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For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?
- a)2000
- b)200
- c)25
- d)20
- e)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is th...
According to the question, the “star function” is only applicable to four digit numbers. The function takes the thousands, hundreds, tens and units digits of a four-digit number and applies them as exponents for the bases 3, 5, 7 and 11, respectively, yielding a value which is the product of these exponential expressions.
Let’s illustrate with a few examples:
*2234* = (32)(52)(73)(114)
*3487* = (33)(54)(78)(117)
According to the question, the four-digit number m must have the digits of rstu, since *m* = (3r)(5s)(7t)(11u).
If *n* = (25)(*m*)
*n* = (52)(3r)(5s)(7t)(11u)
*n* = (3r)(5s+2)(7t)(11u)
n is also a four digit number, so we can use the *n* value to identify the digits of n:
thousands = r, hundreds = s + 2, tens = t, units = u.
All of the digits of n and m are identical except for the hundreds digits. The hundreds digits of n is two more than that of m, so n – m = 200.
The correct answer is B.
Let’s illustrate with a few examples:
*2234* = (32)(52)(73)(114)
*3487* = (33)(54)(78)(117)
According to the question, the four-digit number m must have the digits of rstu, since *m* = (3r)(5s)(7t)(11u).
If *n* = (25)(*m*)
*n* = (52)(3r)(5s)(7t)(11u)
*n* = (3r)(5s+2)(7t)(11u)
n is also a four digit number, so we can use the *n* value to identify the digits of n:
thousands = r, hundreds = s + 2, tens = t, units = u.
All of the digits of n and m are identical except for the hundreds digits. The hundreds digits of n is two more than that of m, so n – m = 200.
The correct answer is B.
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For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer?.
For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are fourdigit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?a)2000b)200c)25d)20e)2Correct answer is option 'B'. Can you explain this answer?.
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