Advanced MathVery hardConsecutive reciprocals summing to a fraction
Advanced Math practice question
The reciprocals of two consecutive positive integers have a sum of 5/6. What is the product of the two integers?
Answer: 6
1/n + 1/(n + 1) = 5/6 gives 6(2n + 1) = 5n(n + 1), so 5n² − 7n − 6 = (5n + 3)(n − 2) = 0 and n = 2; the integers are 2 and 3, with product 6.
Common wrong answers
- If you answered 2
- 2 is the smaller integer.
- If you answered 5
- 5 is the sum of the integers.
- If you answered 12
- 12 uses 3 and 4.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.