Question : A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b =
2a, c = 2b, d = 2c. The pin is divisible by __________.
Option 1: 2, 3, and 5
Option 2: 2, 3, and 7
Option 3: 2, 3, and 13
Option 4: 2, 3, and 11

Question

Question : If $\frac{a}{1 - 2 a} + \frac{b}{1 - 2 b} + \frac{c}{1 - 2 c} = \frac{1}{2}$ , then the value of $\frac{1}{1 - 2 a} + \frac{1}{1 - 2 b} + \frac{1}{1 - 2 c}$ is:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4

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Answer 1

Correct Answer: 2, 3, and 13

Solution : Given, $b = 2 a, c = 2 b, d = 2 c$
Finding all the values in terms of $a$ .
⇒ $c = 2 b = 2 \times 2 a = 4 a$ ..............(1)
Similarly, $d = 2 c = 2 \times 4 a = 8 a$ ..............(2)
Now the pin is $a b c d$ ,
⇒ $a b c d = 1000 a + 100 b + 10 c + d$
⇒ $a b c d = 1000 a + 100 \times 2 a + 10 \times 4 a + 8 a$
$= 1000 a + 200 a + 40 a + 8 a$
⇒ $a b c d = 1248 a$
⇒ $a b c d = (2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 13)$
$∴$ the pin abcd is divisible by 2, 3, and 13.
Hence, the correct answer is 2, 3, and 13.

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Question : A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a, c = 2b, d = 2c. The pin is divisible by __________.Option 1: 2, 3, and 5Option 2: 2, 3, and 7Option 3: 2, 3, and 13Option 4: 2, 3, and 11

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Question : A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b =
2a, c = 2b, d = 2c. The pin is divisible by __________.
Option 1: 2, 3, and 5
Option 2: 2, 3, and 7
Option 3: 2, 3, and 13
Option 4: 2, 3, and 11