# Difference between revisions of "1951 AHSME Problems"

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== Problem 14 == | == Problem 14 == | ||

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

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+ | <math> \textrm{(A)}\ \text{Some statements are accepted without being proved.} </math> | ||

+ | <math> \textrm{(B)}\ \text{In some cases there is more than one correct order in proving certain propositions.} </math> | ||

+ | <math> \textrm{(C)}\ \text{Every term used in a proof must have been defined previously.} </math> | ||

+ | <math> \textrm{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposition.} </math> | ||

+ | <math> \textrm{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.} </math> | ||

[[1951 AHSME Problems/Problem 14|Solution]] | [[1951 AHSME Problems/Problem 14|Solution]] |

## Revision as of 14:19, 26 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 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

## Problem 16

If in applying the quadratic formula to a quadratic equation

it happens that , then the graph of will certainly: