"Jack Is Now 14 Years Older Than Bill. If in 10 Years Jack Will Be Twice as Old as Bill..." — GMAT® Worked Solution

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

Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A) 9

(B) 19

(C) 21

(D) 23

(E) 33

Try it before reading on.

Step 1: Write What's Given and Asked

Given:

• Jack is currently 14 years older than Bill
• In 10 years, Jack will be twice as old as Bill

Asked: Jack's age in 5 years

Step 2: Set Up a Time-Shift Table

Age problems describe relationships at different points in time. The trap is in how you translate "in 10 years Jack will be twice as old as Bill." A time-shift table with periods as columns and people as rows keeps the translation clean.

Use the time periods the problem mentions. Put "Now" first, then "In 10 Years" (the given relationship), then "In 5 Years" (the question):

From the first given statement, $J = B + 14$. That goes in the "Now" column.

Step 3: Translate the Second Relationship From the Table

The problem says "in 10 years Jack will be twice as old as Bill." Reading directly from the "In 10 Years" column:

$J + 10 = 2(B + 10)$

The parentheses are there because you're reading Bill's age at the 10-year mark, not Bill's age now. This is where the table prevents the most common error. Without the table, it's tempting to write $J + 10 = 2B + 10$ or $J + 10 = 2B$, both of which lead to wrong answers.

Step 4: Solve the System of Equations

From the "Now" column:

$J = B + 14$

From the "In 10 Years" column:

$J + 10 = 2(B + 10)$

Distribute the right side:

$J + 10 = 2B + 20$

Subtract 10 from both sides:

$J = 2B + 10$

Now substitute $B + 14$ for $J$ (from the first equation):

$B + 14 = 2B + 10$

Subtract $B$ from both sides:

$14 = B + 10$

Subtract 10:

$B = 4$

Now find $J$:

$J = B + 14 = 4 + 14 = 18$

Step 5: Answer the Question Asked

The question asks for Jack's age in 5 years, not Jack's age now. From the table:

$J + 5 = 18 + 5 = 23$

The answer is (D).

Why This Problem Matters

About 20% of test takers miss this problem, and the most popular wrong answer is (E) 33.

Here's why: the incorrect translation $J + 10 = 2B + 10$ (doubling Bill's current age, then adding 10) combined with $J = B + 14$ produces $J = 28$. Then when you do the final step correctly and add 5 years, you get $28 + 5 = 33$, which is answer choice (E). The translation error produces a wrong value for Jack's current age, and then the correct final step carries that error forward into the answer the question actually asks for. The test isn't being cruel by including (E). It's testing whether you translated the time-shifted relationship correctly, and the wrong answer is the exact result of the most common translation error carried through to the question that was asked.

A smaller group writes $J + 10 = 2B$ (doubling Bill's current age without aging him at all), which produces a different wrong answer.

The time-shift table prevents both errors by separating the aging step from the comparison step. You age each person first (filling in the "In 10 Years" column), then write the comparison using values from that column. The parentheses in $2(B + 10)$ come from reading Bill's cell, not from remembering a rule about order of operations.

The end-of-problem trap also matters here. If you stop at $J = 18$ and don't check what the question actually asked, you might pick a wrong answer or panic thinking you made a math error. Having $J + 5 = ?$ written in your table reminds you that the question is about the 5-year mark, not the present.

Want the full strategy behind this problem? Read: GMAT® Word Translations: Three Systems for Setup and Organization

From Episode 34 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? "A Store Currently Charges the Same Price for Each Towel That It Sells..." — GMAT® Worked Solution.