Multiple choice

If x be the least number which when divided by 15, 18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?

  1. 36

  2. 43

  3. 37

  4. 39
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

LCM(15,18,20,27)=540. Number is 540k+10, divisible by 31. 540k+10≡0(mod 31) gives 13k+10≡0, so 13k≡21. 13⁻¹ mod 31 is 12, so k≡21×12≡4. x=540×4+10=2170. Closest squares: 46²=2116, 47²=2209. Need to add 39 to reach 47².

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