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CAT Questions – Numbers (properties of numbers) with VIDEO Solution

QUESTION 1
Naval writes 28 consecutive numbers. If both the smallest and the largest numbers are perfect squares, which of the following is the smallest number he wrote?
  1. 9
  2. 36
  3. 100
  4. Cannot be uniquely determined
Option: 4
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QUESTION 2
If \({4^a} = 5,\;{5^b} = 6,\;{6^c} = 7,\;and\;{7^d} = 8\) . What is the value of \(a \times b \times c \times d\)
  1. 1
  2. \(\cfrac{3}{2}\)
  3. 2
  4. \(\cfrac{5}{2}\)
Option: 2
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QUESTION 3
Let x, y, and z be positive integers and $\frac{x}{3},\frac{y}{4},\ and\ \frac{z}{6}$ are proper fractions in the simplest form. If $\frac{x+z}{3}+\frac{y+z}{4}+\frac{z}{3}=6$ , Find the value of $x+y+z$
Answer: 10
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QUESTION 4
Let $x=\frac{{{a}_{1}}}{\left| {{a}_{1}} \right|}+\frac{{{a}_{2}}}{\left| {{a}_{2}} \right|}+\frac{{{a}_{3}}}{\left| {{a}_{3}} \right|}...+\frac{{{a}_{10}}}{\left| {{a}_{10}} \right|}$ where ${{a}_{1}},{{a}_{2}},{{a}_{3}},...,{{a}_{10}}$ are real numbers. How many distinct value x can have?
Answer: 11
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QUESTION 5
Find the number of two digit prime number such that both the digits of the number are also prime numbers
Answer: 4
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