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Copper, iron and zinc are chemical elements that occur on the periodic table as single substances. Bronze is an alloy made by melting copper together with tin, so it is a manufactured mixture rather than an element. That makes bronze the only member of the list that is not a naturally occurring element.
Each term in the sequence is three times the term before it: 2 x 3 = 6, 6 x 3 = 18, and 18 x 3 = 54. Applying the same rule once more gives 54 x 3 = 162. Checking backwards, 162 divided by 3 returns 54, which confirms the pattern.
The two legs of the walk are at right angles, so they form the two shorter sides of a right-angled triangle. Using Pythagoras, the straight-line distance is the square root of (3 squared plus 4 squared), which is the square root of 25. That gives 5 km, not the total distance walked.
The courses take 5 parts of the ratio, and those 5 parts equal £2,400, so one part is worth £2,400 divided by 5, which is £480. The whole budget is 3 + 5 = 8 parts, and 8 x £480 = £3,840. Checking the equipment share, 3 x £480 = £1,440, and £1,440 + £2,400 confirms the total.
The first pair links a skilled worker to the characteristic cutting tool of the trade, since a carpenter works with a chisel. The matching relationship for a surgeon is the precision cutting instrument used during operations, which is the scalpel. The other words relate to surgery but do not name the tool that plays the same role for the surgeon.
Combining the clues gives a single order from front to back: Sam, then Ravi, then Priya, then Quinn. Sam is placed ahead of Ravi, and Ravi is already ahead of both Priya and Quinn, so nobody can be in front of Sam. Therefore Sam finished first.
Average speed for a whole journey is the total distance divided by the total time, not the average of the two separate speeds. The distance is 240 + 180 = 420 km and the time is 3 + 2 = 5 hours. Dividing 420 by 5 gives 84 km/h.
Cutting into 27 cubes means a 3 by 3 by 3 arrangement, so only the middle cube of each edge of the large cube keeps exactly two painted faces. A cube has 12 edges, and each edge contributes one such cube. Therefore 12 small cubes have exactly two painted faces.
Every clinic nurse belongs to the group trained in first aid, and that whole group is completely separate from volunteer drivers. Since no one can be in both groups at once, no clinic nurse can be a volunteer driver. The remaining statements either contradict the premises or add claims about volunteer drivers that the premises never support.
The rule shifts every letter one place forward in the alphabet. D becomes E, O becomes P, and G becomes H, giving EPH. Applying the shift to each position separately confirms that no letter is left unchanged or moved by more than one place.
Candid describes someone who speaks openly and honestly, which matches 'frank'. The remaining words concern carefulness, money, or timing, so they do not capture the same meaning.
Fifteen per cent of £80 is £12, because 0.15 × 80 = 12. Subtracting that discount from the original price gives £68.
A non-square rectangle has two lines of symmetry: one through the midpoints of each pair of opposite sides. An equilateral triangle has three, a square has four, and a circle has infinitely many.
Each term is made by doubling the previous term and adding one: 3 × 2 + 1 = 7, then 7 × 2 + 1 = 15, and so on. Applying the rule to 31 gives 31 × 2 + 1 = 63.
Because some artists are painters, and every painter uses brushes, at least those artists who are painters must use brushes. The argument does not establish anything about artists who are not painters.
Reversing DOG gives GOD. Moving each letter one place forward in the alphabet then gives H, P and E, so the coded form is HPE.
Dan occupies the fourth seat. Ben must be immediately left of Cara, and the only placement that also lets Ana avoid both ends is Ben in seat 1, Cara in seat 2 and Ana in seat 3. Therefore Ben sits at the far left.
Adding the French and Spanish counts double-counts the six students who study both, so 18 + 12 − 6 = 24 study at least one language. Of the 30 students, 30 − 24 = 6 study neither.
At the same rate, 4 people need 300 g, so one person needs 300 ÷ 4 = 75 g. For 10 people the amount is 75 × 10 = 750 g.
A speed of 72 km/h equals 20 m/s, since dividing by 3.6 converts kilometres per hour to metres per second. In 25 seconds the train travels 20 × 25 = 500 m, and subtracting its own 200 m length leaves a 300 m platform.
Frugal means careful and sparing with money or resources, so 'thrifty' is the closest synonym. The other choices describe someone who spends freely or lavishly, which is the opposite idea.
There are 5 + 7 + 8 = 20 counters in total, and 7 of them are blue. The required fraction is therefore 7/20, which is already in simplest form.
A week has 7 days, and 100 divided by 7 leaves a remainder of 2. Moving two days on from Wednesday gives Friday.
