Question : If the seven-digit number 52A6B7C is divisible by 33, and A, B, and C are primes, then the maximum value of 2A + 3B + C is:
Option 1: 32
Option 2: 23
Option 3: 27
Option 4: 34
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Correct Answer: 23
Solution : 5 + 2 + A + 6 + B + 7 + C = 20 + A + B + C Possible values of (A + B + C) = 1, 4, 7, 10, 13, 16, 19, 22, 25 Again, 5 + A + B + C – 2 – 6 – 7 = 0 or Multiple of 11 ⇒ 5 + A + B + C – 15 = 0 or Multiple of 11 From the above possible values, for (A + B + C) = 10 we get 0 So, A + B + C = 10 Now, If A = 5, B = 3, C = 2 ⇒ 2A + 3B + C = 10 + 9 + 2 = 21 If A = 3, B = 5, C = 2 ⇒ 2A + 3B + C = 6 + 15 + 2 = 23 If A = 3, B = 2, C = 5 ⇒ 2A + 3B + C = 6 + 6 + 2 = 17 If A = 2, B = 5, C = 3 ⇒ 2A + 3B + C = 4 + 15 + 3 = 22 Hence, the correct answer is 23.
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Question : A six-digit number is divisible by 33. If 54 is added to the number, then the new number formed will also be divisible by:
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 7
Question : If the nine-digit number 3422213AB is divisible by 99, then what is the value of 2A + B?
Option 1: 11
Option 2: 12
Option 3: 10
Option 4: 13
Question : If a 10-digit number 75462A97B6 is divisible by 72, then the value of $\sqrt{8 A-4 B}$ is:
Option 1: $\sqrt{30}$
Option 2: $\sqrt{27}$
Option 3: $\sqrt{21}$
Option 4: $\sqrt{28}$
Question : If the four-digit number 463y is divisible by 7, then what is the value of y?
Option 1: 4
Option 2: 6
Option 3: 3
Option 4: 5
Question : If a nine-digit number 789x6378y is divisible by 72, then the value of xy is:
Option 1: 10
Option 3: 8
Option 4: 15
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