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Algebra Smart Math

[Smart Math] Algebra Problem 4

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

Algebra

Problem

On dividing a number by 1005 the quotient is 785 and the remainder is 108. What is the number?

  1. 785931
  2. 789033
  3. 785033
  4. 789931
  5. 785031

The Usual Method

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The required number is 785 x 1005 + 108

= 788925 + 108

= 789033

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Just check the last digit of 785 x 1005 i.e 5 x 5 = 25, so last digit = 5. Adding 108 will make the last digit = 5 + 8 = 13 i.e 3.

This eliminates options ‘1’, ‘4’ and ‘5’. From between options ‘2’ and ‘3’, option ‘3’ can also be eliminated since, the first three digits in it are 785…The logic here is when 785 is multiplied by a number greater than 1000 (1005 in this case) the answer will surely be greater than 785000 and also when 108 is added to it, the answer will be greater than 785108. Since 785033 < 785108, we eliminate option ‘3’.

Hence answer is option ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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