CAT Exam

In a rectangle the difference between the sum of the adjacent side and the diagonal is half the length of the longer side. What is the ratio of shorter to the longer side ?

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CAT Other Question

ABC is a three digit number in which A is greater than Zero. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B ? The sum of the house numbers less than mine in my street is equal to the sum of the house numbers which are greater than mine.

My house number happens to comprise four digits. What is it?