A number theory problem by Caitlyn Deelah

There is one odd integer N between 400 and 600 that is divisible by both 5 and 11. Find the sum of the digits of N.


The answer is 18.

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7 solutions

Pranjal Jain
Oct 20, 2014

It must be divisible by LCM(5,11)=55. Hence the odd multiple of 55 will be 495. So the answer is 4+9+5= 18 \boxed{18}

i found 495 but didnt add the digits

Aareyan Manzoor - 6 years, 7 months ago

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Dude, Thats bad coz the first thing you do when you solve a question is that you READ it CAREFULLY

Mehul Arora - 6 years, 5 months ago
Mohammad Khaza
Dec 12, 2017

11 × 5 = 55 11 \times 5=55 .it is both odd and divisible by 5 and 11.

so, the answer will be= 440 + 55 = 495 440+55=495

Sabhrant Sachan
Dec 24, 2014

There are Three Numbers Between 400 and 600 that are divisible by 5 and 11 . These are 440 , 495 and 550 and the sum of digits are 8 , 18 and 10 respectively. Only 495 is odd so answer is 18

Joel Shah
Dec 5, 2014

An odd multiple of five must end with the digit five. In a three digit multiple of eleven the first digit and the last digit must add up to the center digit. 5 + 5 = 10, so there cannot be a possible value in between 500 and 600, so the first digit must be 4, 5 +4 = 9, so the number must be 495, 4 +5+9 = 18

Mahdi Raza
May 7, 2020
  • N N must be a multiple of L C M ( 5 , 11 ) = 55 LCM (5, 11) = 55
  • Between the range of 400 400 and 600 600 there are only 3 3 multiples of 55 55 : 440 , 495 , 550 440, 495, 550 .
  • N = 495 N = 495 since that is only odd.
  • Sum of digits of N = 4 + 9 + 5 = 18 N = 4 + 9 + 5 = \boxed{18}
Afreen Sheikh
Dec 24, 2014

well what I did...took 500/(5x11) and quotient was 9 therefore 9*55=495 4+9+5+18

Venky Venkatesh
Dec 3, 2014

Divisible by both 5 and 11 so multiples of 55 between 400 and 600 are 495 or 565 so the sum can be 16 or 18

565 is not a multiple of 55

friends on - 6 years, 5 months ago

565 is not a multiple of 11. 565/11=51.3636...

Hyacinth Muyco - 6 years ago

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