Solving a digit reversal multiplication puzzle to find difference
Question
Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?
Options
45
27
18
9
Explanation
Let p = 10a + b and q = 10b + a. We are given p × q = 2430.
Because the product 2430 ends in exactly one zero, one of the two-digit numbers must be a multiple of 5 (ending in 5 or 0) while the other provides an even factor. However, neither p nor q can end in 0. If b=0, then q would start with 0, disqualifying it as a valid two-digit number. Therefore, one of the numbers must definitively end in 5. Let b = 5. This forces q to start with 5, putting it in the 50s range (51, 52, 53, 54, \dots).
Test numbers in the 50s against the required product 2430:
Calculate the difference between the two integers: |45 - 54| = 9.
Answer: (d).
Question details
Year
2022
Paper
CSAT
Question
Q66
Section
Numerical Ability
Sub-topic
Number Puzzles
Type
Factual single
Difficulty
Hard
Source hint
p x q = 2430, reverse digits
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