The Number System remains one of the most critical and scoring topics in the <a href="https://Staff Selection Commission Combined Graduate Level (SSC CGL)">Staff Selection Commission Combined Graduate Level (SSC CGL)</a> Tier-I Quantitative Aptitude section. If you’ve already read our previous blog where we discussed the weightage and importance of the <a href="https://www.quantsir.com/miscellaneous/ssc-cgl-number-system-weightage-and-importance">SSC CGL Number System</a>, you now understand its significance in cracking the exam. In this blog, we include the SSC CGL Number System Important Questions, which will enhance the level and accuracy of your preparation. But understanding theory isn’t enough. What truly makes the difference is question practice, especially the kind that aligns with previous year trends, evolving difficulty levels, and smart solving strategies. In this follow-up blog, we bring you important and expected questions from each concept of the number system included in the <a href="https://ssc.gov.in/home/notice-board">SSC CGL 2025</a> exam. SSC CGL Number System Important Questions come with clear logic, step-by-step breakdowns, and pro tips to help you attempt similar questions confidently in the exam. <img loading="lazy" alt="SSC CGL Number System Important Questions" src="https://www.quantsir.com/admin/assets/uploads/ckeditor/SSC_CGL_Number_System_Important_Questions_(1).webp" style="height:338px; width:600px"> [Source: Quant Sir] <h2 id="content-id-131214-0">SSC CGL Number System Important Questions - Divisibility-Based Questions</h2> Understanding divisibility rules is crucial to solving number-based puzzles that seem complex at first glance but follow simple patterns when decoded correctly. Q1. If a 9-digit number 985x3678y is divisible by 72, find the value of (4x – 3y). Solution: A number divisible by 72 must also be divisible by both 8 and 9. Last 3 digits (for divisibility by 8): 78y Try y = 4 → 784 is divisible by 8 Sum of digits (for divisibility by 9): 9 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 50 + x → x = 4 to make the sum divisible by 9 (4x – 3y) = (4×4) – (3×4) = 16 – 12 = 4 Answer: 4 Q2. Find the smallest number to be added to 888 so that it becomes divisible by 35. Solution: 888 ÷ 35 = 25 remainder 13 → To make it divisible, add (35 – 13) = 22 Answer: 22 Q3. Find the value of x and y if the number 2074x4y2 is divisible by 88, and then find (4x + 3y). Solution: Divisibility by 88 = divisible by 8 and 11 Last 3 digits (4y2) → divisible by 8 → y = 3 For 11: (2 + 4 + 4 + 0) – (y + x + 7 + 2) = 0 → Try x = 9, y = 3 Then (4x + 3y) = 36 + 9 = 45 Answer: 45 Mastering these rules will help you solve complex patterns with ease, making SSC CGL Number System Important Questions from this area a high-return investment. <h2 id="content-id-131214-1">SSC CGL Number System Important Questions - Factors, Multiples and Co-Prime</h2> These questions test your understanding of how numbers interact in terms of divisibility and factorization. Q1. How many factors of 756 are divisible by 12? Solution: 756 = 22 × 33 × 7 12 = 22 × 3 → Remaining part to consider: 32 × 7 → Number of such factors = (2+1) × (1+1) = 6 Answer: 6 Q2. Find the total number of co-primes to 48 that are less than 48. Solution: Use Euler’s Totient Function 48 = 24 × 3 48 = 48(1 – ½)(1 – ⅓) = 48 × ½ × ⅔ = 16 Answer: 16 Q3. In how many ways can 3420 be written as a product of two numbers? Solution: 3420 = 22 × 32 × 5 × 19 → Total factors = (2 + 1)(2 + 1)(1 + 1)(1 + 1) = 3 × 3 × 2 × 2 = 36 → Ways to write as product of 2 numbers = 36 ÷ 2 = 18 Answer: 18 This section tests your analytical precision, and