A farmer grows Broccoli in his farm that is in the shape of a square. Each Broccoli takes 1 square foot of area in his garden. This year, he has increased his output by 101 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did he produce this year?
Choose the correct choice:
A) 2400	B) 2601	C) 1987	D) 2000	E) Cannot be determined
Explanatory Answer   The shape of the area used for growing Broccoli has remained a square in both the years.   Let the side of the square area used for growing Broccoli this year be X ft.   Therefore, the area of the ground used for cultivation this year = X2 sq.ft.   Let the side of the square area used for growing Broccoli last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of Broccoli grown has increased by 101, the area would have increased by 101 sq ft because each Broccoli takes 1 sq ft space.   Hence, X2 - Y2 = 101   (X + Y)(X - Y) = 101.   101 is a prime number and hence it will have only two factors. i.e., 101and 1.   Therefore, 101 can be expressed as product of 2 numbers in only way = 101 * 1   i.e., (X + Y)(X - Y) = 101* 1   So, (X + Y) should be 101 and (X - Y) should be 1.   Solving the two equations we get X = 51 and Y = 50.   Therefore, number of Broccoli produced this year = X2 = 512 = 2601.   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice A,C and D. as 2400,1987 and 2000 are not the square of any number.   Check Choice B: If this year's produce is 2601, last year's produce would have been  2601 - 101= 
<gadget id="calculator"> 2601 - 101</gadget>
<output>2_500</output>
2500   2500 is the square of 50.   So, 2601 is the answer.   Choice 2601
<result>B</result>
A farmer grows Broccoli in his farm that is in the shape of a square. Each Broccoli takes 1 square foot of area in his garden. This year, he has increased his output by 101 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did he produce this year?