august 2026 sat math answers: Every Math question test-takers recalled from the August 22, 2026 international Digital SAT, the answers students argued for, and which one is actually right.
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The r/Sat official discussion thread for the August 22, 2026 international administration ran past 1,100 comments on test day. Taking the US test instead? The August 22, 2026 US administration was a separate form with different questions — see August 2026 US SAT Math Answers (Reddit Megathread, Solved), built from the 7,085-comment r/Sat US discussion thread. Buried in it is a partial reconstruction of the Math section — students posting what they remembered and arguing about the answers. On most items they disagreed. This page collects every Math item the thread recalled, reports what students actually said and how the votes split, and then works out which answer is correct.
How to read this page. Question descriptions are students' own recall from the thread, quoted as they wrote them. They are incomplete and sometimes inconsistent — where two students remembered different numbers, that's noted. The vote tallies are counts of commenters who committed to an answer. The verdict is ours, worked from the mathematics, and it does not always agree with the popular vote.
Source: r/Sat, Official August 22, 2026, International SAT Discussion Thread — 1,100+ comments, read on test day. Quotations below are from that thread.
Answer key at a glance
| Item | Most-voted student answer | Verdict | Confidence |
|---|---|---|---|
| "What percent of a is b", a = 0.8, b = 24 | 3000% (5 votes) | 3000% | Confirmed |
| Kangaroo mass, increase of 414% | a = 5.14 (1 vote) | 3.79 in our material (279%) | Confirmed |
| Isosceles triangle, height 16√3, base 24√3, legs a√3 | a = 20 (1 vote) | a = 25 in our material (√6 version) | Confirmed |
| f(x) = a((x+4)² − b)((x+4)² − c), find f(−8) + f(−3) | 117 (1 vote), 120 (1 vote) | 120 (the 120 voter was right) | Confirmed |
| Two data sets, smallest difference (Q22, hard module) | 1 (4 votes) | 1 | Confirmed |
| Two tangent spheres, find MN | 30 (1 vote), 168 (1 vote) | MN = 120 | Verified |
| Rental: $20 up to 6 days, $10 each day after | 10x − 10 (1 vote) | 11t + 11 (flat fee covers day 1) | Confirmed |
| Margin of error and sample size | Smaller (2 votes) | Smaller | Confirmed |
| Three parallel lines, 205 < x+y+z < 230 | No convergence | I only | Verified |
| Histogram, minimum mean difference | 0 (2 votes, both admitted guesses) | 1 (0 is unreachable) | Verified |
| Metals: y increases by 15 when c increases by 5 | No answer posted | y = 2x − 530 (rate is 2) | Verified |
Item 1 — "What percent of a is b" (Module 1, final question)
As students recalled it:
"Did anyone get what percentage of a is b. Was it 3000% or 3.33%"
"3000%. 3.33% wasn't even an answer choice I guess. a value was 0.8 I recall. b value was 24 I guess?"
"another question in math m1 last one it was a is what percent of b, it was 3000% right??? A was 0.8 and b was 24"
How the votes split: 3000% — five commenters. 7000% — one commenter. 3.33% — raised as a possibility by the original asker, defended by nobody.
The transferable rule: in "what percent of X is Y", X is always the denominator. Write "Y ÷ X" down before you compute anything. If the answer choices contain a number and its reciprocal (3000% and 3.33%), the test is specifically checking whether you got the base right.
Check yourself: 24 is what percent of 0.8, and 0.8 is what percent of 24? Say both before reading on.
Item 2 — Kangaroo mass increase
As students recalled it:
"Did anyone get that kangaroo population qs where on 60 day weight was k and 110 day weight was ak and it increased 414%, a was 5.14 right?"
"Wait I got that too a red kangaroo? Mine was 709percent tho so I wrote an equals 7.09. But I think I'm wrong cuz it said increased by 709 percent so a is 8.09. Do u remember if it said the older kangaroo was 709% of the younger kangaroo OR the younger kangaroo increased weight by 709%?"
How the votes split: a = 5.14 — one commenter, for the 414% version. A second commenter recalled a 709% version, first answered 7.09, then corrected themselves to 8.09 in the same comment.
Bluebook doesn't have enough hard Module 2 questions. Try a free Math section from TTA and see what you're missing.
Start 1-day free trial →The transferable rule: "increased by p%" and "is p% of" are different sentences and produce different multipliers. Increased by p% → multiply by (1 + p/100). Is p% of → multiply by p/100. That second commenter identified exactly the right question to ask — which of the two phrasings the question used — and that is the whole item.
