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Question Stats: 71% (02:50) correct 29% (03:03) wrong based on 498 sessions

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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 ##### Most Helpful Community Reply Retired Moderator B Joined: 16 Nov 2010 Posts: 1230 Location: United States (IN) Concentration: Strategy, Technology Re: Tourist purchased a total of 30 travellers checks [#permalink] ### Show Tags 3 6 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 _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings ##### General Discussion Senior Manager  B Joined: 11 May 2011 Posts: 284 Re: Tourist purchased a total of 30 travellers checks [#permalink] ### Show Tags 2 1 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. _________________ ----------------------------------------------------------------------------------------- What you do TODAY is important because you're exchanging a day of your life for it! ----------------------------------------------------------------------------------------- Manager  Joined: 24 Jul 2011 Posts: 61 Location: India Concentration: Strategy, General Management GMAT 1: 670 Q49 V33 WE: Asset Management (Manufacturing) Re: Tourist purchased a total of 30 travellers checks [#permalink] ### Show Tags 4 1 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 Math Expert V Joined: 02 Sep 2009 Posts: 59730 Re: Tourist purchased a total of 30 travellers checks [#permalink] ### Show Tags 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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Schools: Berkeley Haas
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Re: Tourist purchased a total of 30 travellers checks  [#permalink]

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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

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 ....
Intern  Joined: 06 Sep 2013
Posts: 11
Re: Tourist purchased a total of 30 travellers checks  [#permalink]

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2
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 Senior Manager  Status: 1,750 Q's attempted and counting Affiliations: University of Florida Joined: 09 Jul 2013 Posts: 473 Location: United States (FL) Schools: UFL (A) GMAT 1: 600 Q45 V29 GMAT 2: 590 Q35 V35 GMAT 3: 570 Q42 V28 GMAT 4: 610 Q44 V30 GPA: 3.45 WE: Accounting (Accounting) Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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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
Manager  Joined: 21 Oct 2013
Posts: 177
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51

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GMATBaumgartner wrote:
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 I took more than 2min to solve this question. Is there any quick way? My approach was this. Initially, Tourist had total 30 travelers checks. Let say say, he initially had x number of$50 travelers checks. So he will have 30-x number of $100 travelers checks. The total worth of the travelers checks is$1800.

x*50 + (30-x)*100 = 1800
x*5+(30-x)*10=180
300-x*5=180
x=24

So he had 24 fifty dollar travelers checks and (30-24=6) hundred dollar travelers checks.

Suppose he spends few checks, remaining number of $50 is y (5*y+6*100)/(y+6) = 80 ----comments:- Weight Average Mean Formula. He did not spend any$100 checks so 6 is as it is.
y=4

he was left with only 4 checks of $50. So he spent 20 checks of$ 50.

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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] ### Show Tags ammuseeru wrote: GMATBaumgartner wrote: 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

I took more than 2min to solve this question. Is there any quick way?

Initially, Tourist had total 30 travelers checks.
Let say say, he initially had x number of $50 travelers checks. So he will have 30-x number of$100 travelers checks.
The total worth of the travelers checks is $1800. x*50 + (30-x)*100 = 1800 x*5+(30-x)*10=180 300-x*5=180 x=24 So he had 24 fifty dollar travelers checks and (30-24=6) hundred dollar travelers checks. Suppose he spends few checks, remaining number of$50 is y

(5*y+6*100)/(y+6) = 80 ----comments:- Weight Average Mean Formula. He did not spend any $100 checks so 6 is as it is. y=4 he was left with only 4 checks of$50. So he spent 20 checks of $50. Answer is D I Also had 2+ minutes until i figured out, that it might be the best way to start plugging in. Start in the middle with plugging in and check if the answer fits the average ov$80.
Start Plugging in 15 and you get 15*50 = 750 spent leaving 1050 USD and 15 tickets averaging $70 > eliminate this answer choice. If youre not sure which way to go, choose one direction, plug in 20 and you get 20*50 = 1000 spent leaving 800 USD and 20 tickets averaging$80.

Very easy, but it took me more than 5min to figure out which method to take ... poor me
Current Student B
Joined: 20 Oct 2014
Posts: 37
GMAT 1: 740 Q49 V42 Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] ### Show Tags 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

let x be the number of $50 checks he had to start with. 50x + 100(30-x) = 1800 Solving, we get x=24 therefore he had 6$100 checks (value $600) After he spends some$50 checks, let y be the total number of checks he has remaining.
Therefore,
80y = 6*100 + 50(y-6) ....... eqauting the value of the checks
we get y=10
Hence we had 10 total checks remaining, out of which 6 were $100 and 4$50.
Therefore, he spend 20 $50 checks. Current Student Joined: 18 Oct 2014 Posts: 795 Location: United States GMAT 1: 660 Q49 V31 GPA: 3.98 Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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It took me more than 2 mins.

