Subject: General Aptitude · Chapter: Number System · Exam: 2010 · Marks: · Difficulty:
The digits indicated by * in 3422213** so that this number is divisible by 99 are
(a)1, 9
(b)3, 7
(c)4, 6
(d)5, 5
Answer
Answer (as printed): A
Explanation
Let the unit's digit be x and ten's digit be y. Then, the number is 3422213yx. Also, 99 = (11 × 9), where 11 and 9 are co-primes. Since the given number is divisible by 9, it follows that (3 + 4 + 2 + 2 + 2 + 1 + 3 + y + x) = (17 + y + x) must be divisible by 9. So, y + x = 1 or y + x = 10. 42 Again, the given number is divisible by 11. So, (x + 3 + 2 + 2 + 3) – (y + 1 + 2 + 4) = x – y + 3 is either 0 or 11. \ (x – y + 3 = 0 or x – y + 3 = 11) ⇒ (y – x = 3 or x – y = 8) Now, (y + x = 1 and y – x = 3) ⇒ y = 2 and x = – 1. 9 (y + x = 1 and x – y = 8) ⇒ x = . 2 13 (y + x = 10 and y – x = 3) ⇒ y = . 2 (y + x = 10 and x – y = 8) ⇒ x = 9 and y = 1. Thus, x = 9, y = 1. So, the required number is 342221319.
Explanation as extracted from the printed page; notation may be imperfect.