Question

BRAIN TEASER!!!

Two people each put a number into the number machine and get 100 on the other side.
Did they both put the same number?

⊕ Yes, definitely
⊕ No, not necessarily

sᴘᴀᴍ ᴡIʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ..​

Answer 1

Answer : yes ,definitely

Explanation:

they both input no. 4 multiplied it to 2 got 8 ans added 2 in this no. got 10 then, they square the no. (10)^2 and obtained the same no. as their output

Answer 2

★ Solution :-

• No, not necessarily

→ Reason ::

The answer option b. The reason because option b states that the two numbers can be either same or different.

✒ Why they can be same ?

By Euclid's Postulates, we know that when equals are added / multiplied by equals, the result is equal. Here if input same numbers at input side of the machine, then the result will be equal. Let's understand this by a proof.

Let the numbers be 4 .

Thus, when they are multiplied by 2, so the result will be 8.

Now when these both numbers are added 2, then the result will be 10.

Then, on squaring 10 we get the result as 100.

Thus we see that if both numbers are equal and they are equal to 4, then only the possible outcome of 100 is available.

So one combination of number is 4 and 4 which shows that both numbers are equal.

✒ Why they can be different ?

We see that two people, each put a number into the machine side. We are not at all given that the numbers cannot be negative . So it is a possibility that one person can put a negative number which after performing the process gives output as 100.

We already got that 4 can be a number which can be put by any person.

So let the another number be -6

Thus, when -6 is multiplied by 2, the result is -12.

Now when 2 is added to -12, the result is -10.

Then, when we square (-10) , we get the outcome as 100.

Thus -6 can also be one of the numbers . So, if both numbers are different, thus one number equals to 4 and another number equals to -6 which will give output as 100.

So another combination of numbers is 4 and -6 which shows that both numbers are different.

Even the pair of numbers in overall can be (4,4), (4, -6), (-6, -6) and (-6, 4).

Here we see that 2 outcomes out of 4 shows that two numbers are different and 2 outcomes shows that both numbers are same. Thus, both the cases have equal probability. This means they cannot be same definitely.

So the correct answer is : No, not necessarily.