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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 6

Here’s and example of a SMART MATH problem for ARITHMETIC.

Arithmetic

Problem

Find the greatest three digit number which when divided by 2, 3, 4 and 5 leaves a remainder of 1, 2, 3 and 4 respectively.

  1. 939
  2. 959
  3. 969
  4. 949
  5. 929

The Usual Method

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First get the LCM of 2, 3, 4 and 5 which is 60. Since the remainders are 1 less than the dividends; the number should be = (n x 60) – 1

The greatest value of ‘n’ for (n x 60) – 1 to be a 3 digit number = 16

\because 16 x 60 – 1 = 960 – 1 = 959

(Ans: 2)

Estimated Time to arrive at the answer = 75 seconds.

Using Technique

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Applying the test of divisibility, observe from options that option ‘1’ and option ‘3’ are both multiples of 3 and hence will not leave any remainder. Hence both options ‘1’ and ‘3’ can be eliminated.

Also, the remainders when 949 and 929 when divided by 4 will give remainder of 1 and not 3 as required. Hence options’4’ and ‘5’ are also eliminated.

Thus we are left out with only option ‘2’, which actually satisfies the conditions and hence is the answer.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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