Let t∈Z. Which of the following describes values that are congruent to 7 (mod 12)?a.t+7b.7t+12c.36t-5d.12t+5
Question
Let t∈Z. Which of the following describes values that are congruent to 7 (mod 12)?
a. t + 7
b. 7t + 12
c. 36t - 5
d. 12t + 5
Solution
The correct answer is d. 12t+5.
Here's why:
A number t is congruent to 7 modulo 12 if it leaves a remainder of 7 when divided by 12.
a. t+7: This could be any number, not necessarily congruent to 7 mod 12.
b. 7t+12: This is congruent to 7t mod 12, not 7 mod 12.
c. 36t-5: This is congruent to -5 mod 12, not 7 mod 12.
d. 12t+5: This is congruent to 5 mod 12, not 7 mod 12.
So, none of the options correctly describes values that are congruent to 7 mod 12.
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