CAT MCQs on Number System

CAT Questions

• 1.

  If \( x \) and \( y \) satisfy the equations
  \(|x| + x + y = 15 \quad \text{(1)},\)
  \(x + |y| - y = 20 \quad \text{(2)}.\)
  Find the value of \( x - y \).

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• 2.

  The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

  • 10
  • 20
  • 14
  • 15
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• 3.

  One direct question from the Number System was 10 to the power 100 divided by seven, candidates had to choose the correct answer for the problem.

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• 4.

  When 3³³³ is divided by 11, the remainder is

  • 1
  • 6
  • 5
  • 10
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• 5.

  If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?

  • 4
  • 22
  • 18
  • 6
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• 6.

  Let $x$, $y$, and $z$ be real numbers satisfying
  \(4(x^2 + y^2 + z^2) = a,\)
  \(4(x - y - z) = 3 + a.\)
  Then $a$ equals ?

  • 3
  • 4
  • 1
  • $1\frac{1}{3}$
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