Philippine PMA Entrance Practice Test.

Answer: B
Let p be the cost of one ballpen. Then one notebook costs p + 12. The total cost is 4(p + 12) + 3p = 195. Expanding gives 4p + 48 + 3p = 195, so 7p + 48 = 195. Subtract 48: 7p = 147. Divide by 7: p = 21. Therefore, one notebook costs p + 12 = 21 + 12 = ₱33. Check: 4(33) + 3(21) = 132 + 63 = 195. A common mistake is to stop at ₱21, which is the ballpen cost, not the notebook cost.

Answer: C
Let S be the capacity of one standard crate and L be the capacity of one large crate. The information gives 6S + 4L = 356 and 3S + 5L = 310. Divide the first equation by 2: 3S + 2L = 178. Now subtract this from the second equation: (3S + 5L) - (3S + 2L) = 310 - 178, so 3L = 132. Divide by 3: L = 44. Check: from 3S + 2(44) = 178, we get 3S = 90, so S = 30. Then 3(30) + 5(44) = 90 + 220 = 310. A likely mistake is to answer 30, which is the standard-crate capacity, not the large-crate capacity.

Answer: C
Area equals length times width, so (x + 8)(x - 3) = 60. Expand: x^2 + 5x - 24 = 60. Move 60 to the left: x^2 + 5x - 84 = 0. Factor: (x + 12)(x - 7) = 0. Thus x = -12 or x = 7. Because the width is x - 3, x = -12 would give a negative width, so reject it. Use x = 7: length = 7 + 8 = 15 and width = 7 - 3 = 4. Perimeter = 2(15 + 4) = 38 meters. A common mistake is to keep the negative root even though it makes no physical sense.

Answer: A
First note the restriction: x - 3 cannot be 0, so x ≠ 3. Multiply both sides by x - 3: x + 2 = 2(x - 3) + 5. Simplify the right side: 2x - 6 + 5 = 2x - 1. So x + 2 = 2x - 1. Subtract x from both sides: 2 = x - 1. Add 1: x = 3. But x = 3 is not allowed because it makes the denominator zero. Therefore, the equation has no real solution. A likely mistake is to report x = 3 without checking the denominator restriction.

Answer: B
The inequality |2x - 3| < 7 means -7 < 2x - 3 < 7. Add 3 to all three parts: -4 < 2x < 10. Divide all parts by 2: -2 < x < 5. The integer values are -1, 0, 1, 2, 3, and 4. Their sum is -1 + 0 + 1 + 2 + 3 + 4 = 9. Check that endpoints are not included because the inequality is strict. A common error is to include -2 or 5, but those would make the absolute value equal to 7, not less than 7.

Answer: B
Rewrite all powers using base 2. Since 4 = 2^2, 4^(x + 1) = (2^2)^(x + 1) = 2^(2x + 2). Since 8 = 2^3, 8^(x - 2) = (2^3)^(x - 2) = 2^(3x - 6). Dividing powers with the same base means subtracting exponents: 2^(2x + 2) / 2^(3x - 6) = 2^[(2x + 2) - (3x - 6)] = 2^(-x + 8). Therefore 2^(-x + 8) = 2^9, so -x + 8 = 9. Thus -x = 1 and x = -1. Check: if x = -1, the left side is 4^0 / 8^(-3) = 1 / (1/512) = 512 = 2^9. A likely mistake is to add exponents when dividing instead of subtracting them.

Answer: C
Let the first term be a and the common difference be d. The third term is a + 2d = 17. The seventh term is a + 6d = 41. Subtract the first equation from the second: 4d = 24, so d = 6. Substitute into a + 2d = 17: a + 12 = 17, so a = 5. The sum of the first 10 terms is S10 = 10/2[2a + (10 - 1)d] = 5[2(5) + 9(6)] = 5(10 + 54) = 5(64) = 320. A common mistake is to multiply the third and seventh terms by 10 directly, but the sum depends on the first term and common difference.

