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Tourist purchased a total of 30 travelers checks in $50 and

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Tourist purchased a total of 30 travelers checks in $50 and [#permalink] New post 26 Aug 2012, 17:57
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A
B
C
D
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Question Stats:

74% (03:16) correct 26% (02:01) wrong based on 102 sessions
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $80?

A. 4
B. 12
C. 15
D. 20
E. 24
[Reveal] Spoiler: OA
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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 26 Aug 2012, 18:22
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vinay911 wrote:
Tourist purchased a total of 30 travellers checks in $50 and $100 denominations.The total worth of the travelers checks is $1800.How many checks of $50 denominations can he spend so that average amount(arithemetic mean) of the remaining travelers checks is $80?

a)4
b)12
c)15
d)20
e)24

This one took me 2+ min.

x+y = 30
50x+100y=1800
Solving both the equation will give you - x = 24 and y = 6.
Now one can start plug-n-play and can figure out that D fits the answer.
x=4, y=6 makes the average amount of the remaining travelers checks to $80.

D wins.

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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 26 Aug 2012, 18:37
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X + y = 30
50x + 100y = 1800
=> X +2y = 36
=> Y = 6 x = 24
Let n be the number
So ((24-n) * 50 + 6*100)/(30-n) = 80

=> 120 – 5n + 60 = 240 -8n
=> 3n = 60
=> n = 20

Answer - D

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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 27 Aug 2012, 07:12
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This can be solved easily using algorithm,
x + y = 30 ---(i)
50x +100y=1800
=> x+2y=36 ---- (ii)

Therefore from equation (i) and (ii) we get, y=6
Let, we can use the algorithm to find how 50 and 100 make the average to 80

................50......................100
............................80
...........(100-80)...............(80-50)
..............=20......................=30
>> ............2 .........................3 (this is the ratio by which 50 & 100 are to be combined to make average of 80)
>> .............4.........................6 (just multiplying both sides with 2, it does not change the ratio)

This means if we have six 100 and four 50 we will get average 80 considering all notes
So, extra 50 notes are 24-4= 20

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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 27 Sep 2013, 04:21
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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 27 Sep 2013, 04:28
Expert's post
GMATBaumgartner wrote:
Tourist purchased a total of 30 travellers checks in $50 and $100 denominations.The total worth of the travelers checks is $1800.How many checks of $50 denominations can he spend so that average amount(arithemetic mean) of the remaining travelers checks is $80?

a)4
b)12
c)15
d)20
e)24


Similar question to practice: a-tourist-purchased-a-total-of-1-500-worth-of-traveler-s-111369.html

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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 27 Sep 2013, 06:37
subhashghosh wrote:
X + y = 30
50x + 100y = 1800
=> X +2y = 36
=> Y = 6 x = 24
Let n be the number
So ((24-n) * 50 + 6*100)/(30-n) = 80

=> 120 – 5n + 60 = 240 -8n
=> 3n = 60
=> n = 20

Answer - D



I am confused as to why cant we do the opposite for this

(24*50 + (6-n)*100)/(30-n)) = 80 ?
The answer doesnt hold then ....
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Re: Tourist purchased a total of 30 travellers checks [#permalink] New post 27 Sep 2013, 06:59
GMATBaumgartner wrote:
Tourist purchased a total of 30 travellers checks in $50 and $100 denominations.The total worth of the travelers checks is $1800.How many checks of $50 denominations can he spend so that average amount(arithemetic mean) of the remaining travelers checks is $80?

a)4
b)12
c)15
d)20
e)24


actually there is no need to calculate the numbers of two checks. Here is how I got the correct answer:

say the number of checks need to be spent to get the final average amount of $80 is x
Average amount= amount of $100 checks / numbers of remaining checks

then 1800-50*x / 30-x =80
x= 20
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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] New post 01 Dec 2013, 22:08
you could set-up a quick table and brute force the answer.

A 4 * 50 200 1800 -200 1600 26 61.54
B 12 * 50 600 1800 -600 1200 18 66.67
C 15 * 50 750 1800 -750 1050 15 70.00
D 20 * 50 1000 1800 -1000 800 10 80.00
E 24 * 50 1200 1800 -1200 600 6 100.00

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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] New post 10 Mar 2014, 07:18
average is 80 $, only pssible total amount for this is 800 $. Hence he can spend 1000 $ which equals to 20 50$ checks.

Answer D.
Re: Tourist purchased a total of 30 travelers checks in $50 and   [#permalink] 10 Mar 2014, 07:18
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