The sum of half, one third, one fourth of a number exceeds the number by 18. The number is ?
1). 144
2). 152
3). 216
4). 200
⇒ Let the number be x,
$(\Rightarrow {\rm{\;}}\frac{x}{2} + \frac{x}{3} + \frac{x}{4}\; = \;x + 18)$
⇒ (6x + 4x + 3x)/12 = x + 18
⇒ 13x/12 = x + 18
⇒ 13x = 12x + 216
∴ x = 216
1. Find the value of (13 – 12 + 23 – 22 + 33 – 32 + ….. + 103 – 102).
2. 2122 + 462 + 842 + 464 + 2130 is divisible by which one of the following integers?
3. In how many different ways can the letters of the word FORMULATE be arranged ?
4. If (47)² is added to the square of a number the answer thus obtained is 2290. What is the number ?
5. Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank?
6. What is the least common multiple of 16, 40 and 64?
9. The sum of a non - zero number and twenty times its reciprocal is 9. What is the number?