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GATE 2021 AE – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

$\oplus$ and $\odot$ are operators such that $p\odot q=p-q$ and $p\oplus q=pq$. Then $(9\odot(6\oplus7))\odot(7\oplus(6\odot5))=$

  1. 40
  2. -26
  3. -33
  4. -40

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Correct answer: (D) -40

Explanation

The operators are defined by $p\odot q=p-q$ and $p\oplus q=pq$. Evaluate the brackets from the inside.

**First part:** $9\odot(6\oplus7)$.
- $6\oplus7=6\times7=42$.
- $9\odot42=9-42=-33$.

**Second part:** $7\oplus(6\odot5)$.
- $6\odot5=6-5=1$.
- $7\oplus1=7\times1=7$.

**Combine:** $(-33)\odot7=-33-7=\mathbf{-40}$ (option D).