OAR
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OAR is a trademark of its owner, which is not affiliated with and does not endorse Test Treasure Publication or TTP Prep.
10 sample questions for the OAR, with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.
Sections covered on the exam: Mathematics, R Eadi Ng Comp R Ehensi On, Reading Comprehension Test, Mechanical Comprehension Test, Scr Ews, Mechani Cal Comp R Ehensi On, Concl Usi On, Tone.
Question 1 · Mathematics
If a is an odd integer and b is an even integer, which of the following must be odd?
Answer: C. a² + 3b
a² is odd and 3b is even, so a² + 3b is odd + even = odd. The factor (a − 1) is even, so (a + b)(a − 1) is even; 3a + a² is odd + odd = even; ab + b has an even factor b in each term, so it is even.
Question 2 · Mathematics
The formula A = P(1 + rt) gives the value of an account with simple interest. Which expression correctly solves this formula for r?
Answer: B. r = (A − P)/(Pt)
Distribute: A = P + Prt. Subtract P: A − P = Prt. Divide by Pt: r = (A − P)/(Pt). Writing A/(Pt) − 1 wrongly subtracts 1 after dividing by Pt; the correct split is A/(Pt) − 1/t.
Question 3 · R Eadi Ng Comp R Ehensi On
Reef-building corals depend on microscopic algae living within their tissues. The algae photosynthesize and pass much of the sugar they produce to the coral, which in turn supplies the algae with shelter and nutrients. When water temperature stays even one or two degrees above the usual summer maximum for several weeks, the partnership breaks down: the algae produce damaging compounds, and the coral expels them. Because the algae give coral much of its color, the coral then appears white, or bleached. Bleaching is not immediately fatal. If temperatures fall soon enough, corals can reacquire algae and recover, although they often grow and reproduce more slowly for a time. If heat stress persists, the corals starve. Reefs that bleach repeatedly, with only a few years between events, have less opportunity to recover before the next episode. Which of the following statements is best supported by the passage?
Answer: D. The duration of heat stress, not only its intensity, affects whether bleached corals survive.
The passage ties bleaching to temperatures sustained 'for several weeks' and says survival depends on whether temperatures fall 'soon enough.' Bleaching is 'not immediately fatal,' the cause is damaging compounds rather than lost sugar, and repeated bleaching leaves less time to recover.
Question 4 · Reading Comprehension Test
Radio signals used to communicate with submarines must overcome a basic obstacle: seawater conducts electricity, and electromagnetic waves are rapidly attenuated as they penetrate it. The higher the frequency, the shallower the depth at which the signal becomes too weak to detect. Very low and extremely low frequencies penetrate farther, allowing a submerged boat to receive messages at modest depths, but these frequencies require enormous antenna systems ashore and carry information only slowly, sometimes a few characters per minute. Submarines seeking higher data rates must come near the surface or deploy a buoy or trailing wire antenna, each of which increases the chance of detection. Designers of submarine communications thus balance bandwidth against stealth. As used in the passage, attenuated most nearly means
Answer: A. weakened
The next sentence explains that the signal 'becomes too weak to detect' at depth, so attenuated means weakened. Nothing in the passage describes the signal bouncing back, arriving late, or changing shape.
Question 5 · Mathematics
A crane hook uses a single movable pulley: one end of the rope is fixed to the beam above, the rope passes under the pulley, and the free end is pulled upward. If the free end is pulled up 6 ft, how far does the load rise?
Answer: D. 3 ft
A single movable pulley is held by 2 rope segments, giving a mechanical advantage of 2. Each foot the load rises shortens both segments by a foot, so the free end moves twice as far as the load: 6 ft ÷ 2 = 3 ft. Assuming the load moves as far as the rope (6 ft) treats it like a fixed pulley.
Question 6 · Mathematics
If p and q are different prime numbers, both greater than 2, which of the following must be divisible by 4?
Answer: C. p² − q²
Both primes are odd, so p − q and p + q are both even, and p² − q² = (p − q)(p + q) is a product of two even numbers, which is divisible by 4. The others fail for some pair: 3 + 7 = 10, 3 × 7 + 1 = 22, and 3 + 5 + 2 = 10 are not divisible by 4.
Question 7 · Mathematics
For what value of k does the system 2x + ky = 5 and 6x + 9y = 12 have no solution?
Answer: C. 3
A linear system has no solution when the lines are parallel but distinct: the x- and y-coefficients are proportional while the constants are not. 6x + 9y is 3 times 2x + 3y, so k = 3. Then tripling the first equation gives 6x + 9y = 15, which contradicts 6x + 9y = 12. Writing the coefficient ratio upside down (k/9 = 6/2) gives 27, and matching the constants' ratio (k/9 = 5/12) gives 15/4, which would still leave a solution.
Question 8 · Concl Usi On
Before standardized shipping containers, cargo was loaded piece by piece, bags, barrels, and crates, by large crews of dockworkers, and a ship might spend as much time in port as at sea. The container itself was a simple steel box. Its impact came from standardization: once containers of common dimensions and fittings could move among ships, trains, and trucks without being unpacked, cranes, vessels, and terminals could be designed around them. Loading times fell, theft and damage declined, and ships grew much larger. The benefits arrived unevenly. Ports that could not invest in new cranes and deep berths lost traffic to those that could, and waterfront employment fell sharply in many cities even as the volume of trade grew. Which of the following statements is best supported by the passage?
Answer: B. The container's value came mainly from the system built around a shared standard, not from the box itself.
The passage calls the box simple and attributes its impact to standardization that let equipment be designed around it. Ports benefited unevenly, and waterfront employment fell while trade grew.
Question 9 · Reading Comprehension Test
Commanders in the age of sail held wide authority over their ships but were held strictly accountable for how they used it. An officer who lost a ship faced a court- martial as a matter of routine, not because guilt was presumed but because the proceeding was the accepted means of establishing whether he had discharged his duty. A captain who had fought his ship skillfully against superior odds might emerge from the inquiry with his reputation enhanced. Conversely, a court could censure a captain for failing to do his utmost, even if the loss itself had been unavoidable. The system placed the emphasis on conduct rather than outcome. As used in the passage, discharged most nearly means
Answer: B. fulfilled
The court-martial asked whether the captain had done what his duty required, so discharged means fulfilled. 'Dismissed' and 'released' borrow the sense of discharging someone from service, and 'fired' borrows the sense of discharging a weapon; neither fits 'discharged his duty.'
Question 10 · Mathematics
TWO BLOCK-AND-TACKLE SYSTEMS Effort Effort 120 lb 200 lb System A System B Figure not to scale. System A holds a 120 lb load with 2 supporting rope segments; System B holds a 200 lb load with 4 supporting rope segments, as shown. Ignoring friction and pulley weight, which system needs the greater effort to hold its load?
Answer: A. System A
Effort = load ÷ number of supporting segments. System A: 120 ÷ 2 = 60 lb. System B: 200 ÷ 4 = 50 lb. Even though B lifts the heavier load, its larger mechanical advantage makes its effort smaller. Judging by the heavier load alone leads to System B.
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