multiplicative-ratio-constraints
Quantities are linked by ratios (R = G/2, B = 2G, or a:b given). Combined with the requirement that all counts are whole numbers, the ratios force totals to lie in a specific arithmetic progression (multiples of some k). The unique answer is the choice that fits the multiplicative scheme.
How to solve
- Change ratio_chain from 1:2:4 to 2:3:5 — totals must now be multiples of 10 instead of 7
- Add a perturbation that changes the ratio from 3:1 to 5:2 (problem 21 style)
- Convert from 'which is possible' to 'find the smallest total possible'
Sub-archetype mix (6)
Click a row to see member problems.
- direct-ratio-scale-up 24% (10)
A single a:b ratio is stated, along with one known value or a total constraint; find the unknown quantity by writing each part as a multiple of k and solving for k.
- chained-ratio-linking 15% (6)
Two or more ratios share a common variable; standardize that shared term via LCM or substitution to express all quantities in a single unified ratio, then answer a count or minimum-total question.
- percent-fraction-recovery 24% (10)
A fraction or percentage of one group equals a known count or another group's fraction; recover the whole population size, or compute what fraction of the combined total one subgroup represents.
- integrality-divisibility-screen 20% (8)
Ratio fractions applied to an unknown total T require T to be a multiple of the LCM of the denominators; combined with a bounding inequality, this divisibility constraint identifies the unique valid answer among the choices.
- ratio-shift-two-state 10% (4)
An initial ratio between two groups is given, then a fixed number of items are added to or transferred between groups, yielding a new ratio; set up a system of two ratio equations to recover the original or final counts.
- multiplicative-rate-or-series 7% (3)
A constant multiplicative factor (a per-unit rate, a similarity scale, or a per-step fraction) must be identified from given data and then either compared across options or applied repeatedly as a geometric series to find a total.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 3 1
- Gr 4 6
- Gr 5 1
- Gr 6 26
- Gr 7 3
- Gr 8 3