"240, 120, 60, 30… What Is the Least Term Greater Than 1?" — GMAT® Worked Solution
From Episode 41 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind sequences problems on the GMAT®, read: GMAT® Sequences: Write Every Term, Use Fractions, and Solve What's Actually Asked.
The Problem
Source: Official Guide for GMAT® Review, 11th Edition
240, 120, 60, 30, …
In the sequence above, each term after the first is one-half of the preceding term. What is the least term of the sequence that is greater than 1?
(A) 32⁄15
(B) 16⁄15
(C) 15⁄8
(D) 15⁄4
(E) 15⁄2
The Setup
Before doing any math, write what the question is asking.
We need the LEAST term that is GREATER than 1. Not the first term less than 1. The last term that's still above 1.
Make that note big on your scratch work. Underline it. Circle it. The most common mistakes on this problem come from selecting the wrong neighbor of the correct term, and a clear note prevents that.
The rule: each term is half the preceding term, or equivalently, divide by 2.
The answer choices are all in fraction form. That's a signal — work in fractions throughout. Converting to decimals adds steps and creates conversion errors when matching back to the answer choices.
Step 1: List the Terms in Fractions
We're given 240, 120, 60, 30. Keep going by dividing each term by 2.
| Term | Value |
|---|---|
| 1st | 240 |
| 2nd | 120 |
| 3rd | 60 |
| 4th | 30 |
| 5th | 15 |
| 6th | 15⁄2 |
| 7th | 15⁄4 |
| 8th | 15⁄8 |
| 9th | 15⁄16 |
Walking through the divisions after term 5:
15 ÷ 2 = 15⁄2
15⁄2 ÷ 2 = 15⁄4
15⁄4 ÷ 2 = 15⁄8
15⁄8 ÷ 2 = 15⁄16
Step 2: Find the Cutoff
Compare each fraction to 1.
15⁄2 = 7.5, greater than 1.
15⁄4 = 3.75, greater than 1.
15⁄8 = 1.875, greater than 1.
15⁄16 = 0.9375, less than 1.
The first term less than 1 is 15⁄16.
Step 3: Identify the Answer
The question asks for the LEAST term GREATER than 1. That's the term right before the first one to drop below 1.
The term right before 15⁄16 is 15⁄8.
The answer is (C).
Why This Problem Matters
About 85% of test takers get this one right, which is on the higher end. But the 15% who miss it tend to miss it for predictable reasons — and those reasons are worth knowing because they show up on harder problems too.
The two most common wrong answers are (D) 15⁄4 and (E) 15⁄2. About 5% pick each.
For (E), one likely cause is treating "the first non-integer term" as "the first term less than 1." When the sequence stops producing integers at term 6, some test takers mentally jump there. But 15⁄2 = 7.5, which is much bigger than 1. The fraction bar isn't what makes a number small.
For (D), one likely cause is decimal-to-fraction conversion errors. If you worked the sequence in decimals — 7.5, 3.75, 1.875, 0.9375 — and tried to match back to fraction answer choices, that conversion step is a common place to slip.
Three things to take away:
Write what's asked. "Least term greater than 1" is one note. It prevents the (D) and (E) mistakes by keeping the cutoff condition visible while you work.
Stay in fractions. When the answer choices are fractions, the problem was designed for fraction arithmetic. Decimals add a conversion step at the end and that's a common place for errors.
List the terms in order. Once they're listed, finding the "term just before" or "term just after" is a glance, not a calculation. Most of the positional mistakes on sequences problems disappear when the list is visible on the page.
These are small habits. The payoff at higher difficulty levels is significant.
Next problem: A Quiz of 10 Questions Where Each Is Worth 4 Points More Than the Last — GMAT® Worked Solution
Back to the strategy article: GMAT® Sequences: Write Every Term, Use Fractions, and Solve What's Actually Asked