Study the given pattern carefully and select the number that can replace the question mark (?) in it.
First row: 21, 12, 19
Second row: 27, 10, 19
Third row: 24, 10, ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
- A19
- B16
- C18
- D17
Solution & Step-by-step Explanation
Let's determine the relationship between columns in each row:
First row: 21,12,19
Let's check the arithmetic combinations:
3
21+12×2
=
3
21+24
=
3
45
=15
=19
Let's try another logic:
(21−19)×6=12→2×6=12
Let's verify if this holds for the second row:
Second row: 27,10,19
(27−19)×something
=10
Let's try:
Row 1:21+12=33→33−14=19
Row 2:27+10=37→37−18=19
(No common pattern)
Let's examine column combinations:
Row 1:21+19=40⟹40−12=28
Let's check:
2×(Column 3)−Column 2=Column 1
Row 1:2×19−12=38−12=26
=21
Let's try:
3
Column 1+Column 2
+constant
Let's look at:
Row 1:
3
21
+12=7+12=19
Let's verify this rule:
3
Column 1
+Column 2=Column 3
Second row:
3
27
+10=9+10=19
This matches the third column exactly!
Third row: Applying this confirmed rule:
3
24
+10=8+10=18
Thus, the missing number is 18.
First row: 21,12,19
Let's check the arithmetic combinations:
3
21+12×2
=
3
21+24
=
3
45
=15
=19
Let's try another logic:
(21−19)×6=12→2×6=12
Let's verify if this holds for the second row:
Second row: 27,10,19
(27−19)×something
=10
Let's try:
Row 1:21+12=33→33−14=19
Row 2:27+10=37→37−18=19
(No common pattern)
Let's examine column combinations:
Row 1:21+19=40⟹40−12=28
Let's check:
2×(Column 3)−Column 2=Column 1
Row 1:2×19−12=38−12=26
=21
Let's try:
3
Column 1+Column 2
+constant
Let's look at:
Row 1:
3
21
+12=7+12=19
Let's verify this rule:
3
Column 1
+Column 2=Column 3
Second row:
3
27
+10=9+10=19
This matches the third column exactly!
Third row: Applying this confirmed rule:
3
24
+10=8+10=18
Thus, the missing number is 18.