# Difference between revisions of "1951 AHSME Problems"

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== Problem 22 == | == Problem 22 == | ||

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+ | The values of <math>a</math> in the equation: <math> \log_{10}(a^{2}-15a) = 2 </math> are: | ||

+ | |||

+ | <math> \textbf{(A)}\ \frac{15\pm\sqrt{233}}{2}\qquad\textbf{(B)}\ 20,-5\qquad\textbf{(C)}\ \frac{15\pm\sqrt{305}}{2} </math> | ||

+ | <math> \textbf{(D)}\ \pm20\qquad\textbf{(E)}\ \text{none of these} </math> | ||

[[1951 AHSME Problems/Problem 22|Solution]] | [[1951 AHSME Problems/Problem 22|Solution]] |

## Revision as of 10:22, 28 August 2011

## Contents

- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 Problem 31
- 32 Problem 32
- 33 Problem 33
- 34 Problem 34
- 35 Problem 35
- 36 Problem 36
- 37 Problem 37
- 38 Problem 38
- 39 Problem 39
- 40 Problem 40
- 41 Problem 41
- 42 Problem 42
- 43 Problem 43
- 44 Problem 44
- 45 Problem 45
- 46 Problem 46
- 47 Problem 47
- 48 Problem 48
- 49 Problem 49
- 50 Problem 50
- 51 See also

## Problem 1

The percent that is greater than is:

## Problem 2

A rectangular field is half as wide as it is long and is completely enclosed by yards of fencing. The area in terms of is:

## Problem 3

If the length of a diagonal of a square is , then the area of the square is:

## Problem 4

A barn with a flat roof is rectangular in shape, yd. wide, yd. long and yd. high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. yd. to be painted is:

## Problem 5

Mr. A owns a home worth dollars. He sells it to Mr. B at a profit based on the worth of the house. Mr. B sells the house back to Mr. A at a loss. Then:

## Problem 6

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to:

## Problem 7

An error of is made in the measurement of a line long, while an error of only is made in a measurement of a line long. In comparison with the relative error of the first measurement, the relative error of the second measurement is:

## Problem 8

The price of an article is cut To restore it to its former value, the new price must be increased by:

## Problem 9

An equilateral triangle is drawn with a side length of A new equilateral triangle is formed by joining the midpoints of the sides of the first one. then a third equilateral triangle is formed by joining the midpoints of the sides of the second; and so on forever. the limit of the sum of the perimeters of all the triangles thus drawn is:

## Problem 10

Of the following statements, the one that is incorrect is:

## Problem 11

The limit of the sum of an infinite number of terms in a geometric progression is $\frac {a}{1 \minus{} r}$ (Error compiling LaTeX. ! Undefined control sequence.) where denotes the first term and $\minus{} 1 < r < 1$ (Error compiling LaTeX. ! Undefined control sequence.) denotes the common ratio. The limit of the sum of their squares is:

$\textrm{(A)}\ \frac {a^2}{(1 \minus{} r)^2} \qquad\textrm{(B)}\ \frac {a^2}{1 \plus{} r^2} \qquad\textrm{(C)}\ \frac {a^2}{1 \minus{} r^2} \qquad\textrm{(D)}\ \frac {4a^2}{1 \plus{} r^2} \qquad\textrm{(E)}\ \text{none of these}$ (Error compiling LaTeX. ! Undefined control sequence.)

## Problem 12

At o'clock, the hour and minute hands of a clock form an angle of:

## Problem 13

can do a piece of work in days. is more efficient than . The number of days it takes to do the same piece of work is:

## Problem 14

In connection with proof in geometry, indicate which one of the following statements is *incorrect*:

## Problem 15

The largest number by which the expression is divisible for all possible integral values of , is:

## Problem 16

If in applying the quadratic formula to a quadratic equation

it happens that , then the graph of will certainly:

## Problem 17

Indicate in which one of the following equations is neither directly nor inversely proportional to :

## Problem 18

The expression is to be factored into two linear prime binomial factors with integer coefficients. This can be one if is:

## Problem 19

A six place number is formed by repeating a three place number; for example, or , etc. Any number of this form is always exactly divisible by:

## Problem 20

When simplified and expressed with negative exponents, the expression is equal to:

## Problem 21

Given: and . The inequality which is not always correct is:

## Problem 22

The values of in the equation: are:

## Problem 23

## Problem 24

## Problem 25

## Problem 26

## Problem 27

## Problem 28

## Problem 29

## Problem 30

## Problem 31

## Problem 32

## Problem 33

## Problem 34

## Problem 35

## Problem 36

## Problem 37

## Problem 38

## Problem 39

## Problem 40

## Problem 41

## Problem 42

## Problem 43

## Problem 44

## Problem 45

## Problem 46

## Problem 47

## Problem 48

## Problem 49

The medians of a right triangle which are drawn from the vertices of the acute angles are and . The value of the hypotenuse is:

## Problem 50

Tom, Dick and Harry started out on a -mile journey. Tom and Harry went by automobile at the rate of mph, while Dick walked at the rate of mph. After a certain distance, Harry got off and walked on at mph, while Tom went back for Dick and got him to the destination at the same time that Harry arrived. The number of hours required for the trip was: