Question

The sum of p consecutive positive integers is 45. What is the value of p?

(1) p is even.
(2) $p<9$.

• A. 2
• B. 4
• C. 6
• D. cannot be determined

Answer 1

The correct option is D

cannot be determined

Sum of first ten 10 consecutive natural numbers is 45 (p=10)
Also, the sum of 14+15+16 = 45 [$\frac{45}{3}$= (15)] (p=3)
Sum of 22+23 = 45 [$\frac{45}{2}$=22.5] (p=2)
Sum of 5, 6, 7, 8, 9, 10 = 45 [$\frac{45}{6}$=7.5] (p=6)
Thus, using both statements also, the answer cannot be determined.

Alternate Method:
$\frac{p}{2}(2a+p-1)=45$
Now, possible values of p are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Out of these, two values of p can be considered - 2 and 6.
Thus, the answer cannot be determined.