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Kim bought a total of $2.65 worth of postage stamps in four

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Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 29 Jun 2014, 03:28
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A
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Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
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Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 19 Nov 2014, 01:56
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Answer = C = 15

............... 1 ............... 5 ................ 10 ............... 25 ................ Total

............... b ................ a ................... 2a ............ a ...................... 265

b + 5a + 20a + 25a = 265

b + 50a = 265

To have b "minimum"; 50a has to be maximum

Nearest to 265 is 250 which is divisibly by 50

265-250 = 15

b = 15
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 29 Jun 2014, 03:57
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manideepgre wrote:
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an
equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps,
what is the least number of 1-cent stamps she could have bought?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


Let us covert all the denominations in terms of 5 cents.
25 cent=5 * 5 cent stamp
10 cent=2* 5 cent stamp

Kim bought equal no of 5 cent and 25 cent stamps and twice as many 10-cent stamps as 5-cent stamps.
Therefore every lot of purchase must vary in multiple 1+5+4(2*2)=10 purchases of 5 cent stamp.
Therefor every lot is worth 50 cents. Closest multiple of 50 to 265 is 250 (50*5).
Therefore Kim has to purchase atleast 15 stamps of 1 cent.

Ans=C
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 29 Jun 2014, 14:14
manideepgre wrote:
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an
equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps,
what is the least number of 1-cent stamps she could have bought?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25



Moved to the proper sub-forum.
Please post your questions in the PS/DS/SC/CR/RC sub-forums and tag properly.
Thank you.
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 11 Jan 2015, 07:25
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Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?

Let:
# of 5 and 25 cents stamps = n
# of 10 cent stamps = 2n
# of 1 cent stamps = m

Therefore:
5n + 25n + 10(2n) + m = 265 cents
50n + m = 265

For least number of 1 cents stamps, maximize 50n. Hence,

50*5 + m = 265 (n max has to be 5. For 6, the cost becomes 300 cents that exceeds his purchase of 265 cents)
m = 15 i.e. 15 stamps 1 cents each

Answer: C
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Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 07 May 2016, 04:30
a * (0,05) + a * (0,25) + 2a * (0,10) + b * 0,01 = 2,65

So, a(0,05+0,25+0,20) + b*0,01 = 2,65 => a * 0,50 + b*0,01 = 2,65

Given that the least answer choice is 25, a>4 (4*0,5 = 2)

So, let's try a=5
5 * 0,50 + b*0,01 = 2,5 + b*0,01
b * 0,01 = 0,15
b=15
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 22 Oct 2016, 17:47
Use the following equation:

1a+5b+10c+25d = 265
b=d
2b=c

Plug in values --> 1a+5b+20b+25b = 265
1a + 50b = 265

bmax = 5 --> 250

265-250 = 15
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 12 Nov 2017, 08:46
manideepgre wrote:
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


We can create the following variables:

a = number of 1-cent stamps

b = number of 5-cent stamps

c = number of 10-cent stamps

d = number of 25-cent stamps

Thus:

2.65 = 0.01a + 0.05b + 0.10c + 0.25d

and

b = d

and

c = 2b

Thus, we have:

2.65 = 0.01a + 0.05b + 0.10(2b) + 0.25b

2.65 = 0.01a + 0.50b

265 = a + 50b

265 - 50b = a

We want the value of b to be as large as possible and still maintain that the value of 265 - 50b is positive and that value will be the least value of a. We see that if b = 5, then a = 15 (if b > 5, then 265 - 5b, or a, will be negative). Thus, the least value of a is 15.

Answer: C
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 23 Feb 2018, 10:49
JeffTargetTestPrep wrote:
manideepgre wrote:
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


We can create the following variables:

a = number of 1-cent stamps

b = number of 5-cent stamps

c = number of 10-cent stamps

d = number of 25-cent stamps

Thus:

2.65 = 0.01a + 0.05b + 0.10c + 0.25d

and

b = d

and

c = 2b

Thus, we have:

2.65 = 0.01a + 0.05b + 0.10(2b) + 0.25b

2.65 = 0.01a + 0.50b

265 = a + 50b

265 - 50b = a

We want the value of b to be as large as possible and still maintain that the value of 265 - 50b is positive and that value will be the least value of a. We see that if b = 5, then a = 15 (if b > 5, then 265 - 5b, or a, will be negative). Thus, the least value of a is 15.

Answer: C


Dear JeffTargetTestPrep , where can I find a detailed general explanation about the topic? If it exists clearly :)
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Re: Kim bought a total of $2.65 worth of postage stamps in four  [#permalink]

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New post 13 Apr 2019, 13:32
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Re: Kim bought a total of $2.65 worth of postage stamps in four   [#permalink] 13 Apr 2019, 13:32
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