Check yourself: a population increases by 250%. What do you multiply the original by? Now: a population is 250% of its original. What do you multiply by?
Item 3 — Isosceles triangle with radical side lengths
As students recalled it:
"Did anyone get that question Triangle isosceles, height was something under root 3 and base was 23 under root 3 and we had to find length of the other leg, we had to do pythagoras right? With the height and with base/2"
"Anybody get an a√6, find a using the height of an isosceles triangle something along those lines?"
"Yes. Height was 16√3 isosceles sides a√3. Base 24√3. a equals 20. Surely"
How the votes split: a = 20 — one commenter, with the full parameters stated. The other two recalled the figure but posted no answer, and one of them remembered the base as 23√3 rather than 24√3.
The transferable rule: the height of an isosceles triangle drawn to the unequal side bisects that side. Always halve the base before applying Pythagoras. Forgetting to halve is the error the question is built to catch, and here it would have produced √(768 + 1728) = √2496, which is not a clean multiple of √3 and so would not have matched any answer choice — a useful self-check.
Check yourself: before applying Pythagoras to an isosceles triangle's height, what must you do to the base, and why?
Item 4 — The nested quadratic (hard Module 2)
Correction (checked against the exam material): the answer is 120, not 117. The symmetry method below is right. The recalled points were not: the graph passes through (−5, 30) and (0, 90), so f(−8) + f(−3) = 90 + 30 = 120. See the corrections section.
As students recalled it:
"i cant attach images but it was f(x) = a((x+4)^2 − b)((x+4)^2 − c), f(−5) = 36, f(0) = 81, find f(−8) + f(−3) — and the answer is 36 + 81 = 117"
"There was a hard math question m2 f(x) = a((x+4)^2 − b)((x+4)^2 − c). I dont remember but there were 2 points. Did anyone get 120?"
How the votes split: 117 — one commenter, who posted the reasoning behind a spoiler tag. 120 — one commenter, offered as an uncertain question.
The transferable rule: when every occurrence of the variable sits inside the same squared bracket (x + k)², the function is symmetric about x = −k. Before doing any algebra, check whether the inputs you've been given and the inputs you're asked about pair up across that line of symmetry. This is one of the highest-value patterns in Digital SAT Advanced Math, and it converts a fifteen-minute problem into a fifteen-second one.
Check yourself: for f(x) = a((x−3)² − b), if f(1) = 12, what is f(5), and how do you know without finding a or b?
Item 5 — Two data sets, smallest difference (Q22, hard module)
As students recalled it:
"Who got q22 of math hard module which two data sets and we had to find smallest difference? It was just like a practice test question and the answer was 1 there and here too right?"
"I think it was in the question bank or in a past test cus i remember doing it and it was 1"
"It was not experimental. It was in the practice 8 bluebook. I didnt even do the question straightly picked 1."
"b) 1"
How the votes split: 1 — four commenters, with no dissent, and two of them independently citing a source (the official question bank and Bluebook Practice Test 8).
What this item actually tells you: the more useful finding here isn't the answer, it's the sourcing. Multiple students recognised a question in the hard Module 2 from the official Bluebook practice material. Questions do get reused. Working the full official question bank buys you more than practice. It buys a real, if unreliable, chance of seeing something familiar on test day.
Item 6 — Two tangent spheres, find MN
As students recalled it:
"Did anyone get the module2 math question about the 2 spheres and the tangent of P and having to find the length of MN? the question said stuff like sphere A's radius is 14 times that of B. and we were given volume of the sphere B."
"I did. Answer was 30. They gave radius for circle A (9). We could find it for circle B using the volume they provided. It came out as 6. Length of MN = 2(6) + 2(9) = 30"
"I got 168 for that. I got the radius as 6 using the volume for b at 288pi so the diameter of the smaller sphere is 12 and the diameter for the larger sphere is 2*6*13 cuz it said b's radius was 13x more. so total 168"
How the votes split: 30 — one commenter. 168 — one commenter. But look closely: they are not answering the same question. One says sphere A's radius is 9; another says it's 13 times sphere B's; the original asker says 14 times.
See which question types are costing you points
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The transferable rule: volume scales with the cube of the radius, so going from a volume to a radius means taking a cube root — and 216, 512, 1000 and 1728 are the cube numbers the SAT reaches for most often. Learn them cold. And for tangent circles or spheres, the centre-to-centre distance is the sum of the radii; adding the two outer radii on top of that gives the full span.