Answer: B
First compute f(k + 2). Substitute k + 2 for t: f(k + 2) = 2(k + 2)^2 - 3(k + 2). Expand: (k + 2)^2 = k^2 + 4k + 4, so f(k + 2) = 2k^2 + 8k + 8 - 3k - 6 = 2k^2 + 5k + 2. Also f(k) = 2k^2 - 3k. Now subtract: f(k + 2) - f(k) = (2k^2 + 5k + 2) - (2k^2 - 3k) = 8k + 2. Set this equal to 26: 8k + 2 = 26, so 8k = 24 and k = 3. Check: f(5) = 35 and f(3) = 9, and 35 - 9 = 26. A likely mistake is to forget to distribute the minus sign over f(k).

Answer: B
By the remainder idea, division by x - 2 gives remainder P(2). So P(2) = 7. Compute P(2): 2(2^3) - 5(2^2) + c(2) + 12 = 16 - 20 + 2c + 12 = 8 + 2c. Set this equal to 7: 8 + 2c = 7, so 2c = -1 and c = -1/2. Now find P(-1): P(-1) = 2(-1)^3 - 5(-1)^2 + (-1/2)(-1) + 12 = -2 - 5 + 1/2 + 12. Combine: -7 + 12 = 5, and 5 + 1/2 = 11/2. A common mistake is to use x = -2 instead of x = 2 for the divisor x - 2.

Answer: C
Let x be the number of hours Pump B takes alone. Then Pump A takes x - 3 hours alone. Since time must be positive and Pump A is faster, x > 3. Their combined rate is 1 tank in 2 hours, or 1/2 tank per hour. So 1/x + 1/(x - 3) = 1/2. Combine the left side: [(x - 3) + x] / [x(x - 3)] = (2x - 3) / [x(x - 3)]. Set equal to 1/2 and cross-multiply: 2(2x - 3) = x(x - 3). Thus 4x - 6 = x^2 - 3x. Move all terms to one side: x^2 - 7x + 6 = 0. Factor: (x - 1)(x - 6) = 0, so x = 1 or x = 6. Since x > 3, reject x = 1. Pump B takes 6 hours. Check: Pump A takes 3 hours; their combined rate is 1/3 + 1/6 = 1/2 tank per hour, so together they take 2 hours. A likely mistake is to choose 3 hours, which is Pump A’s time, not Pump B’s.

Answer: C
First find each side length. From A to B, only the x-coordinate changes: 4 − (−2) = 6 units. From B to C, only the y-coordinate changes: 9 − 1 = 8 units. Because AB is horizontal and BC is vertical, triangle ABC is right-angled at B. The direct distance from C to A is √(6² + 8²) = √(36 + 64) = √100 = 10 units. Total distance = 6 + 8 + 10 = 24 units. Check: this is the familiar 6-8-10 right triangle, so the computed direct side is consistent.

Answer: B
Model the ladder, wall, and ground as a right triangle. Initially, the ladder is the hypotenuse, so the height on the wall is √(13² − 5²) = √(169 − 25) = √144 = 12 meters. After the top slides down 3 meters, the new height is 12 − 3 = 9 meters. The ladder is still 13 meters long, so the new distance from the wall is √(13² − 9²) = √(169 − 81) = √88 = 2√22 meters. Check: 9² + (2√22)² = 81 + 88 = 169, matching the 13-meter ladder.

Answer: B
The mirror method creates two similar right triangles: one formed by the cadet’s eye height and distance to the mirror, and the other formed by the flagpole height and its distance to the mirror. Set up the proportion: flagpole height / 22.5 = 1.6 / 2.5. So the flagpole height is 22.5 × 1.6 ÷ 2.5 = 36 ÷ 2.5 = 14.4 meters. Check: the flagpole is 9 times as far from the mirror as the cadet is, and 1.6 × 9 = 14.4.

Answer: C
The interior angles of a quadrilateral sum to 360°. Add the given expressions: (x + 20) + (2x + 10) + (x + 30) + 80 = 360. Combine like terms: 4x + 140 = 360. Then 4x = 220, so x = 55. Now compute the angles: ∠A = 75°, ∠B = 120°, ∠C = 85°, and ∠D = 80°. The largest angle is 120°. Check: 75 + 120 + 85 + 80 = 360, so the values are consistent.

