Number System, Unit Digit & Remainder
Practice 370+ SSC CGL Number System PYQs online. Unit digit cyclicity, remainder theorem (Wilson & Euler), number of trailing zeros & step-by-step solutions.
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4-Step Solution & Tricks
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Number System, Unit Digit & Remainder:
- Unit Digit Calculation & Power Cyclicity (Cycle of 4)
- Divisibility Rules (3, 7, 8, 9, 11, 72, 88)
- Remainder Theorem: (a + 1)ⁿ / a leaves remainder 1
- Number of Factors & Sum of Factors Formula
- Trailing Zeros in n! = [n/5] + [n/25] + [n/125]
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Number System questions in under 45 seconds:
Divisibility by 72: Check last 3 digits for 8 and sum of digits for 9.
Divisibility by 88: Check last 3 digits for 8 and alternate sum for 11.
Unit digit cyclicity of 2, 3, 7, 8 is strictly 4.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: -7/8, -2/9, 5/12, 4/3
- Step 1: Since, 4 3/13 2 9/02 7 8/08 75 5/12 04 2 = −= − −= − = .
- Step 2: Therefore, −< −< <08/75 02/04 21 3..
- Step 3: Thus, the ascending order of the given fractions is −< −< <7 8 2 9 5/12 4 3
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 3/4
- Step 1: Let the three fractions be x, y and z such that x < y < z.
- Step 2: It is given that z x zx=⇒ 7 6 7 6 Now, the middle fraction y =− = − =7 6 1 3/72 6 5 6 Again, xy z++ = 2/11 24 ⇒+ +=xx 5 6 7 6/59 24 ⇒ + =−67 6/59 24 5 6 xx ⇒ − =13 6/59 20/24 39/24 x ⇒ ×=x 39/24 6/13 3 4
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 8/11
- Step 1: First, convert all the frac- tions into decimals.
- Step 2: 2 3/06 6= .
- Step 3: 3 5/06= .
- Step 4: 8/11 07 3= .
- Step 5: 11/17 06 5= .
- Step 6: Therefore, the largest fraction is 8/11 .
⚡ Speed Tip: Verify intermediate calculations and units.
❓ Frequently Asked Questions (FAQs)
How to test divisibility by 72 in SSC CGL?
A number is divisible by 72 if and only if it is divisible by both 8 (last 3 digits) and 9 (sum of all digits).