Question:
If $1 \times 7 = 8$, $2 \times 7 = 16$, $3 \times 7 = 24$, $4 \times 7 = 32$, then what is the value of $9 \times 7$?
If $1 \times 7 = 8$, $2 \times 7 = 16$, $3 \times 7 = 24$, $4 \times 7 = 32$, then what is the value of $9 \times 7$?
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When sample equalities look wrong arithmetically, treat them as a coding rule. Compare outputs to see if they depend only on the first number, the second, or both.
Updated On: Jul 15, 2026
- 63
- 72
- 81
- 90
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The Correct Option is B
Approach Solution - 1
Pattern check: The right sides are $8,16,24,32$. These are $8\times 1,\;8\times 2,\;8\times 3,\;8\times 4$.
So the rule used in the question is $n \times 7$ is being encoded as $8n$ (i.e., multiply the first number by $8$; the $7$ is a distractor).
Apply the rule to $9 \times 7$: $8 \times 9 = 72$.
So the rule used in the question is $n \times 7$ is being encoded as $8n$ (i.e., multiply the first number by $8$; the $7$ is a distractor).
Apply the rule to $9 \times 7$: $8 \times 9 = 72$.
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Approach Solution -2
The question gives a made-up rule: \( 1 \times 7 = 8 \), \( 2 \times 7 = 16 \), \( 3 \times 7 = 24 \), \( 4 \times 7 = 32 \), and asks for the value of \( 9 \times 7 \) under the same rule. Let's check each option against the pattern:
- 63: This is the ordinary product \( 9 \times 7 \) under real multiplication. But the question is not asking for real multiplication, it is asking us to continue the pattern shown, and 63 does not fit the sequence \( 8, 16, 24, 32 \) at all.
- 72: Looking at the given results, each is exactly \( 8 \) times the first number: \( 8 \times 1 = 8 \), \( 8 \times 2 = 16 \), \( 8 \times 3 = 24 \), \( 8 \times 4 = 32 \). The \( \times 7 \) in each statement is a distractor; the real hidden rule is "multiply the first number by 8". Applying this rule to 9 gives \( 8 \times 9 = 72 \), which matches this option exactly.
- 81: This would be the result of \( 9 \times 9 \), which has no basis in the given pattern of results \( 8, 16, 24, 32 \).
- 90: This would follow if the rule were "multiply by 10", but the given results clearly increase by 8 each time, not by 10, so this does not fit.
Since the true hidden rule is "first number times 8", applying it to 9 gives \( 9 \times 8 = 72 \).
Therefore, the correct answer is 72.
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Approach Solution -3
The four given equations describe an artificial rule rather than real multiplication, so the cleanest way to pin it down is to treat the right-hand values as an arithmetic progression and find its formula. The values are \( 8, 16, 24, 32 \) for \( n = 1, 2, 3, 4 \). This sequence has a first term \( a = 8 \) and a common difference \( d = 8 \) (each term is \( 8 \) more than the last), so its general term is \( a_n = a + (n-1)d = 8 + 8(n-1) = 8n \). Applying this formula for \( n = 9 \) gives \( a_9 = 8 \times 9 = 72 \). Let's check each option against this formula:
- 63: This equals \( 9 \times 7 \) under ordinary multiplication, but \( a_9 = 8 \times 9 = 72 \) from the derived progression formula, not \( 63 \), so this option ignores the pattern entirely.
- 72: This matches \( a_9 = 8n = 8 \times 9 = 72 \) exactly, confirming it fits the arithmetic progression built from the four given terms.
- 81: This would require \( a_n = n^2 \), since \( 9^2 = 81 \), but \( n^2 \) does not match the given data (\( 1^2 = 1 \neq 8 \)), so this formula is inconsistent with the question.
- 90: This would require \( a_n = 10n \), but \( 10 \times 1 = 10 \neq 8 \), so this formula also fails to reproduce the given values.
Since the arithmetic progression formula \( a_n = 8n \), derived directly from the four given equations, gives \( a_9 = 72 \), this is the value consistent with the pattern.
Therefore, the correct answer is 72.
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