Question:medium

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

Step 1: Compare the left side to the right side of each given equation: \( 1 \to 8 \), \( 2 \to 16 \), \( 3 \to 24 \), \( 4 \to 32 \).

Step 2: Notice each right-hand value is exactly 8 times the first number, so the real rule hidden behind the \( \times 7 \) symbol is multiplication by 8, not by 7.

Step 3: Apply this rule to 9: \( 9 \times 8 = 72 \).
\[ \boxed{72} \]
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Approach Solution -2

Another way to pin down the hidden rule is to work backwards from each option: assume that option is correct for \( 9 \times 7 \), figure out what constant multiplier it implies when divided by \( 9 \), and then check whether that same constant reproduces ALL four of the given equations. Let's test each option this way:

  1. 63: Dividing by \( 9 \) gives a constant of \( 7 \), meaning the rule would be ordinary multiplication. Checking this constant against the first given equation, \( 7 \times 1 \) should then equal \( 7 \), while the question states it equals \( 8 \). The constant \( 7 \) fails to reproduce the given data, so this option is wrong.
  2. 72: Dividing by \( 9 \) gives a constant of \( 8 \). Checking this against all four given equations: \( 8 \times 1 = 8 \), \( 8 \times 2 = 16 \), \( 8 \times 3 = 24 \), \( 8 \times 4 = 32 \), every single one matches exactly. This constant is fully consistent with the given data.
  3. 81: Dividing by \( 9 \) gives a constant of \( 9 \). Checking against the first equation, \( 9 \times 1 = 9 \), but the question says the result should be \( 8 \), so this constant does not reproduce the given data either.
  4. 90: Dividing by \( 9 \) gives a constant of \( 10 \). Checking against the first equation, \( 10 \times 1 = 10 \), again not matching the given result of \( 8 \), so this constant fails too.

Only the constant implied by 72 (namely 8) is consistent with every one of the four given equations, confirming that the hidden rule is multiplying the first number by 8.

Therefore, the correct answer is 72.

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