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Q66·CSAT · Prelims 2022

Solving a digit reversal multiplication puzzle to find difference

NumericalNumber PuzzlesFactual singleHard

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

a

45

b

27

c

18

d

9

Answer

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:

Try q = 52, then p = 25. Product = 52 × 25 = 1300 (Too low).
Try q = 54, then p = 45. Product = 54 × 45 = 2430. (Perfect Match).

Calculate the difference between the two integers: |45 - 54| = 9.

When the product of digit-reversed pairs ends in a single zero, immediately eliminate 0 as a digit option and lock one of the terminal digits to exactly 5.

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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