AAPL wrote:Manhattan Prep



In the grid above, the variables, \(a\) through \(p\) are each equal to \(2, 3, 5,\) or \(7\), with exactly one occurrence of each value in any row and in any column. What is the value of \(fgjk\)?

1) \(bcehilno = 35^4\)
2) \((2.25^2)afkp = dgjm\)

In the 16-value grid, each row and column must be composed of exactly one 2, one 3, one 5 and one 7.
Implication:
The grid is composed of four 2's, four 3's, four 5's, and four 7's.

Statement 1:
bcehilno = 5�7�
Since the letters above constitute the four 5's and four 7's, the remaining values must constitute the four 2's and four 3's.
Implication:
The four center values -- f, g, j, and k -- are composed of two 2's and two 3's.
Since each row must include exactly one 2 and one 3, we get two cases:
Case 1: fgjk = 2*3*3*2 = 36
Case 2: fgjk = 3*2*2*3 = 36
Since the product in each case is the same, SUFFICIENT.

Statement 2:
(9/4)²afkp = dgjm
9²/4² = dgjm/afkp
3�/2� = dgjm/afkp
The equation above implies that g and j are both 3's and that f and k are both 2's.
Since each row must include exactly one 2 and one 3, only Case 1 is possible
:fgjk = 2*3*3*2 = 36.
SUFFICIENT.

The correct answer is D.