EngiMetric Arena / Spot the Error
Review this cement order: the bags were rounded down
Competency Quantitative reasoning primary
What you should take away: Recognise that a bag count is a discrete purchase: a fractional requirement must be rounded up, not down.
The situation
What is happening
A 1:2:4 concrete mix at a water-cement ratio of 0.5 is batched at 1 m3. The mix calculator returns 316.8 kg of cement, or 6.336 bags of 50 kg. The site ordered six bags. Review the order.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Cement : sand : aggregate | 1 : 2 : 4 | by volume | Nominal mix proportions. |
| Water-cement ratio | 0.5 | by mass | Batching assumption. |
| Batch volume | 1 | m3 | One cubic metre of finished concrete. |
| Cement required | 316.8 | kg | From the mix engine. |
| Bag size | 50 | kg | Standard bag. |
Assumptions this challenge makes
- The mix proportions are by volume and the cement is measured by mass.
- The bag mass is exactly 50 kg; real bag fill has a tolerance.
- No site wastage is included in the 1 m3 batch.
Your call
Your answer
Hints
- Convert the cement mass into bags and look at the fractional part. Ask what a supplier can actually deliver.
- A bag is a whole unit. Rounding the number of bags down changes the mass of cement in the mix.
- Compare the delivered mass with the required mass. The difference is the shortfall the review is looking for.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- The mix engine returns 316.8 kg of cement for a 1 m3 batch at these proportions.
- At 50 kg per bag that is 6.336 bags. Six bags deliver 300 kg, a shortfall of 16.8 kg or about 5 % of the cement.
- Because bags are discrete, the order must be rounded up to seven bags (350 kg). The surplus is small and is not a reason to under-order.
- A cement-deficient mix loses strength and durability; the saving from one bag is not a defensible trade against the specified mix.
- The correct review finding is therefore about the rounding rule, not about the water content or the nominal proportions.
What this challenge does not establish
- The mix proportions are nominal and by volume; a real mix design would be based on trial batches and material properties.
- No allowance is made for bag-fill tolerance, moisture in the aggregates or site wastage.
- The engine assumes the stated water-cement ratio is the batching target, not a maximum.