Mr. An deposits money in a bank with compound interest $T_n=A(1+r)^n$, where $A$ is the initial principal, $r$ the interest rate per period, $n$ the number of periods, and $T_n$ the principal plus interest after $n$ periods. He deposits 100 million VND at 6.5% per year and does not withdraw principal or interest. After how many years will he receive at least 250 million VND?
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The supplied key prints correct-answer weights of 4 and 6 points. Wrong-answer and blank-answer scoring are not stated; no penalties or blank credit are inferred.
A store sells regular and premium mooncakes. In one day it sold 120 cakes and received 3.6 million VND. A regular cake costs 25 thousand VND and a premium cake costs 40 thousand VND. How many premium cakes were sold?
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Bacillus subtilis grows under ideal conditions by binary fission. Initially there are $2\times10^2$ cells per ml; after 13 hours there are $3.33\times10^9$ cells per ml. After how many minutes does the population double? Round to the nearest integer.
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An object has acceleration $a(t)=-20\cos(2t+\pi/4)$ m/s². Its velocity at $t=\pi/2$ seconds is $15\sqrt2$ m/s. Calculate its initial velocity.
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Mr. Ong wants to build the steel gate shown. Its arch is parabolic. The gate is 5 m wide, its height at each side is 1.5 m, and its maximum height is 2 m, as labeled. Steel costs 660 000 VND per square metre. What is the cost, in thousands of VND?
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At an airport, an airplane is represented by $M$ in the coordinate space $Oxyz$, as shown. Let $H$ be the orthogonal projection of $M$ onto $(Oxy)$. Given $OM=50$, $\angle(\vec i,\overrightarrow{OH})=64^\circ$ and $\angle(\overrightarrow{OH},\overrightarrow{OM})=48^\circ$, find the coordinates of $M$, rounded to one decimal place.
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A mechanic cuts a flat metal sheet to make an upright cylindrical tool box without a lid. The base radius is 0.75 m and the height is 1.8 m. What sheet area is needed, rounded to the nearest tenth?
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A glass construction is a regular square pyramid $S.ABCD$. The base $ABCD$ is a horizontal square of side 10 m, and the height from $S$ to the base is 6 m. What is the total volume when completed, rounded to the nearest unit?
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Dũng can solve many types of Rubik's cubes. During training with a $3\times3$ cube, he records the times for 25 consecutive solves in the table. The time intervals in seconds are $[8;10),[10;12),[12;14),[14;16),[16;18)$, with respective frequencies 4, 6, 8, 4, 3. Which option is closest to the standard deviation of this grouped data? Editorial grading convention: use the school grouped-data standard deviation with divisor n=25; the alternative divisor n−1=24 is compared in the solution.
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The bar charts give company A's market share (%) in Vietnam's phone business during the first ten months of a year: 18, 20, 19, 21, 22, 19, 20, 18, 21, 22. Find the “standard deviation (standard error)” of these market shares, rounded to the nearest tenth.
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An unfair coin has probability 0.6 of “rolling an even number” at each “sowing.” The die is rolled ten consecutive times. Calculate the probability of obtaining at least seven even numbers. (The mixed coin/die terminology is retained from the English source.)
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A hospital uses a rapid test for disease X. (i) The community prevalence is 0.5%. (ii) Sensitivity, the probability of a positive result for a sick person, is 99%. (iii) Specificity, the probability of a negative result for a healthy person, is 95%. A randomly selected community member tests positive. Which option is closest to the probability that this person actually has X?
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A phone is lost in a class. The suspects are An, Binh and Cuong. An says: “I didn't take it. Binh took it.” Binh says: “Cuong took it. An didn't.” Cuong says: “I didn't take it.” Exactly one person told the truth and the other two lied. Who took the phone?
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A person has 101 socks, including 50 pairs of black socks and the rest white. On a dark morning they draw socks at random. What is the minimum number needed to guarantee two socks with the same color AND side (for example, two white left socks)?
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An exam has 20 multiple-choice questions. Each correct answer earns 5 points, each wrong answer loses 2 points, and none are left blank. A student scores 65. How many answers were correct?
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Inflation is a continuing general increase in goods and services prices, reducing currency purchasing power. The source model says that 5% annual inflation reduces one million VND to purchasing power 950 thousand VND after one year. In general it uses $A=P(1-r/100)^n$, where $r$ is the average annual percentage rate, $P$ the initial amount and $A$ its value after $n$ years. If 100 million VND has purchasing power 80 million VND after three years, find the average rate, rounded to the nearest percentage point.
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Economists use the Lorenz curve to model income distribution. Let $x$ be the percentage of households, ordered poorest to richest, and $y$ the total income percentage. The line $y=x$ represents equal incomes; the area between it and $y=f(x)$ for $0\le x\le100$ represents income inequality. The source says the US model in 2005 is $y=(0.00061x^2+0.0218x+1723)^2$, $0\le x\le100$. Find the inequality, rounding to the nearest million. The literal printed constant is 1723, without a decimal point. Editorial answer-entry clarification: enter the full rounded integer area, not its numerical coefficient in millions.
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In tomatoes, A (red) is completely dominant over a (yellow), and B (round) is completely dominant over b (flattened). The loci assort independently. Two purebred plants with different genotypes are crossed and all F1 plants are red and round. F1 self-pollinates to form F2. Mean fruit masses are 120 g for red/round, 100 g for red/flattened, 90 g for yellow/round and 70 g for yellow/flattened. Every F2 plant produces exactly ten tomatoes. What is the average fruit yield per F2 plant, in grams?
The following reaction is balanced: $a\,\mathrm{FeS}_2+b\,\mathrm{O}_2\to c\,\mathrm{Fe}_2\mathrm{O}_3+d\,\mathrm{SO}_2$. Use linear equations to find the smallest positive integer coefficients $a,b,c,d$ that balance it. Calculate $P=a+b+c+d$.
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A ball is dropped from rest from the observation deck on the terrace of Landmark 81 in Ho Chi Minh City, at height 461.3 m. Its falling displacement is $s(t)=4.9t^2$. Neglect air resistance and calculate its velocity when it reaches the ground, in m/s, rounded to the nearest hundredth.