Answer: C
The shape is a rectangle plus two semicircles. The two semicircles together make one full circle. The rectangle area is 60 × 28 = 1680 square meters. Each semicircle has diameter 28 meters, so the circle radius is 14 meters. The combined circular area is πr² = (22/7)(14²) = (22/7)(196) = 22 × 28 = 616 square meters. Total area = 1680 + 616 = 2296 square meters. Check: the answer should be larger than the rectangle area alone, and 2296 is larger than 1680.

Answer: C
The rope covers the sector perimeter: two radii plus the arc length. The two radii total 10 + 10 = 20 meters. The arc is 72° out of 360°, or 72/360 = 1/5 of the full circumference. The full circumference is 2πr = 2(3.14)(10) = 62.8 meters. The arc length is 62.8 ÷ 5 = 12.56 meters. Total rope length = 20 + 12.56 = 32.56 meters. Check: the arc is only one-fifth of the circle, so an arc length of 12.56 meters is reasonable.

Answer: B
Let the path width be w meters. Since the path runs along all inside edges, the central rectangle has dimensions 30 − 2w and 20 − 2w. Its area is 416, so (30 − 2w)(20 − 2w) = 416. Expand: 600 − 60w − 40w + 4w² = 416, so 4w² − 100w + 184 = 0. Divide by 4: w² − 25w + 46 = 0. Factor: (w − 2)(w − 23) = 0, so w = 2 or w = 23. A 23-meter path is impossible because the lot is only 20 meters wide. Therefore w = 2 meters. Check: the central area would be 26 × 16 = 416 square meters.

Answer: C
The perpendicular distance to the 14-meter side is the altitude using that side as the base. First find the area using Heron’s formula. The semiperimeter is s = (13 + 14 + 15)/2 = 21. Area = √[21(21 − 13)(21 − 14)(21 − 15)] = √[21 × 8 × 7 × 6] = √7056 = 84 square meters. Also, area = 1/2 × base × height = 1/2 × 14 × h = 7h. Thus 7h = 84, so h = 12 meters. Check: 1/2 × 14 × 12 = 84, matching the area.

Answer: C
First find the equation of the boundary line. The slope through P and Q is (10 − 2)/(6 − 0) = 8/6 = 4/3. Using point P(0, 2): y − 2 = (4/3)x. Multiply by 3: 3y − 6 = 4x, or 4x − 3y + 6 = 0. The distance from point (7, 1) to line Ax + By + C = 0 is |Ax₀ + By₀ + C| / √(A² + B²). Substitute: |4(7) − 3(1) + 6| / √(4² + (−3)²) = |28 − 3 + 6| / √25 = 31/5. Check: 31/5 = 6.2 units, a positive distance as expected.

Answer: B
The volume of a pyramid is one-third of the base area times the vertical height. The base area is 10 × 10 = 100 square meters. To find the vertical height, use the right triangle formed by the apex, the center of the base, and the midpoint of a base side. The distance from the center of the square to the midpoint of a side is 10/2 = 5 meters. The slant height is 13 meters, so the vertical height is √(13² − 5²) = √(169 − 25) = √144 = 12 meters. Volume = (1/3)(100)(12) = 400 cubic meters. Check: the height is less than the slant height, as it should be.

Answer: C
First, identify the compound subject: “Neither the equipment log nor the updated maps.” With “neither...nor,” the verb should agree with the nearer subject. The nearer subject is “maps,” which is plural, so the verb should be “were,” not “was.” Next, “platoon” is treated as one unit in this sentence, so the possessive pronoun should be “its,” not “their” or “it’s.” “It’s” means “it is,” so it would not fit. Therefore, the correct sentence is: “Neither the equipment log nor the updated maps were available when the platoon checked its route.”

Answer: B
Look at the letter positions in the alphabet: A = 1, C = 3, F = 6, J = 10, O = 15. The increases are +2, +3, +4, +5, so the next increase should be +6. Thus the next letter position is 15 + 6 = 21, which is U. Now look at the numbers: 1, 2, 4, 7, 11. Their increases are +1, +2, +3, +4, so the next increase should be +5. Thus the next number is 11 + 5 = 16. The next code is U16. A likely mistake is to continue only the number pattern or only the letter pattern.

