A positive integer n is completely divisible by 12 and 8. If lies between 5 and 8, exclusive, how many values of n are possible?a)0b)1c)2d)9e)10Correct answer is option 'B'. Can you explain this answer?

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A positive integer n is completely divisible by 12 and 8. If lies between 5 and 8, exclusive, how many values of n are possible?

a)
0
b)
1
c)
2
d)
9
e)
10

Correct answer is option 'B'. Can you explain this answer?

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A positive integer n is completely divisible by 12 and 8. If lies betw...

Given:

To Find: Number of possible values of n

Approach:

To find the number of possible values of n, we will make use of the constraints on n
- Constraint 1: n is completely divisible by 12 and 8
  - i. So, our first step will be to find the LCM of 12 and 8
  - ii. n will be a multiple of this LCM
  - iii. So, we will list the first few multiples of the LCM. These will all be the possible values of n according to Constraint 1.
- Constraint 2: 25 < n < 64
  - From the list of possible values of n obtained from Constraint 1, we will see how many values lie between 25 and 64, exclusive. That will give us the answer.

Working out:

Applying Constraint 2:
- As noted in the Approach, 25 < n < 64
- From Constraint 1, we know that the possible values of n are {24, 48, 72, 96, 120 . . .}
- Out of these, only 1 value, 48, lie between 25 and 64
Getting to the answer:
Thus, we see that only 1 value of n satisfies both Constraints 1 and 2

Therefore, the correct answer is Option B – 1.

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A positive integer n is completely divisible by 12 and 8. If lies between 5 and 8, exclusive, how many values of n are possible?a)0b)1c)2d)9e)10Correct answer is option 'B'. Can you explain this answer?

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