x+y= 30
50x +100y= 1800

Solving the above equation we get x= 24, y=6

Suppose the person can spend 'n' $50 checks, then the equation becomes 50(24-n) + 6*100= 80 (30-n) Solving the equation we get 'n'= 20 chetan2u, please advise if there is any shortcut method for it. _________________ I welcome critical analysis of my post!! That will help me reach 700+ Math Expert V Joined: 02 Aug 2009 Posts: 8326 Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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2
It took me more than 2 mins.

x+y= 30
50x +100y= 1800

Solving the above equation we get x= 24, y=6

Suppose the person can spend 'n' $50 checks, then the equation becomes 50(24-n) + 6*100= 80 (30-n) Solving the equation we get 'n'= 20 chetan2u, please advise if there is any shortcut method for it. Hi, after you have got x= 24 and y=6, you can use weighted average method to find the rest of the answer.. for average of 80, the ratio of # of 50 and # of 100 = $$\frac{100-80}{80-50} = \frac{2}{3}$$.. therefore you should have 2 * 50$ for every 3 *100$... but we have 6 *100$, so # of 50$= $$2 *\frac{6}{3}= 4$$.. and he can spend the REST = $$24-4 = 20$$ _________________ Math Expert V Joined: 02 Aug 2009 Posts: 8326 Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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1
It took me more than 2 mins.

x+y= 30
50x +100y= 1800

Solving the above equation we get x= 24, y=6

Suppose the person can spend 'n' $50 checks, then the equation becomes 50(24-n) + 6*100= 80 (30-n) Solving the equation we get 'n'= 20 chetan2u, please advise if there is any shortcut method for it. Two more methods would be - 1)substitute - you can substitute one by one and find... 2) Logic.. # of 50 is 24 and # of 100 is 6.... so if both are 6, the average is 75$, but we are looking for higher average, 80$, so # of 50$ has to be less than 6... ONLY 24 - 20 =4 fits in..
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Posts: 1217
Tourist purchased a total of 30 travelers checks in $50 and [#permalink] ### Show Tags equation 1: 50x+100y=1800 equation 2: 50(x-z)+100y=80(30-z)➡ 50x+100y=2400-30z therefore, 1800=2400-30z z=20$50 checks he needs to spend
Current Student Joined: 18 Oct 2014
Posts: 795
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] ### Show Tags chetan2u wrote: Divyadisha wrote: It took me more than 2 mins. x+y= 30 50x +100y= 1800 Solving the above equation we get x= 24, y=6 Suppose the person can spend 'n'$50 checks, then the equation becomes

50(24-n) + 6*100= 80 (30-n)

Solving the equation we get 'n'= 20

Two more methods would be -
1)substitute -
you can substitute one by one and find...
2) Logic..
# of 50 is 24 and # of 100 is 6....
so if both are 6, the average is 75$, but we are looking for higher average, 80$, so # of 50 $has to be less than 6... ONLY 24 - 20 =4 fits in.. Thanks for suggesting all approaches _________________ I welcome critical analysis of my post!! That will help me reach 700+ Manager  Joined: 03 Jan 2015 Posts: 72 Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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Took me almost 3 min. but only because I figured out after 2 min. that the best method to solve this question is by plugging in the numbers.
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Posts: 39
Location: India
Concentration: Finance, General Management
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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] ### Show Tags GMATBaumgartner wrote: 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

Let the Number of $50 that we can spend be X. Then, 1800- 50X/30-X = 80 We can solve for X and the answer will be X= 20 Option D Manager  Joined: 18 Jan 2010 Posts: 238 Re: Tourist purchased a total of 30 travelers checks in$50 and  [#permalink]

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GMATBaumgartner wrote:
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 $80? A. 4 B. 12 C. 15 D. 20 E. 24 I present an alternate and fast method to do such problems. These are essentially "mixture" problems and can be done by using alligation approach. Refer following figure: Attachment: Moneybill-1.JPG [ 30.34 KiB | Viewed 3559 times ] Total checks are 30. Total value is 1800. This means average value is (1800/30) = 60. Once we have individual values, we can get the ratios. We find that 100$ checks and 50$checks are in the ratio of 1:4. say 100$ checks are x in no. then 50$checks are 4x in number x+4x = 30, so 5x = 30; x = 6. 100$ --> 6 in Number
50$--> 24 in Number Now let us come to second part. Refer following figure Attachment: Moneybill-2.JPG [ 28.84 KiB | Viewed 3560 times ] Revised average = 80 We find that 100$ checks and 50$checks are in the ratio of 3:2 Now we know that 100$ checks are 6 in number.

3: 2 is same is 6:4.

hence 50$checks will have to be 4 in Number. Originally 50$ checks were 24 in number. So 20 checks will be given away. Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink] 13 Jun 2016, 22:22 Go to page 1 2 Next [ 25 posts ] Display posts from previous: Sort by # Tourist purchased a total of 30 travelers checks in$50 and  