Problems on Numbers Quiz Set 002

Let the number be N. Then ${3/17}$ x N = 9. ⇒ N = 9 x ${17/3}$ = 51

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 18$ ⇒ $b(k + 1) = 18$. Similarly, from the difference we can obtain $b(k - 1) = 8$. Dividing we get ${k + 1}/{k - 1} = 18/8$. By componendo and dividendo, $k = {18 + 8}/{18 - 8}$ = ${13/5}$, which is same as: $2{3/5}$.

Let the numbers be 2n - 3, 2n - 1 and 2n + 1. The sum is 3(2n - 1) = 3 x middle. We are given 3 x middle = -2445, ⇒ middle = $-2445/3$, i.e., middle = -815.

If the above number has to be divisible by 3, the sum of the digits, i.e., 7 + 7 + x + 7 + 5 + 3 + 3 + 4 + 2 + 3, should be divisible by 3. So we can see that $x + 41$ should be divisible by 3. By inspection, x = 1.

Odd numbers are in an AP. First term $a = -1385$, common difference $d = 2$, the last term $t_n$ is given as 813. By the AP formula, $813 = -1385 + (n - 1) × 2$ ⇒ $n = 1 + {{813 - (-1385)}/2} = 1100$.