Question

if n is an integer such that 1nn352 is a six digit number ​

Answer 1

Answer:

15

Step-by-step explanation:

1nn352 is perfectly divisible by 24

only if values of n(0-9) are 2,5,8

These three possible values of n can be added to get you answer i.e. 2+5+8= 15.

Answer 2

complete Question :- If n is an integer such that 1nn352 is a six-digit number exactly divisible by 24, what will be

the sum of the possible values of n ?

Solution :-

we know that,

• If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
• A number is divisible by 8 if the last three digits are evenly divisible by 8.
• If the number is separately divisible by 3 and 8 then the number is also divisible by 24.

So, we can conclude that, if given 6 digit number is divisible by 24 , it must be divisible by 3 and 8.

checking by 8 first we get :-

→ 352/8 = 44 quotient , 0 remainder.

So, it is divisible.

now, in order to divisible by 3 , sum must be divisible by 3.

So,

→ (1 + n + n + 3 + 5 + 2) / 3 = 0 remainder.

→ (11 + 2n) / 3 = 0 remainder.

Putting values of n now, we get,

• if n = 0 => 11 /3 = Remainder not equal to 0.
• if n = 1 => (11 + 2)/3 = Remainder not equal to 0.
• if n = 2 => (11 + 4)/3 = Remainder equal to 0.
• if n = 3 => (11 + 6)/3 = Remainder not equal to 0.
• if n = 4 => (11 + 8)/3 = Remainder not equal to 0.
• if n = 5 => (11 + 10)/3 = Remainder equal to 0.
• if n = 6 => (11 + 12)/3 = Remainder not equal to 0.
• if n = 7 => (11 + 14)/3 = Remainder not equal to 0.
• if n = 8 => (11 + 16)/3 = Remainder equal to 0.
• if n = 9 => (11 + 18)/3 = Remainder not equal to 0.

Therefore,

→ sum of Possible values of n = 2 + 5 + 8 = 15 (Ans.)

Hence, sum of Possible values of n is 15.

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