Question
Download Solution PDFThe converse of the statement “If a number is even, then it is divisible by 2” is given by “If a number is divisible by 2, then it is even”. Here both the statement and its converse are true. With this information, choose the statement among the following four true statements whose converse is also true.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The converse of a true statement must also be true.
Options Analysis:
1. If a triangle is an equilateral, then it is isosceles.
True statement.
Converse: "If a triangle is isosceles, then it is equilateral" is false.
2. If a number is divisible by 6, then it is divisible by 3.
True statement.
Converse: "If a number is divisible by 3, then it is divisible by 6" is false.
3. If the sum of all the digits of a number is divisible by 3, then the number is divisible by 3.
True statement.
Converse: "If a number is divisible by 3, then the sum of its digits is divisible by 3" is also true.
4. If a quadrilateral is a square, then its sides are equal.
True statement.
Converse: "If sides are equal, then it is a square" is false (it could be a rhombus).
∴ Correct answer is: If the sum of all the digits of a number is divisible by 3, then the number is divisible by 3.
Last updated on Jul 11, 2025
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