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?
QUESTION 2
If \({4^a} = 5,\;{5^b} = 6,\;{6^c} = 7,\;and\;{7^d} = 8\) . What is the value of \(a \times b \times c \times d\)
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 $x+y+z$
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?
QUESTION 5
Find the number of two digit prime number such that both the digits of the number are also prime numbers
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?
- 9
- 36
- 100
- Cannot be uniquely determined
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
- \(\cfrac{3}{2}\)
- 2
- \(\cfrac{5}{2}\)
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 $x+y+z$
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?
QUESTION 5
Find the number of two digit prime number such that both the digits of the number are also prime numbers