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Algebra Level 2

A teacher, on attempting to arrange the students in the form of a solid square for a mass drill, found that 24 students were left out. When he increased the size of the square by one, he found that he was short of 25 students. Find the number of students.

600 655 None of the above 625

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Harsha K by Harsha K , 21, India

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4 solutions

Arunima Mitra
Oct 31, 2015

Let the side of the first square be x... Then the side of the second square the teacher made will be x+1..

The number of students in the drill are constant. This implies x 2 x^{2} + 24 = ( x + 1 ) 2 (x+1)^{2} - 25 which gives us 2x=48, and thus x=24..

Now the number of students in the mass drill are x 2 x^{2} +24 = 600 \boxed{600}

4 Helpful 0 Interesting 1 Brilliant 0 Confused
Philip Guest
May 22, 2017

The two squares are 49 apart. 49 is the gnomon of the 25th square (squares increase by consecutive odd numbers 1 + 3 + 5 + 7 etc.). The 25th square is 625. The 24th is 576 (= 625 - 49). 576 + 24 = 625 - 25 = 600.

0 Helpful 0 Interesting 3 Brilliant 0 Confused

Can you please elaborate?

Shubhrajit Sadhukhan - 6 months ago

Sn=1+3+5+.....+49=625; \n.
625-25=600

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Soummo Paul
Oct 26, 2014

Let, students in each side of the square is a = 24 initially a^2 +24 = (a+1)^2 - 25 or, a = 24

So, Total students = a^2 + 24 = 600

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How can you simply just assume the side length of the square to be 24...

Arunima Mitra - 5 years, 7 months ago

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