Difference between revisions of "1988 AJHSME Problems"
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== Problem 18 == | == Problem 18 == | ||
+ | |||
+ | The average weight of <math>6</math> boys is <math>150</math> pounds and the average weight of <math>4</math> girls is <math>120</math> pounds. The average weight of the <math>10</math> children is | ||
+ | |||
+ | <math>\text{(A)}\ 135\text{ pounds} \qquad \text{(B)}\ 137\text{ pounds} \qquad \text{(C)}\ 138\text{ pounds} \qquad \text{(D)}\ 140\text{ pounds} \qquad \text{(E)}\ 141\text{ pounds}</math> | ||
[[1988 AJHSME Problems/Problem 18|Solution]] | [[1988 AJHSME Problems/Problem 18|Solution]] | ||
== Problem 19 == | == Problem 19 == | ||
+ | |||
+ | What is the <math>100\text{th}</math> number in the arithmetic sequence: <math>1,5,9,13,17,21,25,...</math>? | ||
+ | |||
+ | <math>\text{(A)}\ 397 \qquad \text{(B)}\ 399 \qquad \text{(C)}\ 401 \qquad \text{(D)}\ 403 \qquad \text{(E)}\ 405</math> | ||
[[1988 AJHSME Problems/Problem 19|Solution]] | [[1988 AJHSME Problems/Problem 19|Solution]] | ||
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== Problem 21 == | == Problem 21 == | ||
+ | |||
+ | A fifth number, <math>n</math>, is added to the set <math>\{ 3,6,9,10 \}</math> to make the mean of the set of five numbers equal to its median. The number of possible values of <math>n</math> is | ||
+ | |||
+ | <math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ \text{more than }4</math> | ||
[[1988 AJHSME Problems/Problem 21|Solution]] | [[1988 AJHSME Problems/Problem 21|Solution]] | ||
== Problem 22 == | == Problem 22 == | ||
+ | |||
+ | Tom's Hat Shoppe increased all original prices by <math>25\% </math>. Now the shoppe is having a sale where all prices are <math>20\% </math> off these increased prices. Which statement best describes the sale price of an item? | ||
+ | |||
+ | <math>\text{(A)}\ \text{The sale price is }5\% \text{ higher than the original price.}</math> | ||
+ | |||
+ | <math>\text{(B)}\ \text{The sale price is higher than the original price, but by less than }5\% .</math> | ||
+ | |||
+ | <math>\text{(C)}\ \text{The sale price is higher than the original price, but by more than }5\% .</math> | ||
+ | |||
+ | <math>\text{(D)}\ \text{The sale price is lower than the original price.}</math> | ||
+ | |||
+ | <math>\text{(E)}\ \text{The same price is the same as the original price.}</math> | ||
[[1988 AJHSME Problems/Problem 22|Solution]] | [[1988 AJHSME Problems/Problem 22|Solution]] | ||
== Problem 23 == | == Problem 23 == | ||
+ | |||
+ | Maria buys computer disks at a price of <math>4</math> for <dollar/><math>5</math> and sells them at a price of <math>3</math> for <dollar/><math>5</math>. How many computer disks must she sell in order to make a profit of <dollar/><math>100</math>? | ||
+ | |||
+ | <math>\text{(A)}\ 100 \qquad \text{(B)}\ 120 \qquad \text{(C)}\ 200 \qquad \text{(D)}\ 240 \qquad \text{(E)}\ 1200</math> | ||
[[1988 AJHSME Problems/Problem 23|Solution]] | [[1988 AJHSME Problems/Problem 23|Solution]] | ||
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== Problem 25 == | == Problem 25 == | ||
+ | |||
+ | A '''palindrome''' is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: <math>\boxed{1:01}</math>, <math>\boxed{4:44}</math>, and <math>\boxed{12:21}</math>. How many times during a <math>12</math>-hour period will be palindromes? | ||
+ | |||
+ | <math>\text{(A)}\ 57 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 63 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 93</math> | ||
[[1988 AJHSME Problems/Problem 25|Solution]] | [[1988 AJHSME Problems/Problem 25|Solution]] |
Revision as of 16:45, 22 March 2009
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 See also
Problem 1
The diagram shows part of a scale of a measuring device. The arrow indicates an approximate reading of
Problem 2
The product
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
is closest to
Problem 8
Betty used a calculator to find the product . She forgot to enter the decimal points. The calculator showed
. If Betty had entered the decimal points correctly, the answer would have been
Problem 9
Problem 10
Chris' birthday is on a Thursday this year. What day of the week will it be days after her birthday?
Problem 11
is
Problem 12
Suppose the estimated billion dollar cost to send a person to the planet Mars is shared equally by the
million people in the U.S. Then each person's share is
Problem 13
If rose bushes are spaced about foot apart, approximately how many bushes are needed to surround a circular patio whose radius is
feet?
Problem 14
and
are whole numbers and
. The largest possible value of
is
Problem 15
The reciprocal of is
Problem 16
Problem 17
Problem 18
The average weight of boys is
pounds and the average weight of
girls is
pounds. The average weight of the
children is
Problem 19
What is the number in the arithmetic sequence:
?
Problem 20
Problem 21
A fifth number, , is added to the set
to make the mean of the set of five numbers equal to its median. The number of possible values of
is
Problem 22
Tom's Hat Shoppe increased all original prices by . Now the shoppe is having a sale where all prices are
off these increased prices. Which statement best describes the sale price of an item?
Problem 23
Maria buys computer disks at a price of for <dollar/>
and sells them at a price of
for <dollar/>
. How many computer disks must she sell in order to make a profit of <dollar/>
?
Problem 24
Problem 25
A palindrome is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: ,
, and
. How many times during a
-hour period will be palindromes?