Leo starts assembling gift boxes for a charity event.

Question

Leo starts assembling gift boxes for a charity event. He starts working alone, and later Hugo joins him to help finish the job. If a total of 96 boxes are assembled altogether, with some assembled by Leo alone and the rest assembled by Leo and Hugo working together, how many boxes had Leo already assembled by the time Hugo started helping?

(1) Working together, Leo and Hugo assemble 24 boxes per hour.
 (2) Leo and Hugo worked together for a total of three hours.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Leo starts assembling gift boxes for a charity event. He starts working alone, and later Hugo joins him to help finish the job. If a total of 96 boxes are assembled altogether, with some assembled by Leo alone and the rest assembled by Leo and Hugo working together, how many boxes had Leo already assembled by the time Hugo started helping?

(1) Working together, Leo and Hugo assemble 24 boxes per hour.

Knowing only the combined rate does not tell us how many hours they worked together, so we cannot determine how many boxes they assembled after Hugo joined, and therefore we cannot determine how many Leo had already assembled. Not sufficient.

(2) Leo and Hugo worked together for a total of three hours.

Knowing only that they worked together for 3 hours does not tell us their combined rate, so we cannot determine how many boxes were assembled during those 3 hours, and we cannot determine how many of the total 96 boxes Leo had already assembled before Hugo joined. Not sufficient.

(1)+(2) We know they worked together for 3 hours at 24 boxes per hour, so they assembled 24 * 3 = 72 boxes while working together. Since 96 boxes were assembled in total, Leo must have already assembled 96 - 72 = 24 boxes when Hugo started helping. Sufficient.

Answer: C.

DRRAGONZZ · Answer

C. Both sentences are required.

Edskore · Answer

Key Concept Being Tested: Work and Rate problems in Data Sufficiency — specifically whether you can determine a quantity (boxes assembled solo) when rates and times are split across two phases.

Common Trap: Statement 1 gives a combined rate and Statement 2 gives time — students often think "rate × time = work, so S2 alone gives me boxes assembled together, and I can subtract from 96 to get Leo's solo output." This feels right but breaks down because you don't know Leo's individual rate, making it impossible to compute his solo boxes from S2 alone.

Step 1 — Set up variables.
Let L = Leo's rate (boxes/hour), H = Hugo's rate (boxes/hour), t = hours Leo worked alone.
Boxes Leo assembled solo = L × t
Total: L·t + (L + H)·T_H = 96

Step 2 — Test Statement 1 alone.
"Working together, Leo and Hugo assemble 24 boxes per hour." → L + H = 24
Without knowing T_H (how long they worked together), we can't use this. L and t individually remain unknown. Statement 1 alone: INSUFFICIENT.

Step 3 — Test Statement 2 alone.
"Leo and Hugo worked together for 3 hours." → T_H = 3
Total equation becomes: L·t + (L + H)·3 = 96. We still have three unknowns (L, H, t) and one equation. Many solutions exist. Statement 2 alone: INSUFFICIENT.

Step 4 — Combine both statements.
From S1: L + H = 24. From S2: T_H = 3.
Substituting: L·t + 24 × 3 = 96 → L·t + 72 = 96 → L·t = 24
The question asks "how many boxes had Leo assembled by the time Hugo started?" = L·t = 24 boxes.
A single, definitive answer. Both together: SUFFICIENT.

Answer: C

Takeaway: In two-phase Work and Rate DS problems, neither a rate alone nor a time alone is enough — you need both to pin down the work done in that phase, and the combination often resolves cleanly even when it looks like there are too many unknowns.

chloreton · Answer

This is quite easy one.

Total work = 96 boxes. To find : number of boxes L assembled before H joined.

Statement 1 : Rate of L+H = 24 boxes per hour (We don't know how long they worked) - Not sufficient

Statement 2: L & H worked together for 3 hours. (We don't know about the rates) - Not sufficient

Combined, we can tell L&H both worked for 3 hours at the rate of 24 boxes per hour. Their total work = 24*3=72
We know total work = 96. We also know L started working first and then H joined.
The amount of work done by L = 96 - 72 = 24 boxes.

Therefore, C

Leo starts assembling gift boxes for a charity event.

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GMAT Data Sufficiency (DS) Questions

Leo starts assembling gift boxes for a charity event.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

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