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. 24,33
6 The square of an integer CAN equal
6. So KEEP A
B. 36,84
7 The square of an integer CANNOT equal
7 ELIMINATE
C. 42,00
7 The square of an integer CANNOT equal
7 ELIMINATE
D. 49,00
3 The square of an integer CANNOT equal
3 ELIMINATE
E. 64,64
3 The square of an integer CANNOT equal
3 ELIMINATE
Answer:
A
Cheers,
Brent