Check yourself: a sphere has volume 972π. What is its radius?
Item 7 — Rental pricing (Module 2)
Correction (checked against the exam material): the flat fee covers the first day, not the first six days. With the material's numbers ($22 for the first day, $11 for each additional day) the cost is 11t + 11. With the thread's $20/$10 figures it would be 10x + 10. The 10x − 40 verdict below is wrong. See the corrections section.
As students recalled it:
"guys for the question in module 2 about how it's 20 dollars for up to 6 days in the first day and 10 dollars for each day after was answer choice A 10x−10 or B"
"is the question about the first day up to 6 days being 10 dollars and the additional payment being 20 dollars answer was 10x−10 −10 or −20 points"
How the votes split: 10x − 10 — floated by both commenters, neither confident. No other candidate offered.
The transferable rule: in any flat-fee-plus-per-unit problem, the constant is (flat fee) − (rate × number of units the flat fee covers). Then always test your expression against a single concrete case you can compute by hand. Plugging x = 7 into this one takes five seconds and immediately kills the wrong answer. Students in the thread argued about it instead of testing it.
Check yourself: a gym charges $50 for the first 3 months and $15 per month after that. Write the expression for m months, m > 3, then verify it at m = 4.
Item 8 — Margin of error and sample size
As students recalled it:
"the larger sample size would have a smaller margin of error..idr the options but i put a"
"the marginal error decreases yeah cuz sample size increased so less that wtv percent was given"
How the votes split: smaller margin of error — two commenters, no dissent.
The transferable rule: bigger sample → smaller margin of error → narrower confidence interval → more precise estimate. The relationship is not linear — the margin of error falls with the square root of the sample size, so quadrupling the sample halves the margin. You will not be asked to compute it, but you will be asked which direction it moves.
The unresolved items
Three Math items generated real discussion and no usable answer. We're listing them as unresolved rather than guessing.
Three parallel lines with an angle-sum constraint
"what was the answer to module 2 there r three parallel lines and x+y+z was between 200 and 210 and if x can be 28 or 32 degrees"
"The question where it said three parallel lines and x was between 201 and 216. I put I only."
"Did anyone get that one question with three parallel lines and w y z x and something like 205 < x+y+z < 230, it was really ugly"
Three commenters, three different stated ranges (200–210, 201–216, 205–230), and nobody posted a defended answer. Several suspected it was an unscored experimental item. No verdict is possible — the recalled constraints contradict each other.
What is recoverable is the method, and one commenter got there: "W−y equals to x, and y + z equals to 180, and you just gotta put numbers in." That's the right shape. With parallel lines cut by a transversal, co-interior angles sum to 180° and corresponding angles are equal. Use those two facts to rewrite x + y + z in terms of a single variable, then let the given inequality bound that variable, then test which listed values survive. Roman-numeral answer formats ("I only", "I and II") almost always mean the question wants a range checked against candidates, not a single value solved for.
Histogram, minimum mean difference
"what was the answer to the last m2 math question about histogram means"
"If ur referring to the histogram question asking the minimum mean difference I guessed that question and put the answer as 0"
"Did anyone get 0 for histogram?"
Two commenters said 0, and one of them stated plainly that it was a guess. A guessed answer repeated by a second person is not corroboration. Unresolved. Note for prep: "minimum possible difference between the means" is only 0 when the two distributions can be arranged to coincide, and on a histogram with fixed frequencies that is usually impossible — so 0 is a suspicious answer to arrive at by instinct.
The metals question
Now solved (checked against the exam material): the rate is 2, not 3. The item starts with 300 grams of metal X and 70 grams of metal Y, and 10 grams of Y are added for every 5 grams of X, so y = 70 + 2(x − 300) = 2x − 530. See the corrections section.
"Wtf was the metals question it took me 15 mins and i think i still did it wrong. It said y increases by 15 when c increases by 5"
Highly upvoted as a complaint, but nobody posted the question or an answer. Unresolved. The one extractable fact: if y increases by 15 for every increase of 5 in c, the rate of change is 15 ÷ 5 = 3, so the relationship has slope 3 in the y-c plane. Whatever the question asked, that constant was the way in — and fifteen minutes was fourteen minutes too long to spend on it.
Checked against the actual exam material
Everything above this line is student recall. Everything below is the same items checked against the August 2026 Digital SAT Math material itself — the full 201-question reconstruction now in our question bank, where each item has been worked and verified independently. Three items the thread gave up on are answerable. Three of the thread's verdicts are wrong.