A thermometer is an instrument used to measure temperature. In the same way, a barometer is an instrument used to measure atmospheric pressure.
Each term after the first two is the sum of the two previous terms: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, and 3 + 5 = 8. The next term is therefore 5 + 8 = 13.
Ben has the dog and Cara has the fish, so the cat and bird must belong to Ana and Dan. Ana does not own the cat, so she must own the bird, leaving Dan as the owner of the cat.
In one hour, Pipe A fills 1/6 of the tank and Pipe B fills 1/12, so together they fill 1/6 + 1/12 = 1/4 of the tank. The reciprocal of 1/4 is 4, so the tank is filled in 4 hours.
The profit is £50 − £40 = £10. As a percentage of the £40 cost price, the profit is (10/40) × 100 = 25%.
The terms follow the pattern n raised to the power n: 1^1 = 1, 2^2 = 4, 3^3 = 27, and 4^4 = 256. The next term is therefore 5^5 = 3125.
The cut removes the corner but does not remove any entire original face, so all six original faces remain partly intact. The cut also creates one new triangular face, giving 6 + 1 = 7 faces in total.
Scarce describes something that is in short supply, so its opposite must describe something available in large amounts. 'Plentiful' expresses exactly that idea of abundance. The remaining options concern price, concealment or weakness rather than quantity.
Look at the gaps between consecutive terms: 4, 6, 8 and 10. These gaps increase by 2 each time, so the next gap must be 12. Adding 12 to 30 gives 42.
A cockpit is the compartment from which a pilot controls an aircraft. By the same relationship, a captain controls a ship from the bridge. The pair therefore links a person in command to the place from which that person directs the vessel.
Taking north as positive, she moves 3 km north, then 4 km east, then 3 km south. The northward and southward legs cancel, leaving a net displacement of 4 km due east from the start.
Because every engineer belongs to the group of graduates, the engineers themselves are graduates who are engineers. That makes 'Some graduates are engineers' necessarily true. The manager group may overlap with engineers, but the premises do not force any particular overlap.
A mean of 14 across six numbers means the total must be 6 × 14 = 84. The five known numbers add to 71, so the sixth number is 84 − 71 = 13.
Cutting into 27 cubes produces a 3 × 3 × 3 arrangement. Cubes with exactly two painted faces sit in the middle of each edge, away from the corners, and there are 12 edges with one such cube on each.
T is above S, S is above P, P is above Q, and R is below Q. Reading from top to bottom gives T, S, P, Q, R, so R occupies the lowest position.
Each term is double the previous term minus 1: 2 × 2 − 1 = 3, 3 × 2 − 1 = 5, and so on up to 9 × 2 − 1 = 17. Applying the same rule gives 17 × 2 − 1 = 33.
There are 15 balls in total. The probability that the first ball is red is 4/15, and after one red ball is removed the probability that the second is red is 3/14. Multiplying gives 12/210, which simplifies to 2/35.
The series moves forward through the alphabet by a growing number of places: two places to reach D, then three to G, four to K and five to P. The next jump must therefore be six places, and six places after P lands on V.
Every letter of the word is replaced by the letter that follows it in the alphabet, so C becomes D, A becomes B and T becomes U. Applying that same single-step shift to DOG gives D to E, O to P and G to H, producing DPH.
First find the quantity for a single person by dividing 300 g by 4, which gives 75 g. Scaling that rate up to 10 people means multiplying 75 g by 10, giving 750 g in total.
Sara's grandfather has only one son, and that son must be Sara's own father. Since Sara has no siblings, the only daughter her father has is Sara, so the girl described in the statement is Sara.
The poets who are also painters must be dreamers, because every painter belongs to the group of dreamers. That guarantees at least one dreamer who is a poet, which is precisely what the final option states.
A and C already occupy a pair of opposite sides, so the two remaining sides must be taken by B and D. Opposite sides pair up on a square table, so B must face D.
Two rules alternate through the series: double the number, then subtract one, then double again, and so on. After 9 is doubled to give 18, the subtract-one step applies, so the next term is 18 minus 1, which is 17.
Average speed is total distance divided by total time, not the midpoint of the two speeds. The outward trip takes 2 hours and the return trip takes 3 hours, so the train covers 240 km in 5 hours, giving 48 km/h.
At 3:40 the minute hand points at the 8, which is 240° measured clockwise from 12. The hour hand has moved a third of the way from 3 to 4, adding 20° to its 90° position and putting it at 110°, so the gap is 240° minus 110° equals 130°.
The rule squares each of the two numbers and adds the squares together: 9 plus 16 gives 25, and 25 plus 36 gives 61. Applying the same rule to 7 and 8 gives 49 plus 64, which equals 113.