"A Certain Company Retirement Plan Has a Rule of 70 Provision..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

A certain company retirement plan has a "rule of 70" provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?

(A) 2003

(B) 2004

(C) 2005

(D) 2006

(E) 2007

Try it before reading on.

Step 1: Write Down What's Given and What's Asked

Start with the half-math, half-English layer:

Rule: age + years of employment ≥ 70
Hired: 1986
Age when hired: 32
Eligible when: age + years ≥ 70
Asked: what year?

The question asks for a year. The answer choices are years. That makes this a good candidate for plugging in the answers.

Step 2: Pick the Easiest Answer to Test

When plugging in answers, start with the answer that's easiest to work with. Usually that's a round number.

2006 stands out — it's 20 years after 1986, and 20 is easy to calculate with.

Step 3: Test 2006

If the answer is 2006, the employee has worked at the company for $2006 - 1986 = 20$ years.

She was hired at age 32. Twenty years later, she's $32 + 20 = 52$ years old.

Check the rule:

72 is greater than 70. So she's eligible by 2006 — but we need the FIRST year she's eligible. This is too late. The answer is before 2006.

Step 4: Test 2004

Drop down two years to 2004.

Years of employment: $2004 - 1986 = 18$

Age: $32 + 18 = 50$

Check the rule:

68 is less than 70. She's not eligible yet in 2004. The answer is after 2004.

Step 5: Narrow to the Answer

We know 2004 is too early and 2006 is too late. Only one answer choice falls between them.

The answer is (C) — 2005.

If you want to verify: in 2005, she has 19 years of employment and is 51 years old. $51 + 19 = 70$. That meets the rule exactly.

Why This Problem Matters

About 23% of test takers miss this problem. Most of the errors come from setup — getting turned around on the relationship between age, years of employment, and the year of eligibility.

The common mistakes:

Forgetting to add age and years separately. Some test takers calculate years of employment and treat that as the answer. But the rule is age PLUS years, not just years. A 52-year-old with 20 years of service has a sum of 72, not 20.

Miscounting the age. If she was hired at 32 in 1986, her age in 2006 isn't just $2006 - 1986 = 20$. That's her years of employment. Her age is $32 + 20 = 52$. Conflating the two is the trap.

Resisting plugging in answers. Some test takers know how to do the algebra but get turned around on the setup. Plugging in answers bypasses the setup entirely — you test the result directly. But many test takers avoid the technique because it feels like cheating.

It's not cheating. It's a legitimate problem-solving strategy that the GMAT® explicitly tests. Some problems are designed to be faster with plugging in answers than with algebra. Resisting the technique limits your options.

When to use it:

• You're unsure how to set up the algebra
• The answer choices represent a single value (a year, a dollar amount, a number of people)
• The answer choices are spread out enough that testing one or two narrows the field

Start with the answer that's easiest to work with. Be organized with what you write down. Let the wrong answers eliminate themselves.

Want the full strategy behind this problem? Read: GMAT® Word Translations: The Step-By-Step Setup System

From Episode 25 of Real GMAT® Problems (The GMAT® Strategy Podcast).

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