trex16864 wrote:
At a particular store, candy bars are normally priced at $1.00 each. Last week, the store offered a promotion under which customers purchasing one candy bar at full price could purchase a second candy bar for $0.50. A third candy bar would cost $1.00, a fourth would cost $0.50, and so on.
If, in a single transaction during the promotion, Rajiv spent D dollars on N candy bars, where D and N are integers, is N odd?
(1) D is prime.
(2) D is not divisible by 3.
Responding to a pm:
In the question stem, what does "D and N are integers" imply?
This is how the total cost progresses with each new candy bought:
$1 - $1.50 - $2.50 - $3
$4 - $4.50 - $5.50 - $6
$7 - $7.50 - $8.50 - $9
...
Note that we have integer cost whenever we buy candies in multiples of 4 or 1 more than a multiple of 4.
The total cost is a multiple of 3 for every multiple of 4 total candies (N is even) bought.
It is 1, 4, 7, 10, 13 ... etc for every 4a+1 (N is odd) candies bought.
Question: Is N odd?
If N is odd, D = 1 or 4 or 7 or 10 etc
If N is even, D = 3, or 6 or 9 ...
(1) D is prime.
D can be 3 or 7. In one case, N is even, in the other it is odd.
Not sufficient.
(2) D is not divisible by 3.
D cannot be 3, 6, 9 etc. So N is not even. N must be odd.
Sufficient.
Answer (B)
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Karishma
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