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A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv

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A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv  [#permalink]

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New post 23 Dec 2018, 10:09
1
3
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:32) correct 32% (01:37) wrong based on 186 sessions

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A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silver. If there are 130 ounces of gold and silver total, what is the greatest amount of gold that can be in the vault, in ounces?

A. 40
B. 80
C. 120
D. 128
E. 130

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Re: A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv  [#permalink]

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New post 23 Dec 2018, 16:37
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SajjadAhmad wrote:
A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silver. If there are 130 ounces of gold and silver total, what is the greatest amount of gold that can be in the vault, in ounces?

A. 40
B. 80
C. 120
D. 128
E. 130


Let number of 8 ounce tablet of gold be x and of 5-ounce tablet of silver be y.
Then, 8x+5y=130.
We have to maximize x. To do that we have to minimize y, that means finding the value of y for which 8x is an integer. That happens at y=2, 8x+5*2=130, 8x=120. x=15.

Greatest amount of gold= 15*8 ounce=120 ounces. IMO, Option C.
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Re: A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv  [#permalink]

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New post 06 Jan 2019, 11:59
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number of gold tablets = g
no. of silver tabs = s

value of total ounces = 130
8g + 5s = 130

s=(130-8g)/5
for s to be integer --> numerator has to be multiple of 5.
Thus we can eliminate D as 130-128 = 2.

g= (130-5s)/8
only 120,80,40 are multiples of 8.
Highest = 120.

Answer = c.


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Re: A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv  [#permalink]

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New post 28 Jan 2019, 11:37
solution-
8x+5y=130
now put the values according to the options provided.
you will find that 120 is the highest as 5 also needs multiple to fulfill 130
=> x= 15, y = 2
8*15= 120 (C)
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A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv  [#permalink]

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New post 16 Jul 2019, 14:18
I solved by working backwards:

From the highest ammount of gold to the lowest:

e) It can't be 130 ounces of gold because 130 is not a multiple of 8;

d) It can't be 128 ounces of gold because the ammount of silver in this case would be 130-128 = 2. The quantity of silve must be a multiple of 5, hence the alternative is wrong;

c) 120 is a multiple of 8 and 10 is a multiple of 5 so that is the correct answer.
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A vault holds only 8-ounce tablets of gold and 5-ounce tablets of silv   [#permalink] 16 Jul 2019, 14:18
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