A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 401 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year? Choose the correct choice from the following choices:	A) 44001	B) 44000	C) 40400	D) 40401	E) Cannot be determined
Explanatory Answer   The shape of the area used for growing Cauliflower has remained a square in both the years.   Let the side of the square area used for growing Cauliflower 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 Cauliflower last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of Cauliflower grown has increased by 401, the area would have increased by 401 sq ft because each Cauliflower takes 1 sq ft space.   Hence, X2 - Y2 = 401   (X + Y)(X - Y) = 401.   401 is a prime number and hence it will have only two factors. i.e., 401 and 1.   Therefore, 401 can be expressed as product of 2 numbers in only way = 401* 1   i.e., (X + Y)(X - Y) = 401 * 1   So, (X + Y) should be 401 and (X - Y) should be 1.   Solving the two equations we get X = 201 and Y = 200.   Therefore, number of Cauliflower produced this year = X2 = 2012 = 40401   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice A,B and C . as 44001,44000 and 40400 are not the square of any number.   Check Choice D: If this year's produce is 40401, last year's produce would have been  40401- 401= 
<gadget id="calculator"> 40401- 401</gadget>
<output>40_000</output>
40000   40000 is the square of 200.   So, 40401 is the answer.   Choice 40401.
<result>D</result>
A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 401 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?