How many six-digit prime numbers can be formed using all the digits 1, 2, 3, 4, 5, and 6 exactly once (i.e., without repetition)?

Consider the following statements:
Statement I: Any number formed will be divisible by 9.
Statement II: No number formed will be a prime number.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

How many six-digit prime numbers can be formed using all the digits 1, 2, 3, 4, 5, and 6 exactly once (i.e., without repetition)?

Consider the following statements:
Statement I: Any number formed will be divisible by 9.
Statement II: No number formed will be a prime number.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

Sum of digits = 1 + 2 + 3 + 4 + 5 + 6 = 21
21 is divisible by 3 not by 9 &rArr; Any number formed using all these digits will also be divisible by 3 and not by 9.
&rArr; Hence, none of these numbers can be a prime
So:
Statement I: Any such number is divisible by 9 &rarr; Incorrect (Divisible by 3)
Statement II: No such number can be prime &rarr; Correct
Hence, option b is correct.

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M Question 1	⏱ 0
How many six-digit prime numbers can be formed using all the digits 1, 2, 3, 4, 5, and 6 exactly once (i.e., without repetition)? Consider the following statements: Statement I: Any number formed will be divisible by 9. Statement II: No number formed will be a prime number. Select the correct answer from below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.