Answer: B
The sentence contains two independent clauses: “The cadets reviewed the safety plan” and “the weather forced them to revise the route.” The word “however” is a conjunctive adverb, not a coordinating conjunction. When it connects two independent clauses, a semicolon should come before “however,” and a comma should follow it. A comma alone before “however” would create a comma splice. Therefore, the correctly punctuated sentence is: “The cadets reviewed the safety plan; however, the weather forced them to revise the route.”

Answer: D
The phrase “By the time the signal officer arrived” places the arrival in the past. The testing happened before that past arrival, so the past perfect form “had tested” is needed. The second action describes what the team was doing at the time of the arrival, so the past progressive “was waiting” fits. “Tested and waited” makes both actions simple past and does not clearly show that the testing was completed earlier. “Has tested” shifts incorrectly to the present perfect. Therefore, the correct completion is: “had tested; was waiting.”

Answer: A
The problem is pronoun reference. In a sentence such as “When Liza spoke to Mara after the briefing, she said she would submit the report,” the pronoun “she” could refer to either Liza or Mara. A clear revision must name the person who will submit the report or use direct speech in a way that identifies the speaker. The best option states that Liza told Mara the report would be submitted by Liza herself. Therefore, the clearest revision is: “After the briefing, Liza told Mara, ‘I will submit the report before noon.’”

Answer: A
The sentence lists three qualities or actions after “for.” To be parallel, all three items should use the same grammatical form. “Being alert,” “disciplined,” and “they responded quickly” do not match: the third item is a full clause, while the first two are not. A strong revision uses three parallel gerund phrases: “staying alert,” “maintaining discipline,” and “responding quickly.” This also keeps the meaning clear. Therefore, the best revision is: “The commander praised the squad for staying alert, maintaining discipline, and responding quickly.”

Answer: A
The opening phrase “Covered in thick fog” should describe the thing actually covered by fog. In the original sentence, the phrase appears to describe “the driver,” which creates an illogical image. The intended meaning is that the road or area was foggy, making the checkpoint hard to see. The clearest correction names what the fog covered and then states the result. Therefore, the best revision is: “Because thick fog covered the road, the driver could barely see the checkpoint.”

Answer: A
The passage says Mara first wanted to save time by crossing the field. Then she observed deep footprints, asked the caretaker, and learned that walking there could damage roots and track mud indoors. She chose the paved path even though it took longer. This shows that her decision was based on avoiding harm and mess, not on getting lost, following a punishment, or proving that the shortcut was impossible. Therefore, the best explanation is: “She decided that protecting the garden and keeping the halls clean mattered more than saving time.”

Answer: A
The sequence markers give the order. A paragraph that describes a process should begin with “First,” so sentence 2 comes first. Sentence 3 follows because it says “After the discussion,” referring to the hazard-naming discussion in sentence 2. Sentence 1 begins with “Finally,” so it comes after the earlier steps. Sentence 4 works best as the concluding result of the meeting. Therefore, the most coherent order is: 2-3-1-4.

Answer: D
“Affect” is usually a verb meaning “to influence.” “Effect” is usually a noun meaning “result.” The sentence needs a verb after the subject “The delayed announcement,” so “affected” is correct. Later, the phrase “its long-term ___ was minor” needs a noun, so “effect” is correct. The other choices either use the noun where a verb is needed or the verb where a noun is needed. Therefore, the correct sentence is: “The delayed announcement affected morale, but its long-term effect was minor.”

Answer: A
An effective persuasive thesis should be clear, arguable, and specific enough to guide a short essay. It should not be a mere fact, a vague announcement of the topic, or an unrelated claim. The best option directly argues that school clubs should conduct cleanups and gives focused reasons: civic responsibility, teamwork, and visible improvement. That scope is suitable for a one-page essay. Therefore, the most effective thesis is: “School clubs should organize monthly community cleanups because the activity builds civic responsibility, strengthens teamwork, and visibly improves shared spaces.”

Answer: A
Step 1: Identify the stated reason for the delay: a team needed to check the upstream bridge for trapped debris. Step 2: Connect this to the danger described earlier: the current was still strong and carrying branches. Step 3: Check against the tempting mistake: the delay was not because rain was still falling; the passage says the sky was clear and the water had stopped climbing. Therefore, the best answer is: Because hidden debris and a strong current could still make travel dangerous.