One caveat, stated up front: on a few items the structure matches the recall exactly but the numbers differ. Our material covers both the US and international August 2026 forms and is not separated by region, so where the numbers differ we report what our material says rather than assuming a student misremembered. The method is the same either way.
Now resolved — the three items the thread couldn't settle
Item 6, the two tangent spheres — MN = 120. The recall that survives is the one that said sphere A's radius is 9 times sphere B's, with sphere B's volume 288π. That gives r³ = 216, so rB = 6 and rA = 54. MN is the sum of the two diameters: 108 + 12 = 120. Neither posted answer (30 or 168) was right, but both students used the correct method — they were working from wron
olume they both recalled is exactly right.
The three parallel lines — the answer is "I only", and the student who put that was right. The real constraint is 205 < x + y + z < 212, and the question asks which values w − y could take, from I. 26 and II. 32. Because y + z = 180 (co-interior angles), x + y + z collapses to x + 180, so 25 < x < 32. And because w = x + y, w − y = x. So 26 works and 32 does not — the inequality is strict. I only. The commenter who wrote "I put I only" had it, and the commenter who reconstructed "y + z equals 180" had the key step.
The histogram question — the answer is 1, not 0. This is the same item as Item 5 above, recalled a second time under a different description. Two data sets of 23 integers each, shown as histograms, asking for the smallest possible difference between the means. The guessed 0 is wrong. Data set A's smallest possible mean is 910/23 and data set B's largest possible mean is 887/23, and those differ by exactly 23/23 = 1. The two ranges sit adjacent without overlapping, which is precisely why 0 is unreachable — the instinct that 0 "looks like" the minimum is the trap.
Corrected — where this page's own verdict was wrong
Item 4, the nested quadratic — 120, not 117. The student who said 120 was right. The symmetry argument on this page is correct and it is the whole point of the question. What was wrong were the two given points. The material has the graph passing through (−5, 30) and (0, 90), not (−5, 36) and (0, 81). Everything else follows unchanged: −3 and −5 are both one unit from −4 so f(−3) = f(−5) = 30; −8 and 0 are both four units from −4 so f(−8) = f(0) = 90. The sum is 90 + 30 = 120. The lone commenter who asked "did anyone get 120?" had the right answer and no support for it.
Item 7, the rental — the flat fee covers the first day, not the first six days. This is the structural error. In our material the item reads: a flat charge for the first day plus a smaller charge for each additional day, with the whole rule valid for stays up to six days. The phrase "up to 6 days" is the domain of the formula, not what the flat fee buys. With the material's numbers — $22 for the first day and $11 for each additional day — the cost for t days is 22 + 11(t − 1) = 11t + 11. Map that onto the $20/$10 figures the thread recalled and you get 20 + 10(x − 1) = 10x + 10. The subtraction in "10x − 40" comes from assuming the flat fee absorbs six days; there is no version of this item where the constant is negative.
The metals question — the rate is 2, and the item is fully solvable. The recalled "y increases by 15 when c increases by 5" gives rate 3, but the material's version is a mixture problem: it starts with 300 grams of metal X and 70 grams of metal Y, and for every 5 grams of X added, 10 grams of Y are added — a rate of 2, not 3. Writing y as a function of the total mass x of metal X: the amount added is (x − 300), so y = 70 + 2(x − 300) = y = 2x − 530. The fifteen minutes this cost one commenter went on the setup, not the algebra — once you fix the starting amounts and the rate, it is two lines.
Where the numbers differ
The kangaroo. Our material gives the increase as 279% from 110 days to 180 days, which makes a = 1 + 2.79 = 3.79. The thread recalled 414% and 709%. The reasoning on this page is right for all three — "increased by p%" means multiply by (1 + p/100) — so 414% → 5.14 and 709% → 8.09 both follow correctly from their premises. Only the percentage is in dispute.
The isosceles triangle — and the commenter nobody answered was onto something. One student asked, "anybody get an a√6, find a using the height of an isosceles triangle?" and got no reply. Our material has exactly that: base 30√6, height 20√6, legs a√6. Half the base is 15√6, so leg² = (20√6)² + (15√6)² = 2400 + 1350 = 3750, and √3750 = 25√6. So a = 25. The √3 version answered above (a = 20) is internally consistent too; it is a different set of numbers for the same item. Either way the method is identical, and it is the one this page already gives: halve the base first.
