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A company produces baseball cards in equal numbers of regula

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A company produces baseball cards in equal numbers of regula

by BTGmoderatorDC » Fri Feb 01, 2019 5:49 pm

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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

OA D

Source: Princeton Review
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by [email protected] » Sat Feb 02, 2019 11:32 am
Hi All,

We're told that a company produces baseball cards in EQUAL numbers of regular packs of 16 and deluxe packs of 30. On a certain day, the company produces 241 cards. We're asked for the SMALLEST number of additional cards the company needs to produce in order to maintain its regular production practice. This question comes down to basic Arithmetic.

Since the company produces EQUAL numbers of packs of 16 and 30, that means we must be dealing with a multiple of (16+30) = 46 cards. In other words...
1 pack of each = 46 total cards
2 packs of each = 92 total cards
3 packs of each = 138 total cards
Etc.

Since 241 cards is a relatively small number, you might find it easier to simply continue "adding 46" until you get the smallest total that is larger than 241 (as opposed to dividing 241 by 46 and solving for the remainder.

138... 184... 230... 276

276 - 241 = 35 additional cards needed.

Final Answer: D

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by Scott@TargetTestPrep » Wed Feb 06, 2019 6:23 pm
BTGmoderatorDC wrote: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

OA D

Source: Princeton Review
We can let the number of regular packs produced = n; notice that n = the number of deluxe packs also. So we have:

16n + 30n = 241

46n = 241

n = 5 11/241

We see that we have 5 full packs for each type, with 11 cards left. Since one regular pack and one deluxe pack require a total of 46 cards, we see that we need 46 - 11 = 35 more cards.

Answer: D

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edited

by deloitte247 » Thu Feb 07, 2019 12:00 am
Let the number of regular packs produced = n
n = number of regular deluxe packs
$$16 n+30 n = 241$$
$$46 n = 241$$
$$n = \frac{241}{46}$$
$$n = 5\frac{11}{46}$$
This means we have 5 full packs for each type remainder 11 i.e with 11 cards left.
Since one regular pack and one deluxe pack requires a total of 46 cards ; additional cards needed = 46 -11 = 35 more cards
$$answer\ is\ Option\ D$$
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