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Arithmetic Smart Math

[Smart Math] Arithmetic Problem 10

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

Arithmetic

Problem

HCF of two numbers is 1/5th of a number and 1/7th of the other number. The difference between the numbers is 42. What is the LCM?

  1. 734
  2. 735
  3. 524
  4. 510
  5. 786

The Usual Method

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We know that HCF x LCM = product of two numbers

Let HCF = x

\therefore One number = 5x and another number = 7x

\therefore LCM = 35x

Also, difference between numbers = 7x – 5x = 2x = 42 (given)

\therefore x = 21 = HCF.

\therefore LCM = 35 x 21 = 735

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Looking at the information in the problem, it is evident that the LCM is a multiple of 7 and 5. The only option that is a multiple of 7 and 5 amongst the options is option ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 5 seconds.
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