1975 AHSME Problems/Problem 8

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 $\boxed{\textbf{(D) } \text{II and IV only}}$ .

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1975 AHSME Problems/Problem 8

Solution