Quote:
Originally Posted by srikar2097  New Problem!
I'm trying to find some good DI problem to post here. But until that time comes you guys have a crack at this LR problem 
There are 10 statements written on a piece of paper:
1. At least one of statements 9 and 10 is true.
2. This either is the first true or the first false statement.
3. There are three consecutive statements, which are false.
4. The difference between the numbers of the last true and the first true statement
divides the number, that is to be found.
5. The sum of the numbers of the true statements is the number, that is to be found.
6. This is not the last true statement.
7. The number of each true statement divides the number, that is to be found.
8. The number that is to be found is the percentage of true statements.
9. The number of divisors of the number, that is to be found, (apart from 1 and itself)
is greater than the sum of the numbers of the true statements.
10. There are no three consecutive true statements.
Find the minimal possible number? |
No one tried this question
Was it too hard or …?
Anyway the Answer:
The numebr is 420.
If statement 6 is false, it creates a paradox. Hence, Statement 6 must be true.
Consider Statement 2:
* If it is true, it must be the first true statement. Otherwise, it creates a paradox.
* If it is false, it must be the second false statement. Otherwise, it creates a
paradox.
In both the cases, Statement 1 is false.
As Statement 1 is false, Statement 9 and Statement 10 both are false i.e. there are three
consecutive true statements.
1 2 3 4 5 6 7 8 9 10
False - - - - True - - False False
Let\'s assume that Statement 3 is false i.e. there are no three consecutive false
statements. It means that Statement 2 and Statement 8 must be true, else there will be
three consecutive false statements.
1 2 3 4 5 6 7 8 9 10
False True False - - True - True False False
Also, atleast two of Statements 4, 5 and 7 must be true as there are three consecutive true
statements.
According to Statement 8, the number that is to be found is the percentage of true
statements. Hence, number is either 50 or 60. Now if Statement 7 is true, then the number
of each true statement divides the number, that is to be found. But 7 and 8 do not divide
either 50 or 60. Hence, Statement 7 is false which means that Statement 4 and 5 are true.
But Statement 5 contradicts the Statement 8. Hence, our assumption that Statement 3 is
false is wrong and Statement 3 is true i.e. there are 3 consecutive false statements which
means that Statement 8 is false as there is no other possibilities of 3 consecutive false
statements.
Also, Statement 7 is true as Statement 6 is not the last true statement.
1 2 3 4 5 6 7 8 9 10
False - True - - True True False False False
According to Statement 7, the number of each true statement divides the number, that is to
be found. And according to Statement 5, the sum of the numbers of the true statements is
the number, that is to be found. For all possible combinations Statement 5 is false.
There 3 consecutive true statements. Hence, Statement 2 and Statement 4 are true.
1 2 3 4 5 6 7 8 9 10
False True True True False True True False False False
Now, the conditions for the number to be found are:
1. The numebr is divisible by 5 (Statement 4)
2. The numebr is divisible by 2, 3, 4, 6, 7 (Statement 7)
3. The number of divisors of the number, that is to be found, (apart from 1 and itself)
is not greater than the sum of the numbers of the true statements. (Statement 9)
The minimum possible number is 420.
The divisors of 420, apart from 1 and itself are 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21,
28, 30, 35, 42, 60, 70, 84, 105, 140, 210. There are total of 22 divisors. Also, the sum of
the numbers of the true statements is 22 (2+3+4+6+7=22), which satisfies the third
condition.
Linear Mode
