"In a Weightlifting Competition the Total Weight of Joe's Two Lifts..." — GMAT® Worked Solution

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

In a weightlifting competition, the total weight of Joe's two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?

(A) 225

(B) 275

(C) 325

(D) 350

(E) 400

Try it before reading on.

Setting Up the Problem

Start with the foundation: write what's given and what's asked.

• Given: two lifts total 750 pounds; twice the first lift is 300 pounds more than the second lift
• Asked: weight of the first lift

Create meaningful variables. Use $F$ for the first lift and $S$ for the second lift — not $x$ and $y$. The letters themselves remind you what each variable represents, which matters more than it seems once you are several steps into algebra.

Write out what each variable represents:

• $F$ = first lift (in pounds)
• $S$ = second lift (in pounds)

Translating the English Into Equations

The first relationship is straightforward: the two lifts total 750 pounds.

$F + S = 750$

The second relationship takes more care: "twice the weight of his first lift was 300 pounds more than the weight of his second lift."

If translation feels tricky, try the "half math, half English" step first. Write something like:

2 × first = 300 + second

That is not an equation you solve. It is a bridge that captures the logic before you commit to formal algebra. Once it looks right, convert it:

$2F = S + 300$

Now you have two equations:

$F + S = 750$ $2F = S + 300$

Choosing Elimination Over Substitution

Most people default to substitution here — solve one equation for $S$, plug into the other. That works. But elimination is worth trying first.

To use elimination, stack the equations with variables aligned in columns. The first equation already has $F$ and $S$ on the left side. For the second equation, subtract $S$ from both sides so $F$ and $S$ are both on the left:

$2F - S = 300$

Now stack them:

  F + S = 750
 2F - S = 300

The $S$ terms are aligned: $+S$ in the first equation and $-S$ in the second. When you add the equations, $S$ cancels out.

Solving for the First Lift

Add the two equations:

$(F + S) + (2F - S) = 750 + 300$ $3F = 1050$

Divide both sides by 3:

   350
  -----
3 ) 1050
     9
    ---
    15
    15
    ---
     0

$F = 350$

The answer is (D).

Why This Problem Matters

About 10% of test takers miss this one. The math is not complex — it is basic algebra and long division. The mistakes come from translation and setup.

The most common pitfalls:

Translating the second relationship wrong

"Twice the weight of his first lift was 300 pounds more than the weight of his second lift" becomes $2F + 300 = S$ instead of $2F = S + 300$. The 300 is added to the second lift, not to twice the first. Reading carefully and using the "half math, half English" step prevents this.

Mixing up which variable to solve for

The problem asks for the first lift. If you label variables as $x$ and $y$ without writing what they represent, it is easy to solve for the wrong one — especially after several algebra steps. Meaningful labels ($F$ and $S$) keep you oriented.

Defaulting to substitution when elimination is faster

Substitution works here, but it involves an extra step: solve for $S$, substitute, simplify. Elimination eliminates that step (pun intended). It is worth trying on any two-equation system where the coefficients look like they might align.

This problem is a good warm-up. The same habits — write what's given, label variables, use elimination when it fits — scale up to harder word problems where organization is the difference between getting stuck and finding the answer.

Want the full strategy behind this problem? Read: GMAT® Word Problems: A Translation System That Prevents Costly Mistakes

From Episode 32 of Real GMAT® Problems (The GMAT® Strategy Podcast).