Here is a problem on the GMAT practice questions. I solved it a different way, and need to know if I stumbled upon the answer by accident or if what I did would hold true if a different version of the question was on the real test.
"If X is a positive integer, and if the units digit of X^2 is 9 and the units digit of (X+1)^2 is 4, what is the units digit of (X+2)^2?"
(a) 1
(b) 3
(c) 5
(d) 6
(e) 14
The answer is (a).
The following is how I got it.
(X+1)^2 = 4
(X+1) (X+1) = 4
X^2 +2X +1 = 4
X^2 +2X -3 = 0
(X+3) (X-1) = 0
X = -3, X = 1
While plugging in both a 1 and a -3 for X into (X+1)2 = 4 will work, only -3^2 = 9 (as per the original statement in the question stem). So I plugged in -3 into (X+2)^2 and got 1. And that's the answer.
Now here is their explanation:
"Only numbers ending in 3 or 7 would yield a units digit of 9 when squared. Thus, if 9 is the units digit of X^2, then either 3 or 7 must be the units digit of X.
If the units digit is 3, then X+1= 3+1 = 4. This makes the units digit of )X+1)^2 the units digit of4^2, which is 6.
If, however, the units digit is 7, then X+1 = 7+1 = 8. This makes the units digit of (X+1)^2 the units digit of 8^2, which is 4, as is needed in this problem. Therefore, the units digit of X must be 7.
Thus, the units digit of X+2 is 9. This makes the units digit of (X+2)^2 the units digit of 9^2, which is 1.
The correct answer is A."
So my question is - if the question had been phrased differently using different numbers, would I still have derived the correct answer?
"If X is a positive integer, and if the units digit of X^2 is 9 and the units digit of (X+1)^2 is 4, what is the units digit of (X+2)^2?"
(a) 1
(b) 3
(c) 5
(d) 6
(e) 14
The answer is (a).
The following is how I got it.
(X+1)^2 = 4
(X+1) (X+1) = 4
X^2 +2X +1 = 4
X^2 +2X -3 = 0
(X+3) (X-1) = 0
X = -3, X = 1
While plugging in both a 1 and a -3 for X into (X+1)2 = 4 will work, only -3^2 = 9 (as per the original statement in the question stem). So I plugged in -3 into (X+2)^2 and got 1. And that's the answer.
Now here is their explanation:
"Only numbers ending in 3 or 7 would yield a units digit of 9 when squared. Thus, if 9 is the units digit of X^2, then either 3 or 7 must be the units digit of X.
If the units digit is 3, then X+1= 3+1 = 4. This makes the units digit of )X+1)^2 the units digit of4^2, which is 6.
If, however, the units digit is 7, then X+1 = 7+1 = 8. This makes the units digit of (X+1)^2 the units digit of 8^2, which is 4, as is needed in this problem. Therefore, the units digit of X must be 7.
Thus, the units digit of X+2 is 9. This makes the units digit of (X+2)^2 the units digit of 9^2, which is 1.
The correct answer is A."
So my question is - if the question had been phrased differently using different numbers, would I still have derived the correct answer?
