Arithmetic Smart Math

[Smart Math] Arithmetic Problem 11

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



What is the least number by which 2352 is to be multiplied to make it a perfect square?

  1. 2
  2. 3
  3. 4
  4. 6
  5. 18

The Usual Method

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Here we first find the factors of 2352 by factorization.

We will get the factors as = 2^{4}\times 3^{1}\times 7^{2}

In order for the number to be a perfect square, the power of each prime factor should be even. Only 3 has a power of 1 which is odd and hence, 3 is multiplied by 2352 to make it to a perfect square.

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Option ‘3’ can be eliminated as 4 itself is a perfect square. Hence, by multiplying it by any number will not make that number a perfect square. Option ‘5’ can also be eliminated as 18 = 9 x 2 and 9 being a perfect square will not make any number a perfect square and the 2 does not make sense here as it already is in option ‘1’.

Now, simply divide 2352 with 6. \frac{2352}{6}=392 The number 392 is not divisible by 3 hence, you will have to multiply 3 with 2352 to make 2352 a perfect square.

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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