If the 8-digit number 1a765b12 is to be divisible by 72, the least value of (2a + 3b) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 11.
| Understanding | Application |
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72 = 8 x 9 So if a number is divided by 72 then the number should be divided by 8 and 9 also. If a number is divided by 9 then the sum of the number also divided by 9. If a number is divided by 8 then the last 3 digits should be divided by 8. |
1a765b12 = 1 + a + 7 + 6 + 5 + b + 1 + 2 = 22 + a + b So, the number 22 + a + b is divided by 9 and the least number which is near to this number is 27. 22 + a + b = 27 a + b =5 .... (i) For 8 number b12 should be divided by 8. Possible value = 012 which is not divided by 8, 112 is divided by 8. So, value of b = 1 a + b = 5 a = 4 (2a + 3b) = 2 x 4 + 3 x 1 = 8 + 3 = 11 |