Free Practice Question
PS · Problem Solving
705-805
Divisibility/Multiples/Factors
Lowering which of the following numbers by one will result in the least decrease of n?
Answer Choices
Correct answer marked belowA
17
B
19
C
23
29
Correct
E
31
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Explanation
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Official Explanation
Official
The answer is D.
When faced with huge numbers and/or exponents, use smaller numbers and/or exponents that follow the prompt's pattern. If we are looking for the least change (decrease), we need the value that has the most weight to be decreased a little.
To find the smallest decrease in , we need the value that has the most weight to be decreased a little.
• Changing a small number such as 2, to 1, cuts the product in half.
• Changing a larger number such as 4, to 3, decreases the product by .
(And that which gets decreased must be a factor, not the exponent. Decreasing the exponent by 1, see below, is not decreasing by a little.)
Think of . That equals 196.
By definition, an exponent yields exponential increase in value. Decreasing the exponent will yield an exponential decrease - not likely to be the least change.…
When faced with huge numbers and/or exponents, use smaller numbers and/or exponents that follow the prompt's pattern. If we are looking for the least change (decrease), we need the value that has the most weight to be decreased a little.
To find the smallest decrease in , we need the value that has the most weight to be decreased a little.
• Changing a small number such as 2, to 1, cuts the product in half.
• Changing a larger number such as 4, to 3, decreases the product by .
(And that which gets decreased must be a factor, not the exponent. Decreasing the exponent by 1, see below, is not decreasing by a little.)
Think of . That equals 196.
By definition, an exponent yields exponential increase in value. Decreasing the exponent will yield an exponential decrease - not likely to be the least change.…
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What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.
Details
Difficulty
705-805
Type
PS
Category