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24 Feb 2026, 13:23
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28 Feb 2026, 23:17
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A) 2/11 = 0.1818 : 2 different digits
B) 1/3 = 0.333 : 1 different digit
C) 41/99 = 0.3131 : 2 diffrent digits
D) 2/3 0.6666 : 1 different digit
E) 23/37 = 69/111 = 0.621621 : 3 different digits
Answer E.
PS - Had to solve this as I wasn't aware of the factor of 9 rule. could be helpful in saving time.
B) 1/3 = 0.333 : 1 different digit
C) 41/99 = 0.3131 : 2 diffrent digits
D) 2/3 0.6666 : 1 different digit
E) 23/37 = 69/111 = 0.621621 : 3 different digits
Answer E.
PS - Had to solve this as I wasn't aware of the factor of 9 rule. could be helpful in saving time.
gmatraider
15 Apr 2026, 11:10
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REPEATING DECIMAL PATTERNS — WITH EXAMPLES
Core idea:
If the denominator divides 9, 99, 999... then the repeat length is 1, 2, 3... respectively.
---
1-DIGIT REPEAT (divides 9)
1/3:
10^1 − 1 = 9 → divisible by 3
→ repeat length = 1
→ 1/3 = 0.333...
1/9:
10^1 − 1 = 9 → divisible by 9
→ repeat length = 1
→ 1/9 = 0.111...
---
2-DIGIT REPEAT (divides 99)
1/11:
10^2 − 1 = 99 → divisible by 11
→ repeat length = 2
→ 1/11 = 0.090909...
1/99:
10^2 − 1 = 99 → divisible by 99
→ repeat length = 2
→ 1/99 = 0.010101...
---
3-DIGIT REPEAT (divides 999)
1/37:
10^3 − 1 = 999 → divisible by 37
→ repeat length = 3
→ 1/37 = 0.027027027...
1/27:
10^3 − 1 = 999 → divisible by 27
→ repeat length = 3
→ 1/27 = 0.037037037...
---
FINAL MEMORY TRICK
If denominator fits into:
9 → 1-digit repeat
99 → 2-digit repeat
999 → 3-digit repeat
So:
3, 9 → 1 digit
11, 99 → 2 digits
37, 27 → 3 digits
---
EXAM USE
Just look at denominator:
* If it divides 9 → length 1
* If it divides 99 → length 2
* If it divides 999 → length 3
Pick the largest cycle — no calculation needed.
Core idea:
If the denominator divides 9, 99, 999... then the repeat length is 1, 2, 3... respectively.
---
1-DIGIT REPEAT (divides 9)
1/3:
10^1 − 1 = 9 → divisible by 3
→ repeat length = 1
→ 1/3 = 0.333...
1/9:
10^1 − 1 = 9 → divisible by 9
→ repeat length = 1
→ 1/9 = 0.111...
---
2-DIGIT REPEAT (divides 99)
1/11:
10^2 − 1 = 99 → divisible by 11
→ repeat length = 2
→ 1/11 = 0.090909...
1/99:
10^2 − 1 = 99 → divisible by 99
→ repeat length = 2
→ 1/99 = 0.010101...
---
3-DIGIT REPEAT (divides 999)
1/37:
10^3 − 1 = 999 → divisible by 37
→ repeat length = 3
→ 1/37 = 0.027027027...
1/27:
10^3 − 1 = 999 → divisible by 27
→ repeat length = 3
→ 1/27 = 0.037037037...
---
FINAL MEMORY TRICK
If denominator fits into:
9 → 1-digit repeat
99 → 2-digit repeat
999 → 3-digit repeat
So:
3, 9 → 1 digit
11, 99 → 2 digits
37, 27 → 3 digits
---
EXAM USE
Just look at denominator:
* If it divides 9 → length 1
* If it divides 99 → length 2
* If it divides 999 → length 3
Pick the largest cycle — no calculation needed.