Confirmed outright
Three items need no correction at all. The "what percent of a is b" item resolves to 3000% in our material, and the recalled a = 0.8 and b = 24 are exactly right — the majority had it. The margin of error item is smaller, as both commenters said. And the two data sets item is 1, which is worth dwelling on: four commenters agreed, two of them independently traced it to official Bluebook material, and our own independent working of the item lands on 1 as well. When Reddit consensus, a cited official source, and a worked solution all converge, that is as close to certainty as a recall thread gets.
The thread recovered eleven items. The full section was far bigger. Our August 2026 Digital SAT Math reconstruction runs to 201 questions across both forms — every figure, graph and table rebuilt, every answer worked and verified, each item tagged by domain and difficulty. That includes all eleven above and roughly a hundred and ninety the thread never got to. Open a free account to work Digital SAT Math by domain — percent and rates, Advanced Math functions, circles and solids — and meet these patterns before test day rather than in a comment thread afterwards.
What the answer key tells you about the section
Read the confirmed items together and a pattern shows up. Not one of them was hard because of the mathematics. Item 1 was a base-identification test. Item 2 was a phrasing test. Item 4 was a symmetry-recognition test that punished anyone who started doing algebra. Item 7 was a careless-reading test that a five-second substitution would have caught. The computation in every single case was trivial.
That's consistent with what students said about the section overall — Module 1 comfortable, Module 2 punishing, with the pain concentrated in a handful of items that ate five to fifteen minutes each. One commenter noted that a good chunk of the section wasn't solvable with Desmos, and the confirmed items bear that out: graphing does nothing for you on any of the items above.
The single highest-value habit the key exposes: substitute a concrete number to test your expression before committing. It would have resolved Item 7 instantly, and it's the check almost nobody in the thread ran.
Retrieval practice
- In "what percent of a is b", which quantity goes in the denominator?
- What multiplier corresponds to "increased by 414%", and what different multiplier corresponds to "is 414% of"?
- Why does the height of an isosceles triangle require you to halve the base before using Pythagoras?
- If every x in a function sits inside (x + 4)², what is the function symmetric about, and which pairs of inputs give equal outputs?
- A sphere has volume 288π. What is its radius, and what operation gets you there?
- For a flat fee covering the first n units plus a rate r per unit after, what is the constant term in the expression?
- Quadrupling a sample size does what to the margin of error?
Practice the full August 2026 Math set. The questions from the August 2026 US Math forms are collected, with answers, in the August 2026 SAT Math question bank. For other test dates, browse the Digital SAT question bank.
Your next step
- The Reading and Writing key, including the full vocabulary list: August 2026 SAT Reading and Writing answers.
- The next administration’s recall thread, solved the same way: DSAT Sept 2026 Reddit Vocabulary (Thread, Solved) — 37 Words in Context items with the distractor each one lost to.
- Item 5 was recognised from official material — work the full bank: Digital SAT Practice Tests: The Complete Guide.
- Understand what routed you into the hard module: Module 2a vs 2b: How the Digital SAT Adapts.
- Know when the calculator helps and when it doesn't: the complete Desmos guide.
- Estimate your score before release: Digital SAT score calculator.
- Practice the hard-module domains this key exposed (percent and rates, Advanced Math functions, triangle and sphere geometry): start a free account.
Where this sits
Up: Digital SAT Practice Tests: The Complete Guide
See also: the August 2026 Reading and Writing answer key · the adaptive branch explainer · the September 2026 repeat-data prediction analysis · the September 2026 Reddit vocabulary thread, solved
Frequently Asked Questions
What was the answer to the "what percent of a is b" question on the August 2026 SAT?
3000%. With a = 0.8 and b = 24, b is 3000% of a. Five commenters voted for 3000%, and our verdict confirms it.
What is f(-8) + f(-3) in the August 2026 nested quadratic question?
120, not 117. The function is symmetric about x = -4, so f(-3) = f(-5) = 30 and f(-8) = f(0) = 90 in our material, and 90 + 30 = 120. The one student who said 120 was right.
How do you write the rental cost in the August 2026 SAT Math question?
The flat charge covers the first day, not six days. In our material it is $22 for the first day plus $11 for each additional day, so the cost for t days is 11t + 11. With the $20 and $10 figures students recalled, it is 10x + 10.
Are these the official College Board answers?
No. The questions are students' own recall from the r/Sat international discussion thread. The verdicts are ours, worked from the mathematics and then checked against the 201-question August 2026 reconstruction in our question bank.
Is this the US or the international August 2026 SAT?
The international form. The August 22, 2026 US administration was a separate form with different questions and has its own answers page. Our checking material covers both forms and is not separated by region.