Number Arrangement Questions: The Short Answer
Number arrangement questions give a set of three-digit numbers, change them by a rule (arrange the digits in ascending or descending order, reverse the digits, or add 1 to each digit) and then ask about the new numbers: which is the largest, the second smallest, or what is the sum of two digits of one of them. The method is always the same: apply the rule to every number first, write the new numbers in a row, then rank them.
Key takeaway for SSC: Never rank the original numbers. Rewrite all five numbers after the change, then sort them. Every example on this page was checked with a program.
These one-mark questions appear in the reasoning sections of SSC CGL, SSC CHSL, SSC MTS, SSC GD and SSC CPO. A related type asks how many times a digit appears with a given neighbour in a long row of digits; it is covered below.
The Three Common Rules
| Rule | What to do | Example |
|---|---|---|
| Digits in ascending order | Smallest digit first | 583 → 358 |
| Digits in descending order | Largest digit first | 583 → 853 |
| Digits reversed | Read the number backwards | 583 → 385 |
Number Arrangement: Solved Examples
Example 1: Ascending order within each number
Numbers: 583, 629, 714, 362, 945. If the digits within each number are arranged in ascending order, which is the second largest new number?
- New numbers: 358, 269, 147, 236, 459
- In order: 147, 236, 269, 358, 459
- Second largest = 358
Example 2: Descending order within each number
Same numbers: 583, 629, 714, 362, 945. If the digits within each number are arranged in descending order, which is the smallest new number?
- New numbers: 853, 962, 741, 632, 954
- In order: 632, 741, 853, 954, 962
- Smallest = 632
Example 3: Operation on digits after arranging
Numbers: 472, 856, 319, 640, 287. If the digits within each number are arranged in descending order, what is the sum of the first and third digits of the second highest new number?
- New numbers: 742, 865, 931, 640, 872; in order: 640, 742, 865, 872, 931
- Second highest = 872; first digit 8, third digit 2
- Sum = 10
Example 4: Reversed digits
Numbers: 583, 629, 714, 362, 945. If the digits of each number are reversed, which original number gives the smallest new number?
- Reversed: 385, 926, 417, 263, 549; smallest = 263
- Original number = 362
Counting Digits in a Series
Row of digits: 4 7 3 8 5 3 9 2 7 3 6 5 3 1 8 3 4 2 3 7 9 3 5
- How many 3s are immediately preceded by 5 and immediately followed by an odd digit? Groups found: 2 (539, 531). Answer: 2
- How many 3s are immediately preceded by an odd digit and immediately followed by an even digit? Groups: 738, 736. Answer: 2
Method: underline every 3 first, then check its left neighbour, then its right neighbour. Ignore a 3 at either end of the row when the question needs both neighbours.
Common Mistakes in Number Arrangement Questions
- Ranking the original numbers instead of the new ones.
- Mixing up second largest and second smallest. Write the sorted list once and read from the correct end.
- Applying the rule to only some numbers. Rewrite all of them before comparing.
- Reading digits from the wrong number in a digit-sum question. Circle the chosen new number before picking digits.
Number Arrangement Practice Questions with Answers
- Numbers: 735, 418, 962, 507, 284. If the digits within each number are arranged in ascending order, what is the difference between the largest and the smallest new numbers? Answer: 300 (new numbers in order: 57, 148, 248, 269, 357).
- Numbers: 619, 843, 275, 390, 158. If the digits within each number are arranged in descending order, which is the second smallest new number? Answer: 843 (new numbers in order: 752, 843, 851, 930, 961).
For timed practice, take the SSC CGL Reasoning Mini Mock Test 10 and the SSC CHSL Reasoning Mini Mock Test 10.
Number Arrangement FAQs
What does arranging digits within a number mean?
Each number is rewritten using its own digits in the stated order. 583 in ascending order becomes 358; the other numbers are not involved.
What if two new numbers are equal?
SSC questions are framed so that the new numbers are different. If two look equal, recheck the rule you applied.
Are these questions asked in SSC CHSL and SSC MTS?
Yes. The same digit-rearranging and digit-counting questions appear in the reasoning sections of SSC CHSL, SSC MTS, SSC GD, SSC CGL and SSC CPO.
Practice Next
- Topic tests: SSC CGL Reasoning Mini Mock Test 10, SSC CHSL Reasoning Mini Mock Test 10 and SSC CGL General Intelligence and Reasoning Sectional Mock Test 17.
- Related notes: missing number questions for SSC and number series questions for SSC CGL.
- Browse all study notes.