Alexey Z. answered 07/17/26
Experienced SAT Tutor Substantially Improving Student's Test Score
[NOTE 1: My tutoring is highly individualized. My multi-strategy problem solving approach leads to best results with fine-tuning to individual student’s weaknesses and strengths.]
[NOTE 2: Among many other things I teach, is using observation-reading-based shortcuts. This word problem calls for that, especially so, as we are talking about taking the SAT Test. Time-management skills are paramount in this timed test. Developed skills to spot a shortcut can be, and will be, the deciding factor on the Test taking day.]
[NOTE 3: On Wyzant, I am not in the business of solving problems. I am supposed to pass to students my knowledge in skills. I teach getting to the core of a problem. What a word problem means in Math, operations, properties, etc.? Read attentively the text to get that idea. That leads to shortest reasoning and procedural fluency. Developed number sense is always helpful]
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1. [Observation!]
This problem is about a single operation, division with remainder!
12 / 0.60 = 2 * (6 / 0.60) = 20 (exactly, with no remainder)
In this multiple choice, mark: B. 20 apples, $0.00 left
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2. [Observation!]
In this very specific case, where three of the four choices have "remainder" or "excess" of exactly $0.60, the price of one apple, so John may have more or less apples. So choices A), C), D) are invalid.
In this multiple choice, mark: B. 20 apples, $0.00 left
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3. [Back to tutoring]
Note, that in multiple choice, putting down text in solutions #1 and #2 is unnecessary. With the respective mental observations,
#1. [Observation. Mental math 12 / 0.60 = 2 * (6 / 0.60) = 20]. Mark B).
#2. [Observation.] Mark B).
If Observation $2 was made, that would be the fastest way to get the right choice in this very special case. Practice this!
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When solving this problem with a student, are there opportunities to give more?
What if that was an open question?
The elimination method of Solution #2 would not be available! Solution #1 would be the fastest one.
What if mathematical reasoning and complete answers were requested?
Practice precise reasoning and complete answers. Reasoning, based on observations, is presented in the Solutions #1 and #2. (Complete) Answer must be sharp to the point of the question(s).
Answer:
He can buy 20 apples.
He will have no money left.