Answer: B
Step 1: List the conditions: dry months, limited funds, unreliable rainwater supply, and a trial method that reduced water use. Step 2: Eliminate weekly water delivery because the treasurer says funds are insufficient for it. Step 3: Eliminate relying only on the tank because it fills only during storms. Step 4: Choose the plan supported by evidence and budget: low-cost water-saving methods plus stored rainwater when available. Therefore, the best answer is: Use water-saving methods and stored rainwater rather than depend on weekly deliveries.

Answer: C
Step 1: Find the claim being challenged: the engineer says a concrete wall could replace mangroves as protection. Step 2: The fisherfolk leader does not only discuss flood protection; the leader adds that mangroves shelter young fish and support catches. Step 3: This challenges the assumption that replacing mangroves with a wall would preserve the important benefits of mangroves. Therefore, the best answer is: That a concrete wall can replace the mangroves’ important functions.

Answer: D
Step 1: Mara sees a struggling teammate and chooses to help rather than simply hurry. Step 2: She also manages risk by sharing the load and sending a message ahead. Step 3: The outcome confirms that her action prevented injury, though the leader notes communication could improve. Therefore, the best answer is: She showed responsible concern for a teammate while managing the delay.

Answer: A
Step 1: Carlo praised the project, so he was not simply against it. Step 2: He wanted a safety check before the vote, so Ben’s report is closer but still incomplete. Step 3: His support depended on whether the room passed inspection. Therefore, the best answer is: He supported the library idea but wanted a safety inspection before final approval.

Answer: A
Step 1: The sign gives a rule: one person at a time and no carts. Step 2: The carpenter explains why appearance can mislead: children crossing safely does not prove the bridge can handle cart wheel pressure. Step 3: He also notes wet knots may loosen, so the concern includes connections, not only broken poles. Therefore, the best answer is: It may handle careful foot traffic but not concentrated cart loads or loosened ties.

Answer: D
Step 1: Locate the word in context: speakers summarized only the essential points. Step 2: The result was a shorter and clearer meeting, so “essential” refers to the necessary or most important points, not decorative details. Step 3: Check distractors: “secret,” “difficult,” and “officially printed” are not supported by the passage. Therefore, the best answer is: most important.

Answer: D
Step 1: Identify who handled counting: the records team. Step 2: Find when counting happened: before sacks were loaded onto the truck and before leaving the beach. Step 3: This prevents confusion after removal because every sack had already been listed. Therefore, the best answer is: Each sack was recorded before it was taken away from the beach.

Answer: A
Step 1: The rule has benefits: less paper and easier deadline tracking. Step 2: A new problem appears among students with poor internet access. Step 3: The principal’s request for an offline option shows recognition that the online-only rule may treat students unequally. Therefore, the best answer is: It may disadvantage students who have limited internet access.

Answer: B
Step 1: Identify the main action: Tomas provided a clear, updated bus schedule at the stall. Step 2: Identify the result: more travelers stayed nearby and bought snacks. Step 3: Avoid a narrow summary about changing the recipe, because the passage says the cakes did not change. Therefore, the best answer is: Tomas attracted more customers by solving travelers’ need for clear bus information.

Answer: C
Let the starting number of meal packs be x. After the first group receives one-fourth, three-fourths remain: 3x/4. The second group receives 40% of that remainder, so 60% of the remainder is left. Thus the amount left after the second group is (60/100)(3x/4) = (3/5)(3x/4) = 9x/20. This remaining amount is also the third group’s 72 packs plus the 36 packs left over, or 108 packs. So 9x/20 = 108. Multiply both sides by 20/9: x = 108 × 20/9 = 12 × 20 = 240. Check: one-fourth of 240 is 60, leaving 180. Forty percent of 180 is 72, leaving 108. Then issuing 72 leaves 36, so the result is consistent. A common mistake is to take 40% of the original total instead of 40% of what remained.

Answer: D
The second statement guarantees that at least some attentive cadets are radio operators. The third statement says no radio operator is assigned to kitchen detail. Therefore, those attentive cadets who are radio operators are not assigned to kitchen detail. So it must be true that some attentive cadets are not assigned to kitchen detail. The first statement about map readers does not prove that map readers are radio operators, so conclusions connecting map readers to radio operators would be a likely mistake.

