Anthony can purchase bagels at \(\$1.99\) for a specialty bagel and \(\$15.99\) for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?
(1) Anthony spent less than \(\$32.00\)
(2) Anthony spent more than \($31.90\)
Answer: C
Source: Veritas Prep
Anthony can purchase bagels at \(\$1.99\) for a specialty bagel and \(\$15.99\) for a package of one dozen plain bagels.
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Global Stats
1 specialty bagel = $1.99
1 dozen plain bagel = $15.99
Target question: Did Anthony purchase any plain bagels.
Statement 1: Anthony spent less than $32.00
If Anthony spent less than $32.00, there is a probability of buying specialty bagels only or buying a dozen plain bagels only. Since there is nothing more to enable us to get a more definite answer. Hence, statement 1 is NOT SUFFICIENT.
Statement 2: Anthony spent more than $32.00
There's also a possibility of buying special bagels only or buying dozen plain bagels only. Since there is nothing more to enable us to get a more definite answer. Also, statement 2 is NOT SUFFICIENT.
Combining both statements together:
For statement 1: Anthony's expenses < $32.00
For statement 2: Anthony's expenses > $32.00
Therefore, $31.90 < Anthony's expenses < $32.00
This is achievable from purchasing two dozen plain bagels or 1 dozen plain bagels and some specialty bagels in any case plain bagels is purchased. So, Anthony purchased at least 1 plain bagel. Thus, both statements combined together are SUFFICIENT.
Answer = option C
1 dozen plain bagel = $15.99
Target question: Did Anthony purchase any plain bagels.
Statement 1: Anthony spent less than $32.00
If Anthony spent less than $32.00, there is a probability of buying specialty bagels only or buying a dozen plain bagels only. Since there is nothing more to enable us to get a more definite answer. Hence, statement 1 is NOT SUFFICIENT.
Statement 2: Anthony spent more than $32.00
There's also a possibility of buying special bagels only or buying dozen plain bagels only. Since there is nothing more to enable us to get a more definite answer. Also, statement 2 is NOT SUFFICIENT.
Combining both statements together:
For statement 1: Anthony's expenses < $32.00
For statement 2: Anthony's expenses > $32.00
Therefore, $31.90 < Anthony's expenses < $32.00
This is achievable from purchasing two dozen plain bagels or 1 dozen plain bagels and some specialty bagels in any case plain bagels is purchased. So, Anthony purchased at least 1 plain bagel. Thus, both statements combined together are SUFFICIENT.
Answer = option C