"If x = 1 - 3t and y = 2t - 1, for What Value of t Does x = y?" — GMAT® Worked Solution

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

If $x = 1 - 3t$ and $y = 2t - 1$, then for what value of $t$ does $x = y$?

(A) $\dfrac{5}{2}$

(B) $\dfrac{3}{2}$

(C) $\dfrac{2}{3}$

(D) $\dfrac{2}{5}$

(E) $0$

Try it before reading on.

Step 1: Translate the Question Into an Equation

The question asks for the value of $t$ that makes $x$ and $y$ equal, and setting the two given expressions equal to each other states that request as algebra:

$1 - 3t = 2t - 1$

That translation is the whole conceptual load of the problem. The phrasing can read as indirect, and it's asking exactly this: find $t$ so the equation is true. That's what algebra exists to do, which is to hand back the value of an unknown that makes a stated relationship work.

Step 2: Solve for t, Writing Every Operation Under Both Sides

The solving moves are short, and writing each one under both sides of the equation keeps them short in the safest way:

  1 - 3t  =  2t - 1
   +3t        +3t
  ----------------
  1       =  5t - 1
   +1         +1
  ----------------
  2       =  5t
   ÷5          ÷5
  ----------------
  2/5     =  t

Adding $3t$ to both sides gives $1 = 5t - 1$. Adding 1 to both sides gives $2 = 5t$. Dividing both sides by 5 gives the answer:

$t = \frac{2}{5}$

The answer is (D).

Step 3: Where the Wrong Answer Comes From

Choice (A) is $\frac{5}{2}$, the value from solving everything correctly and then flipping the fraction in the final step. About 3% of test takers pick it. The answer choices make it worse: $\frac{5}{2}$, $\frac{3}{2}$, and $\frac{2}{3}$ are all arrangements of the same small numbers, so a flipped final line doesn't look out of place. Even the Khan Academy walkthrough of this problem contains the flip, written on camera and removed in the edit.

Why This Problem Matters

Over 90% of test takers answer this correctly, which is what gives it a low difficulty rating, and about 3% still pick the inverted fraction. Knowing the method and executing it under time pressure are different skills, and this question tests the second one on its very last line.

The habit of writing each operation under both sides is a habit built by missing questions like this one, which is the more expensive way to learn it. It lives on the page rather than in willpower, and it carries over to algebra throughout the exam.

Want the full strategy? Read: GMAT® Execution Habits: The Scratch-Work System for Easy Questions

From Episode 12 of Real GMAT® Problems (The GMAT® Strategy Podcast).