Brent@GMATPrepNow wrote: ↑Mon Nov 21, 2022 7:16 am
What is the units digit of x² - y² ?
(1) x - y is a positive multiple of 3
(2) x + y is a positive multiple of 10
Answer:
C
Source: gmatprepnow.com
Target question: What is the units digit of x² - y² ?
Strategy: When I scan the two statements, I see that they're related to Integer Properties (divisors, multiples, etc.). So, the first question I ask myself is "Are the variables defined as integers? Since we're NOT told x and y are integers, we need to watch out for that.
Statement 1: x - y is a positive multiple of 3
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 6 and y = 3. In this case, x² - y² = (x + y)(x - y) = (6 + 3)(6 - 3)² = (9)(3) = 2
7, which means the answer to the target question is
the units digit of x² - y² is 7
Case b: x = 7 and y = 4. In this case, x² - y² = (x + y)(x - y) = (7 + 4)(7 - 4)² = (11)(3) = 3
3, which means the answer to the target question is
the units digit of x² - y² is 3
Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x + y is a positive multiple of 10
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 6 and y = 4. In this case, x² - y² = (x + y)(x - y) = (6 + 4)(6 - 4)² = (10)(2) = 2
0, which means the answer to the target question is
the units digit of x² - y² is 0
Case b: x = 9.75 and y = 0.25. In this case, x² - y² = (x + y)(x - y) = (9.75 + 0.25)(9.75 - 0.25)² = (10)(9.5) = 9
5, which means the answer to the target question is
the units digit of x² - y² is 5
Statements 1 and 2 combined
If x - y is a positive multiple of 3, then x - y is an INTEGER
Likewise, If x + y is a positive multiple of 10, then x + y is an INTEGER
So, we can be certain that x² - y² = (x + y)(x - y) = (some multiple of 3)(some multiple of 10) = some integer
with units digit 0.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