Answer: B
Separate the sequence into odd-position and even-position terms. Odd positions are 1st, 3rd, 5th, 7th: 5, 10, 17, 26. Their increases are +5, +7, +9, so the next odd-position increase should be +11. Therefore the 9th term is 26 + 11 = 37. Even positions are 7, 14, 28, 56, which double each time, but the blank is the 9th term, not the next even-position term. A likely mistake is to continue the even-position pattern and answer 112, but that would be the 10th term if the pattern continued.

Answer: C
When both clerks work together, their combined rate is 24 + 18 = 42 records per hour. In 2 hours, they encode 42 × 2 = 84 records. Then Clerk A works alone for 1.5 hours at 24 records per hour, so A encodes 24 × 1.5 = 36 records. The total is 84 + 36 = 120 records. Check: all time periods have been counted exactly once. A common mistake is to let both clerks work for the full 3.5 hours, but Clerk B leaves after 2 hours.

Answer: B
The river road is faster in normal conditions, but the passage gives two warnings: dark clouds gathered, and the river road floods after heavy rain. The ridge road is slower and steeper, but it is described as passable because its drainage canal had been cleared. Since the rice had to arrive before evening and the footbridge would close, Mara needed a reliable route, not simply the shortest usual route. Her choice of stronger volunteers also fits the steep climb on the ridge road. A common mistake is to focus only on the forty-minute travel time and ignore the weather risk.

Answer: A
The clearest sentence should show that the plan, not the officers, reduced crowding. It should also combine the ideas without a dangling modifier or unclear pronoun. The sentence “The revised evacuation plan, reviewed twice by the officers, reduced crowding at the gates” correctly identifies the plan as the subject and includes the review detail as a modifying phrase. A likely mistake is to write a sentence where “reviewed twice” seems to describe the officers or where “it” could refer to more than one thing.

Answer: C
The interior angles of a quadrilateral sum to 360°. Add the four angle expressions: (2x + 20) + (3x + 10) + (x + 30) + 90 = 360. Combine like terms: 6x + 150 = 360. Subtract 150 from both sides: 6x = 210. Divide by 6: x = 35. Now compute each angle: 2x + 20 = 2(35) + 20 = 90°; 3x + 10 = 3(35) + 10 = 115°; x + 30 = 35 + 30 = 65°; and the fourth angle is 90°. The largest is 115°. A likely mistake is to stop at x = 35 and choose 35°, but the question asks for the largest angle, not x.

Answer: C
First find the original total score: 5 × 76 = 380. Removing the lowest score of 62 gives 380 − 62 = 318. The new average is 81 over five drills, so the new total must be 5 × 81 = 405. Therefore the new drill score must be 405 − 318 = 87. Check: replacing 62 with 87 increases the total by 25, and an increase of 25 over five scores raises the average by 5 points, from 76 to 81. A common mistake is to add 5 to 62 and answer 67, but the average increase is spread across all five scores.

Answer: B
The coordinator’s argument assumes that group-text announcements would reach the late volunteers better than the bulletin board did. To weaken the argument, look for information showing that group texts would not solve the problem. If most late volunteers were in an area where group-text messages also could not be received, then switching to group texts would probably not improve their arrival time. This directly attacks the proposed solution. A common mistake is to pick a statement that merely praises group texts or restates that the bulletin board was not checked; those do not weaken the argument.

Answer: C
Compare each term with the one before it. From 4 to 9: 4 × 2 + 1 = 9. From 9 to 19: 9 × 2 + 1 = 19. From 19 to 39: 19 × 2 + 1 = 39. From 39 to 79: 39 × 2 + 1 = 79. So the same rule gives 79 × 2 + 1 = 158 + 1 = 159. A common mistake is to look only at the differences 5, 10, 20, 40 and answer 119 by adding 40 again; but the differences are doubling, so the next difference would be 80, also giving 79 + 80 = 159.

Answer: B
Separate the number pattern from the letter pattern. The numbers are 3, 6, 11, 18, 27. Their differences are +3, +5, +7, +9, so the next difference is +11. Thus the next number is 27 + 11 = 38. The letters are A, C, F, J, O. Their alphabet positions are 1, 3, 6, 10, 15. The differences are +2, +3, +4, +5, so the next difference is +6. Position 15 + 6 = 21, which is U. Therefore the next item is 38U. A likely mistake is to continue only one part of the pattern and leave the other unchanged.

