Mathematics
Assertion (A) : If 36p52q9 is divisible by 9, then p + q = 2.
Reason (R) : A number is divisible by 3 if the sum of its digits is divisible by 3.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Answer
Divisibility Rule for 9 : A number is divisible by 9 if the sum of its digits is divisible by 9.
So, if 36p52q9 is divisible by 9, then the sum of digits of 36p52q9, will also be divisible by 9.
⇒ 3 + 6 + p + 5 + 2 + q + 9
⇒ 25 + p + q
⇒ 27 (If, p + q = 2)
Since, 27 is divisible by 3, so if 36p52q9 is divisible by 9, then p + q = 2.
So, assertion (A) is true.
We know that,
A number is divisible by 3 if the sum of its digits is divisible by 3.
This is a correct rule for divisibility by 3.
So, reason (R) is true, but it does not explains assertion.
Hence, option 2 is the correct option.
Related Questions
Statement 1: When the sum of a two - digit number and the number obtained by reversing its digit is divided by 11, the quotient is equal to the sum of two digits.
Statement 2: When the sum of a two digit number and the number obtained by reversing its digit is divided by the sum of the two digit, the quotient is always 11.
Which of the following options is correct ?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A) : 759 = 100 x 7 + 10 x 5 + 1 x 9.
Reason (R) : In a three-digit number 100p + 10q + 1r, the digit p at hundred's place is any whole number from 0 to 9, the digit q at ten's place is any whole number from 0 to 9 and the digit r at unit place is any whole number from 0 to 9.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : Factors of the sum of a three-digit number 542 and the numbers obtained by changing the order of the digits cyclically are 1, 11, 111, 5 + 4 + 2.
Reason (R) : The sum of a three-digit number and the two number obtained by changing the digit cyclically is completely divisible by (i)11, (ii) 111 and (iii) sum of the digit.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : 2574 is divisible by 11 but 7083 is not divisible by 11.
Reason (R) : A number is divisible by 11 if the difference between the sum of its digits in even places and the sum of its digits in odd places is either 0 or divisible by 11.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.