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### Mathematical Skills | Number System

 Q. No. 1: Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X? A : 16 B : 14 C : 18 D : 20 Solution
 Q. No. 2: How many three digit numbers can be formed using the digits 1,2,3,4,5,6,7 and 8 without repeating the digits and such that the tens digit is greater than the hundreds digit and less than the units digit? A : 48 B : 56 C : 64 D : 72 Solution
 Q. No. 3: A set of S consists of i). all odd numbers from 1 to 55.ii). all even numbers from 56 to 150.What is the index of the highest power of 3 in the product of all the elements of the set S? A : 35 B : 48 C : 6 D : 36 Solution
 Q. No. 4: A person use the base x for their number system, where x<=10. A student had to add two-digit numbers. None of the digits was 0. By oversight, he reversed the digits of both the numbers and added them. He later found that the difference between his answer and the correct answer was (84)10. If this value is the maximum possible for x, then what is the value of x. A : 9 B : 7 C : 8 D : 6 Solution
 Q. No. 5: Let X be a four-digit number with exactly three consecutive digits being same and is a multiple of 9. How many such X’s are possible? A : 12 B : 16 C : 19 D : 20 Solution
 Q. No. 6: Find the sun of the digits of the least natural number P, such that the sum of the cubes of the four smallest distinct divisors of P equals 2P. A : 9 B : 8 C : 7 D : 10 Solution
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