A lady grows Broccoli in her garden that is in the shape of a square. Each Broccoli takes 1 square foot of area in her garden. This year, she has increased her output by 79 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 she produce this year?  Choose the correct choice:  A) 1600  B) 1500  C) 1650  D) 1700  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 79, the area would have increased by 79 sq ft because each Broccoli takes 1 sq ft space.   Hence, X2 - Y2 = 79   (X + Y)(X - Y) = 79.   79 is a prime number and hence it will have only two factors. i.e., 79 and 1.   Therefore, 79 can be expressed as product of 2 numbers in only way = 79 * 1   i.e., (X + Y)(X - Y) = 79 * 1   So, (X + Y) should be 79 and (X - Y) should be 1.   Solving the two equations we get X = 40 and Y = 39.   Therefore, number of Broccoli produced this year = X2 = 402 = 1600.   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice B,C and D. as 1500,1650 and 1700 are not the square of any number.   Check Choice A: If this year's produce is 1600, last year's produce would have been  1600 - 79= 
<gadget id="calculator"> 1600 - 79</gadget>
<output>1_521</output>
1521   1521 is the square of 39.   So, 1600 is the answer.   Choice 1600
<result>A</result>
A lady grows Broccoli in her garden that is in the shape of a square. Each Broccoli takes 1 square foot of area in her garden. This year, she has increased her output by 79 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 she produce this year?