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Number Ranking

Agniveer (All) · Logical Reasoning

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Core Concept

Read this first — the foundation of the topic

Number Ranking is a logical reasoning problem where you are given a series of numbers or positions, and you must determine the rank or position of a particular number or person in a sequence—either from left to right or right to left. CORE CONCEPT In Number Ranking problems, you need to find where a number sits in a given order. The question might ask: 'What is the rank of number X from the left?' or 'If we reverse the sequence, what becomes the position of Y?' The key is to count carefully and apply simple directional rules. KEY RULES & PROPERTIES 1. Always identify the total count of numbers/items in the sequence. 2.

Rank from left means counting from position 1 on the left side. 3. Rank from right means counting from position 1 on the right side (reverse counting). 4. If an item's rank from left is R, then its rank from right = (Total Count + 1) – R. 5.

The middle position exists only if total count is odd. 6. Direction matters—left and right are opposite directions. FORMULA BLOCK Rank from Right = (Total Number of Items + 1) − Rank from Left Rank from Left = (Total Number of Items + 1) − Rank from Right Total Items = Rank from Left + Rank from Right − 1 EXAM PATTERNS SSC CGL typically asks: - Direct rank questions: 'Find rank of X from left/right' - Reverse rank questions: 'If reversed, what is position?' - Both-side rank: 'A is 5th from left and 8th from right. Find total count' - Position-based: 'How many items between positions?' SHORTCUT/TRICK Always use the formula: Rank from Right = (Total + 1) − Rank from Left.

This avoids counting errors. If you know any two values (total and one rank), you instantly find the other. WORKED EXAMPLE Sequence: 12, 25, 30, 45, 60, 75, 88, 92 Question: What is the rank of 60 from the right? Step 1: Count total items = 8 Step 2: Identify rank of 60 from left = 5 (it's the 5th number) Step 3: Apply formula: Rank from Right = (8 + 1) − 5 = 9 − 5 = 4 Answer: 60 is at rank 4 from the right. Verification: From right: 92(1st), 88(2nd), 75(3rd), 60(4th) ✓ COMMON MISTAKE Students often confuse rank with count. If 60 is 5th from left, it doesn't mean 5 items are to its left—only 4 items are to its left.

Rank includes the item itself.

🔑 Key Points

Rank from Right = (Total Items + 1) − Rank from Left; memorise this formula.
Rank from left = counting from position 1 starting at leftmost item.
Rank from right = reverse counting from rightmost item as position 1.
If rank from left is R and total is T, items to the left = R − 1.
Items between two ranks = |Rank₁ − Rank₂| − 1 (subtract 1 to exclude both positions).
Direction change always uses the complement formula; direct counting saves time only for small lists.

📌 Exam Facts

In a sequence of N items, if rank from left is L, then rank from right is always (N + 1) − L.
Number of items to the left of rank R = R − 1.
Number of items to the right of rank R = N − R.
If an item is 6th from left and 4th from right, total count = 6 + 4 − 1 = 9.
Middle position in a sequence of odd numbers (e.g., 7 items) = position 4.
Between rank 3 and rank 8 in a sequence, number of items = 8 − 3 − 1 = 4.
When a sequence is reversed, rank from left becomes rank from right in the new order.
Total items = Rank from Left + Rank from Right − 1 (this is a rearrangement of the main formula).

🚀 60-Second Revision

Formula King: Rank from Right = (Total + 1) − Rank from Left. Write it once before exam starts.
Trap: Rank ≠ Count of items on one side. Rank 5 means 4 items to the left, not 5.
Quick Check: If rank from left is L and total is T, rank from right must be T + 1 − L; verify mentally.
Direction Matters: Left = normal order, Right = reverse order. Don't flip them.
Formula Rearrange: If given rank from left and right, find total = L + R − 1. Easy bonus question.
Middle Alert: In odd sequences (5, 7, 9 items), the middle rank = (Total + 1) ÷ 2.
Between Positions: Items between rank A and rank B = |A − B| − 1. Exclude endpoints.

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