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

## What is the units digit of x² - y² ?

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### GMAT/MBA Expert

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**Posts:**16176**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

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[email protected] wrote: ↑Mon Nov 21, 2022 7:16 amWhat 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