Problem of the Day


If f(n)=1154\cdot1156 for some integer, n, which of the following expressions could be equal to f(n)?

A. 3n-2
B. 5n-2
C. 5n+3
D. 7n-2
E. 11n+10

Reveal Answer

Answer

[latexpage]

E. $11n+10$

See the Solution

Solution

[latexpage]

$1154\cdot1156=(1155-1)(1155+1)=1155^2-1$. Thus, this product is one less than a multiple of $1155$.

Also, note that $1155=3\cdot5\cdot7\cdot11$, so the product is also one less than a multiple of 3, 5, 7, and 11. Answer choice E is 10 more than a multiple of 11, which is the same as being one less than a multiple of 11. For example, 21 is one less than a multiple of 11 (22), and ten more than a multiple of 11 (11). All of the other answer choices are not consistent with the fact that the product is one less than a multiple of 3, 5, 7, and 11, so ‘E’ is the answer.


Comments are closed.