Problem Solving

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:00 am

Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30?

A. 426
B. 430
C. 443
D. 460
E. 486

Answer: D
Source: GMAT paper tests

The 3 options:
$1.50 per pack of 100 = 1.5 cents per envelope
$1.00 per pack of 50 = 2 cents per envelope
$0.03 per individual envelope = 3 cents per envelope

Since the packs of 100 are the best value, let's buy as many of these as we can.

4 packs of 100 costs $6.00 (we still have $1.30 left to spend)
1 packs of 50 costs $1.00 (we still have $0.30 left to spend)
10 individual envelopes costs $0.30 (we've spent all of the money)

Number of envelopes purchased = 400 + 50 + 10 = 460
Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:00 am

Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30?

A. 426
B. 430
C. 443
D. 460
E. 486

Answer: D
Source: GMAT paper tests

Solution:

We see that the cost per envelope of a pack of 100 envelopes is 1.50/100 = $0.015 and that of a pack of 50 envelopes is 1/50 = $0.02. Since the cost per envelope is the cheapest when buying a pack of 100 envelopes, we should buy as many packs of 100 envelopes first, followed by packs of 50 envelopes, and then followed by single envelopes.

Using this scheme, we can buy 4 packs of 100 envelopes, with 7.3 - 6 = $1.30 left. We then buy 1 pack of 50 envelopes, with 1.3 - 1 = $0.30 left. Finally, we can buy 10 single envelopes with the $0.30 we have left. Therefore, we can buy a maximum total of 4 x 100 + 50 + 10 = 460 envelopes.

Answer: D