What will come at the place of question mark 4 9 2 3 5 7 8 1 ?

- (a)6
- (b)3
- (c)5
- (d)9
Answer
Why
Correct — A.
Rule: every row, column and diagonal adds to 15 (a magic square of 1 to 9).
Row 1: 4 + 9 + 2 = 15
Row 2: 3 + 5 + 7 = 15
Row 3: 8 + 1 + ? = 15, so ? = 6
Column 3: 2 + 7 + 6 = 15 ✓
Diagonal: 4 + 5 + 6 = 15 ✓
? = 6 → option (a).
Why the others are wrong
- (b)3 — 3 makes row 3 add to 8 + 1 + 3 = 12, not 15. It also repeats the 3 already in row 2.
- (c)5 — 5 makes row 3 add to 14 and repeats the 5 at the centre. Column 3 would read 2 + 7 + 5 = 14.
- (d)9 — 9 makes row 3 add to 18 and repeats the 9 in row 1. The diagonal 4 + 5 + 9 would reach 18 too.
Concept
The picture shows a 3 × 3 grid: 4 9 2 on top, 3 5 7 in the middle, and 8 1 ? at the bottom. It is the classic magic square, the digits 1 to 9 placed so every row, column and diagonal shares one sum.
That sum is (1 + 2 + … + 9) ÷ 3 = 45 ÷ 3 = 15. Subtract the two known numbers in any line through the blank to find it.
This arrangement, 4 9 2 / 3 5 7 / 8 1 6, is known as the Lo Shu square. A second check needs no sums: the grid holds each digit 1 to 9 once, and 6 is the digit not yet placed.
Key facts
- A 3 × 3 magic square of the digits 1 to 9 has magic sum 15.
- Its centre is always 5.
- Magic sum of an n × n square of 1 to n²: n(n² + 1) ⁄ 2.
Study next
Common traps
- Hunting for a product or digit rule across the row before testing sums
- Trusting the row sum without a second line, a column or diagonal, through the blank
The grid comes with no instruction, so test the simplest shared rule, equal sums, across all three rows before trying anything harder.
Related PYQs
No directly related past PYQ was found.