practicing these SSC CGL Number System Important Questions ensures you don’t miss out on easy marks. <h2 id="content-id-131214-2">SSC CGL Number System Important Questions - HCF and LCM</h2> These questions often hide behind word problems. A strong grip on factorization helps in decoding them quickly. Q1. Six bells toll at intervals of 2, 4, 6, 8, 10, and 12 seconds. After how many seconds will they toll together again? Solution: Find LCM LCM(2, 4, 6, 8, 10, 12) = 120 seconds Answer: 120 seconds Q2. A and B are prime numbers such that A > B and LCM(A, B) = 209. Find B2 – A. Solution: → 209 = 11 × 19 → A = 19, B = 11 → B2 – A = 121 – 19 = 102 Answer: 102 Q3. Find the largest number that leaves the same remainder when it divides 444, 804, and 1344. Solution: → Take differences: 804 – 444 = 360, 1344 – 804 = 540 HCF(360, 540) = 180 Answer: 180 These recurring concepts form the base of many word problems, and cracking them strengthens your hold over the SSC CGL Number System Important Questions. <h2 id="content-id-131214-3">SSC CGL Number System Important Questions - Remainders and Last Digit</h2> These questions require understanding modular arithmetic and last-digit cycles. Q1. Find the last digit of 222555 + 555222. Solution: 5any = 5 2555 → Cycle: 2, 4, 8, 6 → 555 ÷ 4 = remainder 3 → 8 → Sum: 5 + 8 = 13 → Last digit = 3 Answer: 3 Q2. Find the remainder when 83421579 is divided by 1001. Solution: → Use the triplet method (from right): 579 + 83 – 421 = 241 Answer: 241 Q3. Find the last digit of (47)97. Solution: → 7’s cycle: 7, 9, 3, 1 → 97 mod 4 = 1 → last digit = 7 Answer: 7 Recognizing remainder cycles and digit patterns is key to solving high-level SSC CGL Number System Important Questions in under a minute. <h2 id="content-id-131214-4">SSC CGL Number System Important Questions - Counting, Factorials & Trailing Zeros</h2> These are rare but useful in mixed-section and higher-level questions. Q1. How many trailing zeroes are there in 145!? Solution: → Count how many 5s are in its prime factors: = [145/5] + [145/25] + [145/125] = 29 + 5 + 1 = 35 trailing zeros Answer: 35 trailing zeros Q2. Tanya typed numbers from 1 to n and pressed keys 1692 times. Find n. Solution: 1-digit numbers: 9 → 9 digits 2-digit: 90 → 90 × 2 = 180 → Remaining = 1692 – (180 + 9) = 1503 → 1503 ÷ 3 = 501 three-digit numbers So, total = 9 + 90 + 501 = 600 Answer: 600 Q3. Find the number of senior citizens who receive an odd number of blankets if 70 workers donate in this pattern. <ul> <li>Each senior citizen receives blankets equal to the number of their divisors</li> <li>Only perfect squares have an odd number of factors</li> <li>From 1 to 70, perfect squares = 1, 4, 9, 16, 25, 36, 49, 64 → 8 seniors</li> </ul> Answer: 8 Seniors Though less frequent, these questions often appear as surprise entries; solving them prepares you comprehensively for all types of SSC CGL Number System Important Questions. The SSC CGL Number System Important Questions discussed above are not only aligned with past exam patterns but also designed to sharpen your logical thinking and numerical aptitude. Under the expert mentorship of <a href="https://www.quantsir.com/">Quant Sir</a>, mastering these questions becomes far more intuitive and strategic. Our techniques are tailored for SSC CGL aspirants who aim to score higher without getting trapped in lengthy calculations. With consistent practice of <a href="https://www.quantsir.com/topic-wise-test">mock tests</a> and the right guidance, you can transform the Number System from a difficult topic into a scoring opportunity. So, follow QuantSir’s tips, revise these concepts regularly, and stay exam-ready!

