SEAMO 2027 - Paper C - SET 03 - Self-study

SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.

In 2023, Singapore’s birthday, 9 August, fell on a Wednesday. In which year will it next fall on a Wednesday?

Abel lies on Monday, Tuesday and Wednesday, and tells the truth on the other days. Bernice lies on Thursday, Friday and Saturday, and tells the truth on the other days. On which day do they both say, “I lied yesterday”?

The sum of the first 2023 digits after the decimal point in $\frac17$ is the four-digit number $\overline{abcd}$. Find $a+b+c+d$.

The seven-digit number $\overline{20xy15z}$ is divisible by 792. Find $x+y+z$.

Find the value of $\frac13+\frac1{15}+\frac1{35}+\frac1{63}+\cdots+\frac1{483}+\frac1{575}$.

Evaluate $2023\times\frac{119}{17}-2023\times\frac{17}{119}$.

Frank and Ben each bought some sheets of paper. If they use 40 and 80 sheets per day respectively, Frank has 500 sheets left when Ben runs out. If they instead use 80 and 40 sheets per day respectively, Frank has 20 sheets left when Ben runs out. How many sheets did they have altogether?

Find the ones digit of $3^{2020}+4^{2021}+5^{2022}$.

Find the integer part of $S=\dfrac{1}{\frac1{2020}+\frac1{2021}+\cdots+\frac1{2025}}$.

Wording clarification: the source says “integer value”. Here this means the integer part (the greatest integer not exceeding the expression), as indicated by the supplied integer options.

Three-digit numbers are formed using three different digits chosen from $0,2,3,5,8$, each used exactly once. What is the probability that a randomly chosen such number is even?

At 2:45 PM, the smaller angle between the hour and minute hands is $x^\circ$, where $0<x<180$. Find $x$.

Two squares of areas $m$ and $n$ are inscribed in a larger square as shown. Find $m:n$.

The perimeter of square $ABCD$ is 20 cm. Point $E$ lies on diagonal $AC$, and the marked angles $a=\angle DBE$ and $b=\angle EBC$ are equal. Find $AE$, in cm.

Which listed value of $k$ makes $2^{137}+k$ divisible by 127?

The figure consists of a square of side 50 cm and three identical semicircles, one of which is shaded. Find the total area of the shaded parts. Take $\pi=3.14$.

Find the area of the shaded region, in $\text{cm}^2$, in the diagram with a 10 cm horizontal diameter and a 20 cm base.

Diagram convention used: the 10 cm segment is a horizontal diameter; the 20 cm base is parallel to it and tangent to the circle, as drawn.

Three scholars, Sam, Rex and Ted, study English, Math, Science, Dance, Music and Art. The Science and Math students are neighbours. Rex is the youngest. Sam exercises with the Dance, Music and Math students. The Dance student is older than the English student. Rex plays chess with the Music and English students. Each student studies two subjects. Which two subjects does Ted study?

Team A takes 12 days and Team B takes 9 days to complete a project alone. Team A works on it for $x$ days, then hands it over to Team B. The project is completed in 10 days altogether. Find $x$.

The source asks: “$p$ and $q$ are prime numbers. Given $2p+5q=2019$, find $p-q$.” Its original options are A: 992, B: 984, C: 889, D: 968, E: None of the above. Analyse whether the stated conditions uniquely determine $p-q$, and justify your answer.

Source limitation: no restriction selecting a unique prime pair is printed, and the cover instructions supply none. Retain all original choices as source material; give a reasoned analysis rather than assuming that one choice must be uniquely implied.

A six-digit number $\overline{2003\square\square}$ is divisible by 99. What is the sum of its digits?