DAT DAT Math Tip – Compare Expressions (Inequalities) | DAT Destroyer

---

Members do not see this ad.

If ab < 0, and b is positive, what can we say about the following?


Statement 1: a(b + 1)
Statement 2: a(b – 1)


Choices:
A) Statement 1 is larger
B) Statement 2 is larger
C) Both are equivalent
D) Cannot be determined


Answer: B — Statement 2 is larger


Explanation:
Since ab < 0, a must be negative (because b is positive). Let’s test a few values:


If b = 1, a = –1

1. a(b + 1) = –1(1 + 1) = –2
2. a(b – 1) = –1(1 – 1) = 0

If b = 2, a = –1

1. a(b + 1) = –1(2 + 1) = –3
2. a(b – 1) = –1(2 – 1) = –1

Because a is negative, multiplying by the smaller quantity (b – 1) produces a larger value.
So, Statement 2 is greater.


Key takeaway:
Understanding how signs affect inequalities is essential on the DAT Quantitative Reasoning section.


If you’re struggling with math concepts like this, the Math Destroyer offers hundreds of targeted QR practice problems to strengthen your skills before test day.