What This Episode Covers
Episode 35 of Real GMAT® Problems focuses on plugging in answers — one of the most versatile strategies on the GMAT® and the backbone of many quant questions that cannot be "solved" by setting up a single equation. The episode works through three Official Guide problems that range from a straightforward warm-up to a trickier question involving exponents and variable substitution.
The central theme is that many GMAT® quant questions are designed so that the answer choices are part of the solution process. Rather than deriving an answer from scratch, you test each option against the constraints in the problem. This approach is not a shortcut or a hack — it is the intended method for a significant number of questions on the exam.
Along the way, we reinforce the same habits that run through the entire series: write what is given and what is asked, use clear visual organization (columns, labeled variables, one row per answer choice), and execute consistently whether a problem feels easy or hard.
Problems Covered
Problem 1 — Warm-Up: If 0 ≤ x ≤ 4 and y < 12, which cannot be xy? Options: −2, 0, 6, 24, 48. We test each answer by finding values of x and y in the given ranges that produce that product. Key insight: x cannot be negative but y can be, so negative products are possible. The trap is option A — about 10% of test-takers forget that y can be negative because they are psychologically anchored by the x ≥ 0 constraint. Option E (48) is the answer because it requires y = 12 when x = 4, but y must be strictly less than 12. Good visual organization — columns for x, y, and xy — keeps the work clean.
Problem 2 — Mid-Level: N is divisible by 25, √N > 25, which could be N/25? Options: 22, 23, 24, 25, 26. For each option, set N/25 equal to the answer and solve for N. The key constraint is √N > 25, which means N > 625 (i.e., N > 25 × 25). Since N = (answer) × 25, only option E (26 × 25 = 650) exceeds 625. The 17% trap answer is D (25), because test-takers who rush misread "greater than" as "greater than or equal to" or lose track of the square root constraint mid-problem. Writing all constraints on the page before computing prevents this.
Problem 3 — Harder: V = 1/(2r)³, if r is halved, V is multiplied by what? Options: 64, 8, 1, 1/8, 1/64. Two viable approaches: algebra (simplify original V = 1/8r³, substitute r/2, compare) or fabricated-number substitution (plug in r = 2, compute both values, find the multiplier). The algebraic approach is fast but 15% of test-takers pick 1/8 instead of 8 — an easy inversion error when fractions are involved. Plugging in a number makes the comparison more concrete: V goes from 1/64 to 1/8, which is multiplication by 8. Answer: B.
Key Takeaways
- Many GMAT® questions are designed to be solved with the answer choices. If there is no clean equation to set up, test each option systematically. This is not a backup plan — it is often the intended approach.
- Write what is given and what is asked every time. On Problem 2, the square root constraint is the entire question. If it is not written on your page, it is easy to forget once you start computing.
- Use columns and labels for organized guess-and-test. One column for each variable, one row per answer choice. This takes seconds and eliminates the most common source of errors.
- Watch for psychological anchoring. On Problem 1, the x ≥ 0 constraint primes you to think everything is positive — but y has no lower bound. Writing constraints explicitly counteracts this.
- Plugging in a fabricated number can rescue algebraic traps. On Problem 3, the fraction inversion error (picking 1/8 instead of 8) disappears when you compute with concrete numbers. If you tend to make sign or direction errors with fractions, this is a safer path.
- Save computation until the end. Leave products in factored form (e.g., 22 × 25 instead of 550) as long as possible. Factored forms make comparisons easier and reduce the chance of arithmetic errors.
Related Reading
- Real GMAT® Problems — Ep. 37 — Divisibility Shortcuts — uses the same guess-and-test framework on divisibility questions
- Real GMAT® Problems - Ep. 38 - The Power of Testing Numbers — builds directly on this episode's plugging-in-answers framework with number properties problems