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Difference between revisions of "1951 AHSME Problems"
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The percent that <math>M</math> is greater than <math>N</math>, is:
 
The percent that <math>M</math> is greater than <math>N</math>, is:
  
−
(A) <math>\frac {100(M - N)}{M}</math>
+
<math> \mathrm{(A) \ } \frac {100(M - N)}{M} \qquad \mathrm{(B) \ } \frac {100(M - N)}{N} \qquad \mathrm{(C) \ } \frac {M - N}{N} \qquad \mathrm{(D) \ } \frac {M - N}{M} \qquad \mathrm{(E) \ } \frac {100(M + N)}{N} </math>
−
 
 
−
(B) <math>\frac {100(M - N)}{N}</math>
 
−
 
 
−
(C) <math>\frac {M - N}{N}</math>
 
−
 
 
−
(D) <math>\frac {M - N}{M}</math>
 
−
 
 
−
(E) <math>\frac {100(M + N)}{N}</math>
 
  
  
Line 23: Line 15:
 
If the length of a diagonal of a square is <math>a + b</math>, then the area of the square is:
 
If the length of a diagonal of a square is <math>a + b</math>, then the area of the square is:
  
−
(A) <math>(a + b)^2</math>
+
 
−
(B) <math>\frac {1}{2}(a + b)^2</math>
+
<math> \mathrm{(A) \ } (a+b)^2 \qquad \mathrm{(B) \ } \frac {1}{2}(a+b)^2 \qquad \mathrm{(C) \ } a^2+b^2 \qquad \mathrm{(D) \ } \frac {1}{2}(a^2+b^2) \qquad \mathrm{(E) \ } \text{none of these} </math>
−
(C) <math>a^2 + b^2</math>
 
−
(D) <math>\frac {1}{2}(a^2 + b^2)</math>
 
−
(E) none of these
 
  
 
[[1951 AHSME Problems/Problem 3|Solution]]
 
[[1951 AHSME Problems/Problem 3|Solution]]
Line 34: Line 23:
 
A barn with a roof is rectangular in shape, 10 yd. wide, 13 yd. long and 5 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:
 
A barn with a roof is rectangular in shape, 10 yd. wide, 13 yd. long and 5 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:
  
−
(A) 360
+
 
−
(B) 460
+
<math> \mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720 </math>
−
(C) 490
 
−
(D) 590
 
−
(E) 720
 
  
 
[[1951 AHSME Problems/Problem 4|Solution]]
 
[[1951 AHSME Problems/Problem 4|Solution]]
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Mr. <math>A</math> owns a home worth <math>\</math>10,000.  He sells it to Mr. <math>B</math> at a 10 % profit based on the worth of the house.  Mr. <math>B</math> sells the house back to Mr. <math>A</math> at a 10 % loss.  Then:
 
Mr. <math>A</math> owns a home worth <math>\</math>10,000.  He sells it to Mr. <math>B</math> at a 10 % profit based on the worth of the house.  Mr. <math>B</math> sells the house back to Mr. <math>A</math> at a 10 % loss.  Then:
  
−
(A) <math>A</math> comes out even
+
 
−
(B) <math>A</math> makes <math>\</math>1100 on the deal
+
<math> \mathrm{(A) \ } \text{A comes out even} \qquad \mathrm{(B) \ } \text{A makes 1100 on the deal} \qquad \mathrm{(C) \ } \text{A makes 1000 on the deal} \qquad \mathrm{(D) \ } \text{A loses 900 on the deal} \qquad \mathrm{(E) \ } \text{A loses 1000 on the deal} </math>
−
(C) <math>A</math> makes <math>\</math>1000 on the deal
 
−
(D) <math>A</math> loses <math>\</math>900 on the deal
 
−
(E) <math>A</math> loses <math>\</math>1000 on the deal
 
  
 
[[1951 AHSME Problems/Problem 5|Solution]]
 
[[1951 AHSME Problems/Problem 5|Solution]]
Line 110: Line 93:
 
it happens that <math>c = b^2/4a</math>, then the graph of <math>y = f(x)</math> will certainly:
 
it happens that <math>c = b^2/4a</math>, then the graph of <math>y = f(x)</math> will certainly:
  
−
(A) have a maximum
+
 
−
(B) have a minimum
+
<math> \mathrm{(A) \ } \text{have a maximum} \qquad \mathrm{(B) \ } \text{have a minimum} \qquad \mathrm{(C) \ } \text{be tangent to the x-axis} \qquad \mathrm{(D) \ } \text{be tangent to the y-axis} \qquad \mathrm{(E) \ } \text{lie in one quadrant only} </math>
−
(C) be tangent to the <math>x</math>-axis
+
 
−
(D) be tangent to the <math>y</math>-axis
 
−
(E) lie in one quadrant only
 
  
 
[[1951 AHSME Problems/Problem 16|Solution]]
 
[[1951 AHSME Problems/Problem 16|Solution]]

Revision as of 11:40, 10 January 2008

Problem 1

Solution

Problem 2

The percent that $M$ is greater than $N$, is:

$\mathrm{(A) \ } \frac {100(M - N)}{M} \qquad \mathrm{(B) \ } \frac {100(M - N)}{N} \qquad \mathrm{(C) \ } \frac {M - N}{N} \qquad \mathrm{(D) \ } \frac {M - N}{M} \qquad \mathrm{(E) \ } \frac {100(M + N)}{N}$


Solution

Problem 3

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


$\mathrm{(A) \ } (a+b)^2 \qquad \mathrm{(B) \ } \frac {1}{2}(a+b)^2 \qquad \mathrm{(C) \ } a^2+b^2 \qquad \mathrm{(D) \ } \frac {1}{2}(a^2+b^2) \qquad \mathrm{(E) \ } \text{none of these}$

Solution

Problem 4

A barn with a roof is rectangular in shape, 10 yd. wide, 13 yd. long and 5 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:


$\mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720$

Solution

Problem 5

Mr. $A$ owns a home worth $$10,000. He sells it to Mr. $B$ at a 10 % profit based on the worth of the house. Mr. $B$ sells the house back to Mr. $A$ at a 10 % loss. Then:


$\mathrm{(A) \ } \text{A comes out even} \qquad \mathrm{(B) \ } \text{A makes 1100 on the deal} \qquad \mathrm{(C) \ } \text{A makes 1000 on the deal} \qquad \mathrm{(D) \ } \text{A loses 900 on the deal} \qquad \mathrm{(E) \ } \text{A loses 1000 on the deal}$

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

If in applying the quadratic formula to a quadratic equation

\[f(x) \equiv ax^2 + bx + c = 0\],

it happens that $c = b^2/4a$, then the graph of $y = f(x)$ will certainly:


$\mathrm{(A) \ } \text{have a maximum} \qquad \mathrm{(B) \ } \text{have a minimum} \qquad \mathrm{(C) \ } \text{be tangent to the x-axis} \qquad \mathrm{(D) \ } \text{be tangent to the y-axis} \qquad \mathrm{(E) \ } \text{lie in one quadrant only}$


Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

Problem 26

Solution

Problem 27

Solution

Problem 28

Solution

Problem 29

Solution

Problem 30

Solution

See also

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