Question bank AMC12 1971

The number of digits in the number $N=2^{12}\times5^8$ is:

If $b$ men take $c$ days to lay $f$ bricks, then the number of days it will take $c$ men working at the same rate to lay $b$ bricks is:

If the point $(x,-4)$ lies on the straight line joining the points $(0,8)$ and $(-4,0)$ in the $xy$-plane, then $x$ is equal to:

After simple interest for two months at $5\%$ per annum was credited, a Boy Scout Troop had a total of $\$255.31$ in the Council Treasury. The interest credited was a number of dollars plus the following number of cents:

Points $A,$ $B,$ $Q,$ $D,$ and $C$ lie on the circle shown, and the measures of arcs $BQ$ and $QD$ are $42^\circ$ and $38^\circ,$ respectively. The sum of the measures of angles $P$ and $Q$ is:

Let $*$ be a symbol denoting the binary operation on the set $S$ of all nonzero real numbers as follows: for any $a,$ $b\in S,$ $a*b=2ab.$ Which statement is not true?

$2^{-(2k+1)}-2^{-(2k-1)}+2^{-2k}$ is equal to:

The solution set of $6x^2+5x\lt4$ is the set of all values of $x$ such that:

An uncrossed belt is fitted without slack around two circular pulleys with radii of $14$ inches and $4$ inches. If the distance between the points of contact of the belt with the pulleys is $24$ inches, then the distance between the centers of the pulleys in inches is:

Each of a group of $50$ girls is blonde or brunette and is blue-eyed or brown-eyed. If $14$ are blue-eyed blondes, $31$ are brunettes, and $18$ are brown-eyed, then the number of brown-eyed brunettes is:

The numeral $47$ in base $a$ represents the same number as $74$ in base $b.$ Assuming both bases are positive integers, the least possible value of $a+b,$ written as a Roman numeral, is:

For each integer $N\gt1,$ define positive integers to be congruent if they leave the same nonnegative remainder when divided by $N.$ If $69,$ $90,$ and $125$ are congruent in one such system, then in that same system, $81$ is congruent to:

If $(1.0025)^{10}$ is evaluated correct to $5$ decimal places, then the digit in the fifth decimal place is:

The number $2^{48}-1$ is exactly divisible by two numbers between $60$ and $70.$ These numbers are:

An aquarium on a level table has rectangular faces and is $10$ inches wide and $8$ inches high. When it was tilted, the water in it just covered an $8$-inch by $10$-inch end but only three-fourths of the rectangular bottom. The depth of the water when the bottom was again made level was:

After finding the average of $35$ scores, a student carelessly included the average with the $35$ scores and found the average of these $36$ numbers. The ratio of the second average to the true average was:

A circular disk is divided by $2n$ equally spaced radii $(n\gt0)$ and one secant line. The maximum number of nonoverlapping areas into which the disk can be divided is:

The current in a river flows steadily at $3$ miles per hour. A motorboat traveling at a constant rate in still water goes downstream $4$ miles and then returns to its starting point. The trip takes one hour, excluding turning time. The ratio of the downstream rate to the upstream rate is:

If the line $y=mx+1$ intersects the ellipse $x^2+4y^2=1$ exactly once, then the value of $m^2$ is:

The sum of the squares of the roots of the equation $x^2+2hx=3$ is $10.$ The absolute value of $h$ is equal to: