Categories
Arithmetic Smart Math

[Smart Math] Arithmetic Problem 14

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

Arithmetic

Problem

What is the least number which must be subtracted from 10420 to make it a perfect square?

  1. 219
  2. 200
  3. 189
  4. 25
  5. 16

The Usual Method

[contentblock id=google-adsense-post]

10420 can be written as:

10420 = 10000 + 420

The square root of 10000 = 100

Now, by trail and check method, check for squares of numbers greater than 100.

120^{2}=14400 as 14400 > 10420 hence the square root should be < 120.

110^{2}=12100 as 12100 > 10420 hence the square root should be < 110.

105^{2}=11025 as 11025 > 10420 hence the square root should be < 105.

102^{2}=10404 as 10404 < 10420 hence the required square root should be 102.

To bring 10420 to 10404, we have to subtract 10420 – 10404 = 16.

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

[contentblock id=google-adsense-post]

Simply subtract each option from 10420 starting with the least number and check for perfect square as follows:

e. 10420 – 16 = 10404 = 100^{2}+2\times 100\times 2+2^{2}=102^{2} (Perfect Square)

(Note: We are taking option ‘5’ first as it is the one with the lowest number.)

No need to check any further.

Hence, option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published. Required fields are marked *