent to the expression above?
A) 4(2)−2=6
“To the man with only a hammer, everything is a nail.” The Law of the Instrument is a cognitive bias that describes the tendency to overly rely on a familiar tool or approach, even when other options may be more effective—like PIYON!
2 2+5
B) 4(2)−
=7.71
3 2+2
C) 4(2)−2+
=6.75
𝟓 𝟐+𝟐
D) 𝟒(𝟐) − 𝟐 +
= 𝟕. 𝟐𝟓 ✓
Easy peasy nice and easy.
“Wait! Where did you get 2? Is this what the SAT wants you to do? What if x were 0.1234? I hate math!”
You hate math? Do you hate pushing buttons too? Unlikely, if you have a phone or computer or both 138 . You probably push buttons all day every day! This question just requires pushing buttons on a calculator if you plug in 2 for x . Where did you get 2? The question didn’t specify anything about the variable x . It’s just a placeholder. It didn’t say that it had to be greater than 100 or a negative integer or a decimal. So it can be anything: 2 is just a nice and neat number.
Is this what the SAT wants you to do?
1) Who cares what the SAT wants you to do? 2) It probably does not want you to plug in numbers.
Here is that quote again about the math section from the College Board. “You’ll answer questions that test your ability to solve problems involving algebra,” blah, blah, blah.
Solve problems involving algebra and solve problems with algebra aren’t quite the same thing. For the question we just solved, technically, the solution-pathway involves algebra, but you don’t have to solve it with algebra. There are other ways (we just used one), hence the title of this chapter: Algebra Alternatives.
“Will I get penalized if I solve things without algebra?” “The SAT doesn’t care what you do. PIYON. Algebra. Flip a coin 139 . Just get it right!”
138 By some estimates, people who do not work in technology, push from 3000 to 6000 buttons daily . 139 Please don’t do this.
139
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