CMI Data Science 2025 | Part B | Question: 1

Question

A girl writes five consecutive positive integers on a blackboard. She then erases one of them. The sum of the remaining four numbers is $2025.$ What number did she erase?

Answer 1

Let the five consecutive numbers be:

x, x+1, x+2, x+3, x+4x

Their total sum is:

x+(x+1)+(x+2)+(x+3)+(x+4) = 5x+10

Let the number erased be e. Then:

5x+10 − e = 2025

⇒ e = 5x+10−2025

⇒ e = 5x−2015

Now, e must be one of the five numbers:

x, x+1, x+2, x+3, x+4

Let’s check each:

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Try e = x:

x = 5x−2015

⇒ 4x = 2015

⇒ x = 503.75 (Not integer)

Try e = x+1:

x+1 = 5x−2015

⇒ 4x = 2016

⇒ x = 504 (Integer)

So, the five numbers are:

504, 505, 506, 507, 508 

Total sum: 504+505+506+507+508 =2530

Remove x+1 = 505

Sum of remaining = 2530−505 = 2025

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Final Answer:

The erased number is 505.

Comments

bascially hit and trial for getting that number to be integer .