Ratio & proportion
Ratio word problems usually give you a:b and b:c and ask for a:c. The two ratios describe b with different numbers, so scale each until b matches — use the lowest common multiple of the two b-terms — then read the outer numbers straight off. Reduce the result before comparing it against the options.
Chained ratios are the most mechanical marks in the section and the ones most often dropped to a careless slip. The whole difficulty is that the middle quantity is described twice with different numbers, and the fix is a single LCM. Once the shared term matches, the answer is simply the two outer terms.
Try it against the clock. Ratio & Proportion runs at 90s easy, 105s medium and 120s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
In 'Riley to Quinn is 2:3' and 'Quinn to Jordan is 2:5', Quinn is the bridge. It is written as 3 in one ratio and 2 in the other, and that mismatch is the entire problem.
The LCM of 3 and 2 is 6. This is the number the bridge quantity will be written as in both ratios, and it is always the smallest one that works.
2:3 becomes 4:6 and 2:5 becomes 6:15. Both terms of a ratio must be multiplied by the same factor — changing only the bridge term silently changes the relationship.
With 4:6 and 6:15 the chain gives Riley:Jordan = 4:15. Check whether it reduces; the unreduced form is a standard distractor placed right beside the key.
| You are given | Scale to |
|---|---|
| 2:3 and 2:5, bridge 3 and 2 | LCM 6 — becomes 4:6 and 6:15 |
| 2:3 and 4:3, bridge 3 and 4 | LCM 12 — becomes 8:12 and 12:9 |
| 3:5 and 2:3, bridge 5 and 2 | LCM 10 — becomes 6:10 and 10:15 |
| Bridge terms already equal | No scaling — read the outer terms |
| Result shares a common factor | Reduce before checking options |
Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
The ratio of Jamie to Avery is 2:3.
The ratio of Avery to Drew is 2:3.
What is the ratio of Jamie to Drew?
The ratio of Morgan to Casey is 2:5.
The ratio of Casey to Jordan is 6:5.
What is the ratio of Morgan to Jordan?
The ratio of Sam to Taylor is 2:3.
The ratio of Taylor to Avery is 3:5.
What is the ratio of Sam to Avery?
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
Turning 2:3 into 2:6 to match a 6 changes the ratio itself. Both terms move by the same factor, so 2:3 becomes 4:6.
Multiplying the outer terms directly gives a number that is right only by accident. The bridge must be written identically in both ratios first.
Riley:Jordan and Jordan:Riley are both printed. Write the order the question asked for next to your working before you look at the options.
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
It is 4:15. Quinn is 3 in the first ratio and 2 in the second, so both scale to 6: the first becomes 4:6 and the second 6:15. Leaving the first term at 2 means you scaled the bridge without scaling its partner, and 2:15 is an available option.
Only when the bridge terms are already equal. Otherwise the two ratios are measuring the middle quantity in different units and multiplying across compares things that were never on the same scale. The result happens to be right sometimes, which is what makes the habit dangerous.
Because 6:15 reduces to 2:5. The key is the reduced form, and the unreduced version is frequently printed one line away as a distractor. Reduce as a final reflex, the same way you would with any fraction.
Make b the same number in both. Take the lowest common multiple of the two b-terms, scale each ratio in full so that b becomes that value, then read the first term of the first ratio against the last term of the second. Reduce the result.
Any common multiple gives the correct ratio, because the result reduces to the same thing. The LCM simply keeps the numbers small, which is what saves you seconds under a clock. Using a larger multiple only means more reducing at the end.
Do it pairwise. Match the first bridge and collapse the first two ratios into one, then treat that result as your new first ratio and match the second bridge. Trying to align all three quantities at once is where the arithmetic usually breaks.
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