The Number System remains one of the most critical and scoring topics in the <a href="https://Staff Selection Commission Combined Graduate Level (SSC CGL)">Staff Selection Commission Combined Graduate Level (SSC CGL)</a> Tier-I Quantitative Aptitude section. If you&rsquo;ve already read our previous blog where we discussed the weightage and importance of the <a href="https://www.quantsir.com/miscellaneous/ssc-cgl-number-system-weightage-and-importance">SSC CGL Number System</a>, you now understand its significance in cracking the exam. In this blog, we include the SSC CGL Number System Important Questions, which will enhance the level and accuracy of your preparation.

But understanding theory isn&rsquo;t enough. What truly makes the difference is question practice, especially the kind that aligns with previous year trends, evolving difficulty levels, and smart solving strategies.

In this follow-up blog, we bring you important and expected questions from each concept of the number system included in the <a href="https://ssc.gov.in/home/notice-board">SSC CGL 2025</a> exam. SSC CGL Number System Important Questions come with clear logic, step-by-step breakdowns, and pro tips to help you attempt similar questions confidently in the exam.

<img loading="lazy" alt="SSC CGL Number System Important Questions" src="https://www.quantsir.com/admin/assets/uploads/ckeditor/SSC_CGL_Number_System_Important_Questions_(1).webp" style="height:338px; width:600px" />

[Source: Quant Sir]

<h2>SSC CGL Number System Important Questions - Divisibility-Based Questions</h2>

Understanding divisibility rules is crucial to solving number-based puzzles that seem complex at first glance but follow simple patterns when decoded correctly.

Q1. If a 9-digit number 985x3678y is divisible by 72, find the value of (4x &ndash; 3y).

Solution: A number divisible by 72 must also be divisible by both 8 and 9.

Last 3 digits (for divisibility by 8): 78y

Try y = 4 &rarr; 784 is divisible by 8

Sum of digits (for divisibility by 9): 9 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 50 + x

&rarr; x = 4 to make the sum divisible by 9

(4x &ndash; 3y) = (4&times;4) &ndash; (3&times;4) = 16 &ndash; 12 = 4

Answer: 4

Q2. Find the smallest number to be added to 888 so that it becomes divisible by 35.

Solution: 888 &divide; 35 = 25 remainder 13 
&rarr; To make it divisible, add (35 &ndash; 13) = 22

Answer: 22

Q3. Find the value of x and y if the number 2074x4y2 is divisible by 88, and then find (4x + 3y). 
 
Solution: Divisibility by 88 = divisible by 8 and 11

Last 3 digits (4y2) &rarr; divisible by 8 &rarr; y = 3

For 11: (2 + 4 + 4 + 0) &ndash; (y + x + 7 + 2) = 0

&rarr; Try x = 9, y = 3

Then (4x + 3y) = 36 + 9 = 45

Answer: 45

Mastering these rules will help you solve complex patterns with ease, making SSC CGL Number System Important Questions from this area a high-return investment.

<h2>SSC CGL Number System Important Questions - Factors, Multiples and Co-Prime</h2>

These questions test your understanding of how numbers interact in terms of divisibility and factorization.

Q1. How many factors of 756 are divisible by 12?

Solution: 756 = 22 &times; 33 &times; 7

12 = 22 &times; 3 &rarr; Remaining part to consider: 32 &times; 7

&rarr; Number of such factors = (2+1) &times; (1+1) = 6

Answer: 6

Q2. Find the total number of co-primes to 48 that are less than 48.

Solution: Use Euler&rsquo;s Totient Function

48 = 24 &times; 3

48 = 48(1 &ndash; &frac12;)(1 &ndash; ⅓) = 48 &times; &frac12; &times; ⅔ = 16

Answer: 16

Q3. In how many ways can 3420 be written as a product of two numbers?

Solution: 3420 = 22 &times; 32 &times; 5 &times; 19 &rarr; Total factors = (2 + 1)(2 + 1)(1 + 1)(1 + 1) = 3 &times; 3 &times; 2 &times; 2 = 36

&rarr; Ways to write as product of 2 numbers = 36 &divide; 2 = 18

Answer: 18

This section tests your analytical precision, and practicing these SSC CGL Number System Important Questions ensures you don&rsquo;t miss out on easy marks.

<h2>SSC CGL Number System Important Questions - HCF and LCM</h2>

These questions often hide behind word problems. A strong grip on factorization helps in decoding them quickly.

Q1. Six bells toll at intervals of 2, 4, 6, 8, 10, and 12 seconds. After how many seconds will they toll together again?

Solution: Find LCM

LCM(2, 4, 6, 8, 10, 12) = 120 seconds

Answer: 120 seconds

Q2. A and B are prime numbers such that A &gt; B and LCM(A, B) = 209. Find B2 &ndash; A.

