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UPSC Prelims

Mathematics

Theme:

Elementary Algebra / प्रारंभिक बीजगणित

Q57 2015, Elementary Algebra

If ABC x DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E?

यदि ABC × DEED = ABCABC; जहाँ A, B, C, D और E भिन्न अंक हैं, तो D और E के मान क्या है ?

Explanation

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1. Correct Answer
     The correct answer is Option C: D=1, E=0.
2. Explanation
     To solve the problem, we need to find the values of D and E such that when the number ABC is multiplied by DEED, the result is ABCABC. This implies that DEED is a number that, when multiplied by ABC, results in a number that is ABC repeated twice.
     Let's break down the problem:
     ● Step 1: Understand the structure of the multiplication.
           ○ ABCABC is essentially ABC * 1001 (since 1001 = 1000 + 1, and ABCABC = ABC * 1000 + ABC).
           ○ Therefore, DEED must be equal to 1001.
     ● Step 2: Determine the digits D and E.
           ○ DEED = 1001 can be broken down into digits: D = 1, E = 0, E = 0, D = 1.
           ○ This means D = 1 and E = 0.
     ● Step 3: Verify the solution.
           ○ If DEED = 1001, then multiplying any three-digit number ABC by 1001 will indeed result in ABCABC.
           ○ For example, if ABC = 123, then 123 * 1001 = 123123, which confirms the pattern.
     Therefore, the values of D and E that satisfy the equation are D = 1 and E = 0.

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Q 57. 2015, Elementary Algebra

Mathematics

यदि ABC × DEED = ABCABC; जहाँ A, B, C, D और E भिन्न अंक हैं, तो D और E के मान क्या है ?

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John Doe

Mathematics

यदि ABC × DEED = ABCABC; जहाँ A, B, C, D और E भिन्न अंक हैं, तो D और E के मान क्या है ?

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John Doe

Explanation

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