Categories

# [Smart Math] Arithmetic Problem 11

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

### Problem

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

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

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.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

## One reply on “[Smart Math] Arithmetic Problem 11”

Bennysays:

Do you have any more good examples similar to arithmetic problem 11?

Thanks,

Benny.