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SEAMO 2026 Paper D SET 3 – Self-practice

Question 1

Which of the following numbers is the largest?
  1. 1
  2. $\sqrt2$
  3. $\sqrt[3]3$
  4. $\sqrt[4]4$
  5. $\sqrt[6]6$

Question 2

If $|x-10|+x-10=0$, what is the range of x?
  1. $x<10$
  2. $x>10$
  3. $x\le10$
  4. $x\ge10$
  5. None of the above

Question 3

How many triangles are there in the figure below?

Question illustration
  1. 12
  2. 16
  3. 18
  4. 20
  5. None of the above

Question 4

Using the digits 1, 2, 3, and 4, without repeat, one can form distinct 3-digit numbers. What is the average of all possible numbers formed?
  1. 200
  2. 225.5
  3. 275
  4. 277.5
  5. None of the above

Question 5

Find the sum of the coefficients in the expansion of $(x^2+2x+3)^3(3x^2+2x+1)$.
  1. 1140
  2. 1200
  3. 1254
  4. 1296
  5. None of the above

Question 6

How many fractions in $\frac1{99},\frac2{99},\frac3{99},\ldots,\frac{98}{99}$ cannot be reduced to a simpler form?
  1. 45
  2. 60
  3. 75
  4. 90
  5. None of the above

Question 7

What is the area of the square ABCD below?

Question illustration
  1. 64
  2. 72
  3. 84
  4. 100
  5. None of the above

Question 8

A teacher wrote three numbers on the whiteboard: 4875, 4563, and N, where N is a positive integer. He then asked the class to compute the lowest common multiple of the three numbers. One student misread 4875 as 4275. However, the student still gets the correct answer. What is the least possible value of N?
  1. 1755
  2. 2375
  3. 2535
  4. 3705
  5. None of the above

Question 9

Evaluate $\sqrt{31\times30\times29\times28+1}$.
  1. 800
  2. 810
  3. 812
  4. 869
  5. None of the above

Question 10

Find the total number of integers in the sequence 20, 22, 24, …, 2020 that are divisible by 3 but not 5.
  1. 158
  2. 225
  3. 252
  4. 270
  5. None of the above

Question 11

$a_1,a_2,a_3,\ldots$ is an arithmetic sequence with common difference 1. Given $a_1+a_2+\cdots+a_{98}=137$, find $a_2+a_4+\cdots+a_{98}$.
  1. 89
  2. 91
  3. 93
  4. 97
  5. None of the above

Question 12

Let a and b be positive real numbers such that $\frac1a+\frac1b=\frac5{a-b}$. Evaluate $\left(\frac ab+\frac ba\right)^2$.
  1. 29
  2. $16\sqrt5$
  3. $25\sqrt2$
  4. 36
  5. None of the above

Question 13

Evaluate $\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{1+\cdots}}}}$.
  1. $\sqrt2$
  2. $\sqrt3$
  3. 2
  4. $1+\sqrt2$
  5. None of the above

Question 14

How many integers between 0 and $10^4$ have their sum of digits equal to 5?
  1. 52
  2. 54
  3. 56
  4. 58
  5. None of the above

Question 15

Two circles with centers M and N are tangent to a line P at A and B, respectively, as shown below. Given AB = 25, MN = 24, and quadrilateral ABNM has area 300, evaluate the product of the radii of the two circles.

Question illustration
  1. 120
  2. 144
  3. 150
  4. 176
  5. None of the above

Question 16

Using the digits 1,2,3,4 and 5 without repeat, one can form distinct 5-digit numbers and arrange them in ascending order. What is the $100^{\mathrm{th}}$ number?
  1. 45132
  2. 51243
  3. 52314
  4. 54123
  5. None of the above

Question 17

Find the number of positive integers $n\le2020$ such that $\lfloor n/2\rfloor+\lfloor n/3\rfloor+\lfloor n/6\rfloor=n$. Here $\lfloor x\rfloor$ denotes the greatest integer not exceeding x.
  1. 240
  2. 312
  3. 330
  4. 336
  5. None of the above

Question 18

A circle is inscribed in a triangle of side lengths 3, 4 and 5. What is the radius of the circle?

Question illustration
  1. 1
  2. $\sqrt2$
  3. $\sqrt3$
  4. 2
  5. None of the above

Question 19

For $1\le x\le10$, let $f(x)=|x-2|-|x-3|+|2x-12|$. Evaluate the sum of the minimum and maximum values of f(x).
  1. $15/2$
  2. 8
  3. $19/2$
  4. 10
  5. None of the above

Question 20

How many positive integers n less than 100 make $\frac{n^2+4n+6}{n+3}$ a fraction in its lowest terms?
  1. 32
  2. 52
  3. 66
  4. 90
  5. None of the above