QUESTION

CSAT

Easy

Maths

Prelims 2023

A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+CA + B + C?

Select an option to attempt

Explanation

It's given that, ABC×D=37DDABC \times D = 37DD

Wherein A, B, C and D are different non-zero digits.

So, ABC=37DDD=3700+10D+DD=3700D+11ABC = \frac{37DD}{D} = \frac{3700 + 10D + D}{D} = \frac{3700}{D} + 11

The possible values of D, such that ABC is an integer, are 1, 2, 4, and 5.

If D=1D = 1, ABC=3700+11=3711ABC = 3700 + 11 = 3711. It can be rejected as ABC is a three-digit number. If D=2D = 2, ABC=1850+11=1861ABC = 1850 + 11 = 1861. It can be rejected as ABC is a three-digit number. If D=5D = 5, ABC=740+11=751ABC = 740 + 11 = 751. It can be rejected as here B=D=5B = D = 5. If D=4D = 4, ABC=925+11=936ABC = 925 + 11 = 936.

So, A+B+C=9+3+6=18A + B + C = 9 + 3 + 6 = 18

Hence, option A is correct.

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