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AMO 2025 Secondary 1 (Grade 7)

Question 1

Which interval is the solution set of $|2x-7|<6$?

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  1. $1.0<x<8.0$
  2. $0.5<x<6.5$
  3. $2.5<x<7.5$
  4. $2.0<x<13.0$

Question 2

At a local school, 70% of middle school students have a smartphone. Students are asked at random until one has a smartphone. What is the probability, as a percentage, that at least four students must be asked? Clarification: use independent trials, each with a 70% chance; the source does not specify a finite-population sampling model.

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  1. 5.1%
  2. 3.2%
  3. 2.7%
  4. 1.8%

Question 3

What is the repeating block of digits in the decimal expansion of $5/7$?

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  1. 345678
  2. 565656
  3. 714715
  4. 714285

Question 4

Two 12-faced dice, each numbered 1 to 12, are rolled together. What is the probability that their sum is 15? Assume fair, independent dice.

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  1. $1/18$
  2. $5/36$
  3. $5/72$
  4. $11/72$

Question 5

In how many ways can the seven letters of SALUKIS be rearranged? The result need not be an English word.

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  1. 3520
  2. 3200
  3. 2880
  4. 2520

Question 6

Evaluate $(x+5)(x^2-5x+25)$ when $x=10$.

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  1. 1125
  2. 1970
  3. 2025
  4. 3750

Question 7

Numbers $x,y,z$ satisfy $x+y-z=9$, $x-y+z=15$, and $x+y+z=25$. Find $xyz$.

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  1. 450
  2. 480
  3. 800
  4. 960

Question 8

What value does $S=1/3+1/9+1/27+1/81+1/243+\cdots$ approach as more terms are included?

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  1. $1/2$
  2. $1/4$
  3. $4/5$
  4. $8/9$

Question 9

Mr. Brown needs to print math models. His first 3D printer alone takes 60 hours and his second alone takes 90 hours. How many hours do both printers working together need? Assume constant independent rates.

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  1. 30 hours
  2. 36 hours
  3. 65 hours
  4. 75 hours