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Here is a representative Quantitative Reasoning problem involving prime factorization — a concept that appears frequently on the DAT in disguised form.
Problem
224 = (2^a)(7^b)
What is a / b ?
A) 7
B) 5
C) 7/5
D) 5/5
E) 1/7
Try solving it before looking at the explanation.
Factor 224 completely into prime factors:
224 = 2 × 112
112 = 2 × 56
56 = 2 × 28
28 = 2 × 14
14 = 2 × 7
Therefore:
224 = (2^5)(7^1)
So:
a = 5
b = 1
a / b = 5
Correct Answer: B
Prime factorization questions test whether students recognize structure rather than perform complicated calculations. On the DAT, numbers are often presented in forms that reward breaking them down first.
If you would like additional DAT Quantitative Reasoning practice problems, feel free to reply and I can post more.
If you’re preparing for the DAT or OAT, the Math Destroyer and the full DAT/OAT Destroyer series are designed to strengthen your problem-solving skills with targeted, exam-focused practice.
Learn more about our resources here:
2026 Math Destroyer – DAT and OAT Quantitative Reasoning Prep
2026 DAT Destroyer – High-Yield DAT Science Study Guide
For additional free help, join our DAT Destroyer Study Group on Facebook. Inside the group you’ll find:
• Dr. Romano’s Free Biology Review
• Daily math questions posted by our team
• A supportive community of motivated students
Facebook
www.facebook.com
We also offer DAT and OAT classes — available both online and in-person in Staten Island, NY:
Summer 2026 DAT & OAT Classes | Dr. Jim Romano | DAT Destroyer
Problem
224 = (2^a)(7^b)
What is a / b ?
A) 7
B) 5
C) 7/5
D) 5/5
E) 1/7
Try solving it before looking at the explanation.
Solution
Factor 224 completely into prime factors:
224 = 2 × 112
112 = 2 × 56
56 = 2 × 28
28 = 2 × 14
14 = 2 × 7
Therefore:
224 = (2^5)(7^1)
So:
a = 5
b = 1
a / b = 5
Correct Answer: B
Prime factorization questions test whether students recognize structure rather than perform complicated calculations. On the DAT, numbers are often presented in forms that reward breaking them down first.
If you would like additional DAT Quantitative Reasoning practice problems, feel free to reply and I can post more.
If you’re preparing for the DAT or OAT, the Math Destroyer and the full DAT/OAT Destroyer series are designed to strengthen your problem-solving skills with targeted, exam-focused practice.
Learn more about our resources here:
2026 Math Destroyer – DAT and OAT Quantitative Reasoning Prep
2026 DAT Destroyer – High-Yield DAT Science Study Guide
For additional free help, join our DAT Destroyer Study Group on Facebook. Inside the group you’ll find:
• Dr. Romano’s Free Biology Review
• Daily math questions posted by our team
• A supportive community of motivated students
www.facebook.com
We also offer DAT and OAT classes — available both online and in-person in Staten Island, NY:
Summer 2026 DAT & OAT Classes | Dr. Jim Romano | DAT Destroyer