Answer: B
Look for a rule connecting the first two numbers in each row to the third number. In Row 1, 3 × 4 = 12, and 3 + 4 = 7. Then 12 + 7 = 19. In Row 2, 5 × 6 = 30, and 5 + 6 = 11. Then 30 + 11 = 41. So the rule is: third number = product of the first two numbers + their sum. For Row 3, 7 × 8 = 56, and 7 + 8 = 15. Then 56 + 15 = 71. A common wrong approach is to add a constant difference between third-column values, but the row operation is more consistent.

Answer: A
There are two changes happening at the same time. First, the arrow rotates clockwise: ↑, →, ↓, ←, so the next arrow returns to ↑. Second, the two squares swap positions each frame: ■ □, then □ ■, then ■ □, then □ ■, so the next arrangement is ■ □. Combining both parts, Frame 5 is ↑ ■ □. A likely mistake is to track only the arrow rotation and ignore the square swap, or to swap the squares without rotating the arrow.

Answer: C
Check the differences between consecutive terms. From 5 to 8 is +3. From 8 to 14 is +6. From 14 to 23 is +9. From 23 to 35 is +12. The differences increase by 3 each time: 3, 6, 9, 12. The next difference is 15. Therefore the next term is 35 + 15 = 50. A common mistake is to add 12 again and get 47, but the differences themselves are increasing.

Answer: C
The operations repeat in a cycle. Starting at 2: 2 × 3 = 6, then 6 × 3 = 18, then 18 + 2 = 20. The same cycle repeats: 20 × 3 = 60, then 60 × 3 = 180, then 180 + 2 = 182. Since the cycle is multiply by 3, multiply by 3, add 2, the next operation after 182 is multiply by 3. So 182 × 3 = 546. A likely mistake is to see the last move was +2 and add 2 again, but the pattern is cyclical, not a constant addition.

Answer: C
Treat the letter and number as two related but separate sequences. The letter positions are B = 2, D = 4, G = 7, K = 11, P = 16. The increases are +2, +3, +4, +5, so the next increase is +6. Position 16 + 6 = 22, which is V. The numbers are 3, 6, 10, 15, 21. Their increases are +3, +4, +5, +6, so the next increase is +7. Thus the next number is 21 + 7 = 28. The next item is V28. A likely mistake is to use the same increase for both parts, but the letter increases start at +2 while the number increases start at +3.

Answer: C
The center tile stays the same throughout the pattern. Each stage has four arms, and each arm has as many tiles as the stage number. So Stage 1 has 1 center tile + 4 arm tiles = 5. Stage 2 would have 1 + 4(2) = 9. In general, Stage n has 1 + 4n tiles. For Stage 7, compute 1 + 4(7) = 1 + 28 = 29. A likely mistake is to add 4 only six times to Stage 1 but lose track of the center tile; doing it carefully still gives 5 + 6(4) = 29.

Answer: C
Start from Monday: C2. Move one day at a time. Tuesday: C advances three letters to F, and 2 × 2 + 1 = 5, so Tuesday is F5. Wednesday: F advances to I, and 5 × 2 + 1 = 11, so Wednesday is I11. Thursday: I advances to L, and 11 × 2 + 1 = 23, so Thursday is L23. Friday: L advances to O, and 23 × 2 + 1 = 47, so Friday is O47. A likely mistake is to make only three changes from Monday to Friday, but Monday to Friday requires four daily changes: Monday to Tuesday, Tuesday to Wednesday, Wednesday to Thursday, and Thursday to Friday.

Answer: C
This pattern is clearer if we separate the odd-positioned terms from the even-positioned terms. Odd positions are 1st, 3rd, 5th, 7th, and 9th: 7, 9, 13, 19, 27. Their increases are +2, +4, +6, +8. Even positions are 2nd, 4th, 6th, and 8th: 10, 14, 22, 34. Their increases are +4, +8, +12. The missing term is the 10th term, so it belongs to the even-positioned sequence. The even-position differences increase by 4 each time, so the next increase is +16. Therefore the missing term is 34 + 16 = 50. A likely mistake is to compare every neighboring pair and miss the two interleaved sequences.