Difference between revisions of "1975 AHSME Problems/Problem 8"

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==Problem==
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If the statement "All shirts in this store are on sale." is false, then which of the following statements must be true?  
 
If the statement "All shirts in this store are on sale." is false, then which of the following statements must be true?  
  
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If not all the shirts in the store are on sale, then the answer is <math>\boxed{\textbf{(D) } \text{II and IV only}}</math>.
 
If not all the shirts in the store are on sale, then the answer is <math>\boxed{\textbf{(D) } \text{II and IV only}}</math>.
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==See Also==
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{{AHSME box|year=1975|num-b=7|num-a=9}}
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{{MAA Notice}}

Latest revision as of 16:53, 19 January 2021

Problem

If the statement "All shirts in this store are on sale." is false, then which of the following statements must be true?

I. All shirts in this store are at non-sale prices.

II. There is some shirt in this store not on sale.

III. No shirt in this store is on sale.

IV. Not all shirts in this store are on sale.


$\textbf{(A)}\ \text{II only} \qquad  \textbf{(B)}\ \text{IV only} \qquad  \textbf{(C)}\ \text{I and III only} \qquad  \textbf{(D)}\ \text{II and IV only} \qquad  \textbf{(E)}\ \text{I, II and IV only}$


Solution

Solution by e_power_pi_times_i


If not all the shirts in the store are on sale, then the answer is $\boxed{\textbf{(D) } \text{II and IV only}}$.

See Also

1975 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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