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If \(\gt\) = ÷, \(\lt\) = +, × = = and # = −, then which of the following equations is correct ?

  • A.24 × 4 \(\gt\) 20 \(\lt\) 2 # 16
  • B.24 \(\lt\) 4 \(\gt\) 20 # 2 × 16
  • C.24 # 4 \(\lt\) 20 × 2 \(\gt\) 16
  • D.24 \(\gt\) 4 × 20 \(\lt\) 2 # 16

Answer: D

The correct equation is 24 \(\gt\) 4 × 20 \(\lt\) 2 # 16.

Replace each symbol: \(\gt\) becomes ÷, \(\lt\) becomes +, × becomes =, and # becomes −. The last option then reads

\[ \begin{aligned} 24 \div 4 &= 20 + 2 - 16 \\ 6 &= 6 \end{aligned} \]

which is true. The others fail:

  • 24 = 4 ÷ 20 + 2 − 16 gives 24 = −13.8.
  • 24 + 4 ÷ 20 − 2 = 16 gives 22.2 = 16.
  • 24 − 4 + 20 = 2 ÷ 16 gives 40 = 0.125.

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