P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?a)8b)16c)12d)4e)9Correct answer is option 'B'. Can you explain this answer?

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P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers' is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?

a)
8
b)
16
c)
12
d)
4
e)
9

Correct answer is option 'B'. Can you explain this answer?

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P and Q are two two-digit numbersTheir product equals the product of t...

To solve this question, we need to find the number of ordered pairs (P, Q) that satisfy the given conditions.

Let's analyze the conditions step by step:

Condition 1: The product of P and Q equals the product of the numbers obtained on reversing them.

Let's assume that P is a two-digit number with tens digit a and units digit b, and Q is a two-digit number with tens digit c and units digit d.

According to the given condition, we have:

P * Q = (10b + a) * (10d + c)

Expanding the equation, we get:

P * Q = 100bd + 10(ad + bc) + ac

Condition 2: None of the digits in P or Q is equal to the other digit in it or any digit in the other number.

This condition implies that the digits of P and Q should be distinct. So, we have the following restrictions:

a ≠ b, a ≠ c, a ≠ d
b ≠ c, b ≠ d
c ≠ d

Condition 3: The product of tens digits of the two numbers is a composite single-digit number.

The tens digits of P and Q are a and c, respectively. We need to find the number of ordered pairs (a, c) such that the product of a and c is a composite single-digit number.

Let's list all the possible values for a and c:

a = 1, c = 4 (product = 1 * 4 = 4)
a = 1, c = 6 (product = 1 * 6 = 6)
a = 2, c = 3 (product = 2 * 3 = 6)
a = 2, c = 5 (product = 2 * 5 = 10, not a single-digit number)
a = 3, c = 2 (product = 3 * 2 = 6)
a = 3, c = 7 (product = 3 * 7 = 21, not a single-digit number)
a = 4, c = 1 (product = 4 * 1 = 4)
a = 4, c = 7 (product = 4 * 7 = 28, not a single-digit number)
a = 5, c = 2 (product = 5 * 2 = 10, not a single-digit number)
a = 5, c = 9 (product = 5 * 9 = 45, not a single-digit number)
a = 6, c = 1 (product = 6 * 1 = 6)
a = 6, c = 8 (product = 6 * 8 = 48, not a single-digit number)
a = 7, c = 3 (product = 7 * 3 = 21, not a single-digit number)
a = 7, c = 4 (product = 7 * 4 = 28, not a single-digit number)
a = 8, c = 6 (product = 8 * 6 = 48, not a single-digit number)
a = 9, c = 5 (product = 9 * 5 = 45, not a single-digit number)
a = 9, c = 7 (product =

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P and Q are two two-digit numbersTheir product equals the product of t...

We can represent the two-digit numbers as "ab" and "cd", where "a", "b", "c", and "d" are digits.

The values of the numbers can be written as 10a + b and 10c + d.

By solving the equation (10a + b)(10c + d) = (10b + a)(10d + c), we find that ac = bd.

Since ac represents a composite single digit, the possible values for ac are 4, 6, 8, and 9.

Out of these four options, we can eliminate 4 and 9 because the digits must be distinct.

Therefore, ac can be either 6 or 8.

For ac = 6, there are 2 possibilities for a and c: (2, 3) or (3, 2).

For ac = 8, there are 2 possibilities for a and c: (2, 4) or (4, 2).

In total, we have 2 * 2 = 4 possibilities for the pairs (a, c) and (b, d) that satisfy the conditions.

Hence, the correct answer is 16.

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P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?a)8b)16c)12d)4e)9Correct answer is option 'B'. Can you explain this answer?

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