SSAT Upper Level Quantitative Flashcards: Divisibility Rules

What this deck covers

This deck focuses on Divisibility Rules, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify whether $13,530$ is divisible by $10$.

Answer: Yes, because the last digit is $0$. The rule for 10 is met as the number ends in 0, confirming divisibility.

Flashcard 2: State the divisibility rule for $5$.

Answer: Divisible by $5$ iff the last digit is $0$ or $5$. Since $10 \equiv 0 \pmod{5}$, the number is divisible by 5 precisely when its units digit is 0 or 5.

Flashcard 3: Identify whether $10^6-1$ is divisible by $9$.

Answer: Yes, $10^6-1=999999$ and $9+9+9+9+9+9=54$ is divisible by $9$. The sum of digits 54 is divisible by 9 ($54 \div 9 = 6$), confirming divisibility.

Flashcard 4: Identify whether $4,572$ is divisible by $3$.

Answer: Yes, because $4+5+7+2=18$ and $18$ is divisible by $3$. The sum 18 is divisible by 3 since $18 \div 3 = 6$, applying the rule for 3.

Flashcard 5: Identify whether $5,376$ is divisible by $8$.

Answer: Yes, because the last three digits $376$ are divisible by $8$. Applying the rule for 8, 376 divided by 8 equals 47, an integer, confirming divisibility.

Flashcard 6: Identify whether $93,615$ is divisible by $5$.

Answer: Yes, because the last digit is $5$. The rule for 5 is satisfied as the number ends in 5, making it divisible by 5.

Flashcard 7: Identify whether $73,205$ is divisible by $2$.

Answer: No, because the last digit $5$ is odd. The units digit 5 is odd, so the number is not even and thus not divisible by 2.

Flashcard 8: State the divisibility rule for $8$.

Answer: Divisible by $8$ iff the last three digits form a multiple of $8$. Since $1000 \equiv 0 \pmod{8}$, divisibility by 8 is determined by the last three digits being a multiple of 8.

Flashcard 9: What is the remainder when $10^7$ is divided by $9$?

Answer: $1$. Since $10 \equiv 1 \pmod{9}$, $10^7 \equiv 1 \pmod{9}$, yielding remainder 1.

Flashcard 10: State the divisibility rule for $4$.

Answer: Divisible by $4$ iff the last two digits form a multiple of $4$. Since $100 \equiv 0 \pmod{4}$, divisibility by 4 depends only on the last two digits forming a multiple of 4.

Flashcard 11: State the divisibility rule for $11$ using alternating digit sums.

Answer: Divisible by $11$ iff the alternating sum of digits is a multiple of $11$. Since $10 \equiv -1 \pmod{11}$, the alternating sum of digits determines congruence modulo 11.

Flashcard 12: Identify whether $10^4+10^2+1$ is divisible by $3$.

Answer: Yes, $10^4+10^2+1=10101$ and $1+0+1+0+1=3$. The sum of digits is 3, which is divisible by 3 ($3 \div 3 = 1$), confirming divisibility.

Flashcard 13: State the divisibility rule for $2$.

Answer: Divisible by $2$ iff the last digit is even ($0,2,4,6,8$). A number is divisible by 2 if it is even, which is determined solely by the parity of its units digit.

Flashcard 14: State the divisibility rule for $9$.

Answer: Divisible by $9$ iff the sum of digits is divisible by $9$. Since $10 \equiv 1 \pmod{9}$, a number is congruent to the sum of its digits modulo 9.

Flashcard 15: Identify whether $10^5+10^3$ is divisible by $10$.

Answer: Yes, $10^5+10^3=101000$ ends in $0$. The expression simplifies to 101000, which ends in 0, satisfying the rule for 10.

Flashcard 16: Identify whether $2,418$ is divisible by $6$.

Answer: Yes, it is divisible by $2$ and $3$. It satisfies the rules for both 2 (even) and 3 (sum 15 divisible by 3), hence divisible by 6.

Flashcard 17: State the divisibility rule for $3$.

Answer: Divisible by $3$ iff the sum of digits is divisible by $3$. Since $10 \equiv 1 \pmod{3}$, a number is congruent to the sum of its digits modulo 3.

Flashcard 18: Identify whether $47,190$ is divisible by $9$.

Answer: No, because $4+7+1+9+0=21$ and $21$ is not divisible by $9$. The sum 21 is not divisible by 9 (between 18 and 27), so the number is not divisible by 9.

Flashcard 19: Identify whether $7,128$ is divisible by $4$.

Answer: Yes, because the last two digits $28$ are divisible by $4$. Applying the rule for 4, 28 divided by 4 equals 7, an integer, confirming divisibility.

Flashcard 20: What is the remainder when $10^5+7$ is divided by $3$?

Answer: $2$. Since $10 \equiv 1 \pmod{3}$, $10^5 +7 \equiv 1+7=8 \equiv 2 \pmod{3}$.