## Quant Question Of The Day : 13

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# Numbers

The number of persons who booked ticket for the New Year’s concert is a perfect square. If 100 more persons booked ticket then the number of spectators would be a perfect square plus 1. If still 100 more persons booked ticket then the number of spectators would be again a perfect square. How many persons booked ticket for the concert?

### Solve our previous ‘questions of the day’

1 Quant Question Of The Day : 12

2 Quant Question Of The Day :11

3. Quant Question Of The Day : 10

### 15 comments

### Reply

Greater than 40.

Hehe ‘Greater than 1’ is also correct :p

Approach sir 😛

Sir, I meant the square root of the number of people who attended the concert will be greater than 40. This is because no squares of natural numbers below 40 fit the pattern as mentioned in the question 🙂

People who attended concert =2401

49^2,50^2,51^2

My approach:

a^2+100=b^2+1

b^2-a^2=99

b^2+101=c^2

c^2-b^2=101

(c-b)(c+b)=101

Since 101 is prime

So, factors must be prime and 1

c-b=1 means c=b+1

c+b=101 means 1+2b=101

b= 50

c=51

Hence a=49

Well done! Abhishek 🙂

Let’s see if you hit the target on today’s ‘Question of the Day’:

http://tathagat.mba/quant-question-of-the-day-30-06-2018/

2401

Well done ! Shubhra

Take a shot at today’s ‘Question Of The Day ‘ http://tathagat.mba/quant-question-of-the-day-30-06-2018/

2401

2401