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Stage 1 · Number theory

10 problems · · mathsolympiadprep.com

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1. The number 10 101 is equal to

   (A) $1000+100+1$ (B) $1000+10+1$ (C) $10\,000+10+1$ (D) $10\,000+100+1$ (E) $100\,000+100+1$

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2. When the four digits of $2024$
   are added, the result is

   1. A$10$
   2. B$8$
   3. C$224$
   4. D$44$
   5. E$16$

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3. What is the remainder when 14 is divided by 5?

   1. A$0$
   2. B$1$
   3. C$2$
   4. D$3$
   5. E$4$

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4. The integer 2014 is between

   (A) $\text{10 0 and 10 1}$ (B) $\text{10 1 and 10 2}$ (C) $\text{10 2 and 10 3}$ (D) $\text{10 3 and 10 4}$ (E) $\text{10 4 and 10 5}$

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5. The ones (units) digit of 542 is 2. When 542 is multiplied by 3, the ones (units) digit of the result is

   1. A$9$
   2. B$3$
   3. C$5$
   4. D$4$
   5. E$6$

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6. The value of $\sqrt{37}$ is
   closest to

   1. A$5$
   2. B$6$
   3. C$7$
   4. D$18$
   5. E$74$

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7. The number one million is

   1. A$10^3$
   2. B$10^4$
   3. C$10^5$
   4. D$10^6$
   5. E$10^7$

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8. Thirty-six hundredths is equal to

   1. A$0.36$
   2. B$360$
   3. C$3.6$
   4. D$0.036$
   5. E$0.0036$

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9. In a certain year, July 1 was a Wednesday. In that year, July 17
   was a

   1. A$\text{Thursday}$
   2. B$\text{Saturday}$
   3. C$\text{Tuesday}$
   4. D$\text{Friday}$
   5. E$\text{Wednesday}$

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10. Which of the following integers is closest to 0?

    1. A$-1$
    2. B$2$
    3. C$-3$
    4. D$4$
    5. E$-5$

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Answer key — Stage 1 · Number theory

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4. $D$ open
5. $E$ open
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7. $D$ open
8. $A$ open
9. $E$ open
10. $C$ open

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