1003099407
Level:
B
If we convert the fraction \( \frac27 \) to a decimal, then the \( 32 \)nd digit after the decimal point is:
\( 8 \)
\( 1 \)
\( 2 \)
\( 7 \)
B
1003099406
Level:
B
In mathematics, the product of all positive integers less than or equal to a non-
negative integer \( n \) is denoted by \( n! \). For example: \( 5!=5\cdot4\cdot3\cdot2\cdot1=120 \). Which of the following
statements is true?
\( 16! \) is divisible by \( 91 \).
\( 16! \) is divisible by \( 71 \).
\( 16! \) is divisible by \( 51 \).
\( 16! \) is divisible by \( 41 \).
1003099405
Level:
B
The number \( 5\cdot11\cdot17 \) has exactly:
eight positive integer divisors
six positive integer divisors
seven positive integer divisors
five positive integer divisors
1003099404
Level:
B
The number \( 725233+x \) after dividing by \( 9 \) is to give a remainder of \( 5 \). Which of the given numbers shall we substitute for \( x \)?
\( 1 \)
\( 3 \)
\( 2 \)
\( 8 \)
1003099403
Level:
B
The number \( x \) when divided by \( 7 \) gives a remainder of \( 3 \). The number \( x \) can be written in the form:
\( 7n+3\text{, }n\in\mathbb{N} \)
\( 3n+7\text{, }n\in\mathbb{N} \)
\( 7(n+3)\text{, }n\in\mathbb{N} \)
\( 3(n+7)\text{, }n\in\mathbb{N} \)
1003099402
Level:
B
How many odd double-digit numbers give the reminder of \( 2 \) when divided by \( 9 \) and are divisible by \( 13 \) as well?
\( 1 \)
\( 2 \)
\( 3 \)
\( 4 \)
1003099401
Level:
B
The number \( 43256232a2 \) is divisible by \( 9 \) if
\( a= 7 \).
\( a= 1 \).
\( a= 0 \).
\( a= 4 \).
1003099510
Level:
B
What is the value of \( \sqrt[4]{2\sqrt2}\sqrt[8]{32} \)?
\( 2 \)
\( 2^{\frac12} \)
\( 2^{\frac34} \)
\( 2^0 \)
1003099507
Level:
B
The multiplicative inverse of \( \frac2{\sqrt3-1} \) is:
\( \frac1{\sqrt3+1} \)
\( \frac2{\sqrt3+1} \)
\( \frac{-2}{\sqrt3-1} \)
\( \frac{1-\sqrt3}2 \)
1003099506
Level:
B
The additive inverse of \( \frac1{5-2\sqrt5} \) is:
\( \frac{-5-2\sqrt5}5 \)
\( \frac{-1}{2\sqrt5-5} \)
\( \frac{-1}{2\sqrt5+5} \)
\( 5-2\sqrt5 \)