Vincen wrote:If x = y^2, and x and y are positive integers, which of the following could be the value of x?
A. 24,336
B. 36,847
C. 42,007
D. 49,003
E. 64,643

For this question, we need only examine the UNITS DIGIT of each answer choice.
Here's why:
We're told that x is the square of an integer (so X COULD equal 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc)

Notice that if y has units digit 1, then the y² = (---1)² = -----1.
So, if y has units digit 1, then x will have units digit 1

ASIDE: Notice that we need only focus on the units digit of y²
Keep going...
(---2)² = -----4.
(---3)² = -----9.
(---4)² = -----6.
(---5)² = -----5.
(---6)² = -----6.
(---7)² = -----9.
(---8)² = -----4.
(---9)² = -----1.
(---0)² = -----0.

So, the SQUARE on an integer must have one of the following UNITS DIGITS: 0, 1, 4, 5, 6 or 9

Now check the answer choices:
A. 24,336 The square of an integer CAN equal 6. So KEEP A
B. 36,847 The square of an integer CANNOT equal 7 ELIMINATE
C. 42,007 The square of an integer CANNOT equal 7 ELIMINATE
D. 49,003 The square of an integer CANNOT equal 3 ELIMINATE
E. 64,643 The square of an integer CANNOT equal 3 ELIMINATE

Answer: A

Cheers,
Brent