Solution: &rarr; 209 = 11 &times; 19 &rarr; A = 19, B = 11

&rarr; B2 &ndash; A = 121 &ndash; 19 = 102

Answer: 102

Q3. Find the largest number that leaves the same remainder when it divides 444, 804, and 1344.

Solution: &rarr; Take differences:

804 &ndash; 444 = 360, 1344 &ndash; 804 = 540

HCF(360, 540) = 180

Answer: 180

These recurring concepts form the base of many word problems, and cracking them strengthens your hold over the SSC CGL Number System Important Questions.

<h2>SSC CGL Number System Important Questions - Remainders and Last Digit</h2>

These questions require understanding modular arithmetic and last-digit cycles.

Q1. Find the last digit of 222555 + 555222.

Solution: 5any = 5

2555 &rarr; Cycle: 2, 4, 8, 6 &rarr; 555 &divide; 4 = remainder 3 &rarr; 8

&rarr; Sum: 5 + 8 = 13 &rarr; Last digit = 3

Answer: 3

Q2. Find the remainder when 83421579 is divided by 1001.

Solution: &rarr; Use the triplet method (from right):

579 + 83 &ndash; 421 = 241

Answer: 241

Q3. Find the last digit of (47)97.

Solution: &rarr; 7&rsquo;s cycle: 7, 9, 3, 1

&rarr; 97 mod 4 = 1 &rarr; last digit = 7

Answer: 7

Recognizing remainder cycles and digit patterns is key to solving high-level SSC CGL Number System Important Questions in under a minute.

<h2>SSC CGL Number System Important Questions - Counting, Factorials &amp; Trailing Zeros</h2>

These are rare but useful in mixed-section and higher-level questions.

Q1. How many trailing zeroes are there in 145!?

Solution: &rarr; Count how many 5s are in its prime factors:

= [145/5] + [145/25] + [145/125] = 29 + 5 + 1 = 35 trailing zeros

Answer: 35 trailing zeros

Q2. Tanya typed numbers from 1 to n and pressed keys 1692 times. Find n.

Solution: 1-digit numbers: 9 &rarr; 9 digits

2-digit: 90 &rarr; 90 &times; 2 = 180

&rarr; Remaining = 1692 &ndash; (180 + 9) = 1503

&rarr; 1503 &divide; 3 = 501 three-digit numbers

So, total = 9 + 90 + 501 = 600

Answer: 600

Q3. Find the number of senior citizens who receive an odd number of blankets if 70 workers donate in this pattern.

<ul>
	<li>Each senior citizen receives blankets equal to the number of their divisors</li>
	<li>Only perfect squares have an odd number of factors</li>
	<li>From 1 to 70, perfect squares = 1, 4, 9, 16, 25, 36, 49, 64 &rarr; 8 seniors</li>
</ul>

Answer: 8 Seniors

Though less frequent, these questions often appear as surprise entries; solving them prepares you comprehensively for all types of SSC CGL Number System Important Questions.

The SSC CGL Number System Important Questions discussed above are not only aligned with past exam patterns but also designed to sharpen your logical thinking and numerical aptitude. Under the expert mentorship of <a href="https://www.quantsir.com/">Quant Sir</a>, mastering these questions becomes far more intuitive and strategic. Our techniques are tailored for SSC CGL aspirants who aim to score higher without getting trapped in lengthy calculations. With consistent practice of <a href="https://www.quantsir.com/topic-wise-test">mock tests</a> and the right guidance, you can transform the Number System from a difficult topic into a scoring opportunity. So, follow QuantSir&rsquo;s tips, revise these concepts regularly, and stay exam-ready!

SSC CGL Number System Important Questions - Weightage

SSC CGL Number System Important Questions - Weightage

SSC CGL LCM and HCF - Weightage and Importance

SSC CGL HCF and LCM Important Questions - Weightage

Click to get the infographics of the SSC CGL Number System Important Questions for the different questions that can be asked, along with their weightage.

SSC CGL Number System Important Questions - Divisibility-Based Questions

SSC CGL Number System Important Questions - Factors, Multiples and Co-Prime

SSC CGL Number System Important Questions - HCF and LCM

SSC CGL Number System Important Questions - Remainders and Last Digit

SSC CGL Number System Important Questions - Counting, Factorials & Trailing Zeros

SSC CGL Number System Important Questions - Weightage

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