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Roses can be purchased individually for $4.30...

by swerve » Thu Jan 04, 2018 8:11 am
Roses can be purchased individually for $4.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?

A. 156
B. 162
C. 318
D. 324
E. 325

The OA is C.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.
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by DavidG@VeritasPrep » Thu Jan 04, 2018 9:44 am
swerve wrote:Roses can be purchased individually for $4.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?

A. 156
B. 162
C. 318
D. 324
E. 325

The OA is C.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.
If we're trying to maximize the number of roses, we want to purchase as many roses as possible in bundles of two dozen, as that's the best deal.
If we're paying $50 for each bouquet of two-dozen, then the most we can spend on these bouquets is $650, as this is the largest multiple of 50 under 680. 50 goes into 650 13 times. So for $650, we can buy 13 bouquets of 24 flowers each, or 24*13 = 312 flowers.

A and B are out.

We've got $30 left to spend. Clearly we can't afford the dozen roses for $36. If we can't afford 12 more roses then the correct answer must be less than 324 (As 312 + 12 = 324.) Eliminate D and E.

We're left with C. No need to do more math.
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by Scott@TargetTestPrep » Mon Aug 12, 2019 5:44 pm
swerve wrote:Roses can be purchased individually for $4.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?

A. 156
B. 162
C. 318
D. 324
E. 325
Note first that the cheapest price per rose is obtained by buying a 2-dozen bouquet. Thus, we want to buy as many 2-dozen bouquets as possible.

Since 650/50 = 13, 13 x 24 = 312 roses can be purchased for 650 dollars when buying them 2 dozen at a time.

With the remaining 30 dollars, 6 more roses can be purchased, for a total of 318 roses.

Answer: C

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