Two Brain Crackers - Problem Solving

[Guest]

Source: Princeton Review, GMAT Diagnostic - Adaptive GMAT Test #1

Q1:
A company produces baseball cards in equal numbers of regular packs of 16 and deluxe packs of 30. If, on a certain day a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice?
A) 5 B) 11 C) 21 D)35 E)46

Any ideas how to break this problem?

Q2:
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses at the restaurant? (Assume that all boxes are filled to capacity)
A) 96 B) 240 C)256 D) 384 E) 480

With this question I came up to the equation m = (15x - 16)/28, where m is the number of 12-glasses boxes and x is what we are looking for. At this point I have to plug each of the answer choices to see which one will give an integer (number of boxes must be integer). I was not able to came up with a better solution but this plugging seems to be time devastating on the exam if it had to be applied. Any better ideas?

Thanks.

[Guest]

Source: Princeton Review, GMAT Diagnostic - Adaptive GMAT Test #1


A company produces baseball cards in equal numbers of regular packs of 16 and deluxe packs of 30. If, on a certain day a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice?
A) 5 B) 11 C) 21 D)35 E)46

Here's my shot.

16x+30x = 241

46x = 241

x = 5.(Long string of decimals) This tells us that 5 will be the greatest equal number of packs they can produce without going over.

So we plug in 5 for X and get 16(5) + 30(5) = 230

241-230 = 11

I chose answer B



Q2:
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses at the restaurant? (Assume that all boxes are filled to capacity)
A) 96 B) 240 C)256 D) 384 E) 480

Glasses Per Box # of Boxes Total Glasses
Small 12 x 12x
Large 16 x+16 16x+256

Total n/a 2x+16 28x+256

The problem tells us that the average # of glasses per box is 15 so:
(Total # of Glasses) / (Total # of Boxes ) = 15

28x + 256
------------ = 15
2x + 16

28x + 256 = 30x + 240

2x = 16

x = 8

Plug into top formula to get 28(8) + 256 = 480

ANSWER E.

Both of these problems were really difficult and took me like 10 minutes each to play with. I'm not sure if these are 100% right so let me know.

[Spencer]

My chart didn't look right for #2 on the posting so here's a better picture of it:

[Guest]

Hi,

Thank you very much for the solutions you propose.

According to Princeton Review the correct answers are
- Q1: the correct answer is 'D) 35' not 'B) 11' - the latter (B) was my answer too.
- Q2: the correct answer is 'E) 480' - you are right

Regards.

P.S. Now I start to suspect that there might be a mistake in the answer of Q1 because I have found another question in the same test which obviously had a wrong answer pointed as right. Unfortunately, the test provides only answer choices - no explanations :(

[Logic]

Regarding Q1:

Following just a pure logic we can look at the answer choices A) 5 B) 11 C) 21 D) 35 E) 46 and try to eliminate some of them.

We know that they produce two packs with 16 and 30 cards, then the correct answer must be a number between 0 and 15 inclusive otherwise they can produce an extra pack of 16 cards. So we can eliminate answer choices C, D and E

According to me, Princeton pointed a wrong answer for right in Q1. If the answer is 35 then they why can't they produce an extra pack of 30 and thus leave only 5 more to produce in order to 'maintain their regular production practice' (whatever they mean by this mumbo-jumbo).

[guest 420]

hallo

[TheUnseenGuest]

In Regards to Q1:

Here's my shot.
16x+30x = 241
46x = 241
x = 5.(Long string of decimals) This tells us that 5 will be the greatest equal number of packs they can produce without going over.
So we plug in 5 for X and get 16(5) + 30(5) = 230
241-230 = 11
I chose answer B

You were very close to the answer. However, what you found was the excess of 5 equal 16 & 30 pack cards.

230 cards = 5 packs of 16 & 30 pack cards.

Since we have 241 cards that means we have 11 excess cards.

The next number of cards to create and equal number of packs is 276.
276 = 6(16) + 6(30)

Therefore, the minimum number of cards to produce the next full pack is:
276 - 241 = 35

The answer is (D).

[guest]

Here's another way of looking at Q1. The key is that the company has to produce an EQUAL number of th 16 card packs and 30 card packs. So the total number of cards produced has to be a factor of (30+16) or 46. 241 is not a factor of 46 (easy to tell, as 46 is even and 241 is not). The next factor of 46 after 241 is 46*6 = 276. So the company needs to produce 35 more cards in order to be able to manufacture an equal number of 16 card packs and 30 card packs.

Q2 - You can solve this as two simutaneous equations. Let S = number of small boxes (12 glasses each) and L = number of large boxes (16 glasses each)

eq 1) the average number of glasses per box is 15: (12S+16L)/(S+L)=15
eq2) There are 16 more of the larger boxes: L-S =16

Take eq1 and combine like terms: L-3S =0
Substitue L=16+S from (2)
eq 1 becomes S+16-3S = 0
2S = 16
S = 8
Plug the value S =8 into either of the first equations and you get L =24

So the total number of glasses is equal to 12S+16L = 12*8+16*24 = 480

Cheers

[RonPurewal]

the solutions on this thread are wonderful.