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fameatop
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Micheal purchased a total of $1,200 worth of traveler’s chec 26 Jul 2013, 23:31
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35% (medium)

Question Stats:

74% (02:25) correct 26% (02:33) wrong based on 315 sessions

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Micheal purchased a total of $1,200 worth of traveler’s checks in $10 and $50 denominations. During the trip he cashed 15 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?

(A) $830
(B) $800
(C) $770
(D) $730
(E) $700
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Marcab
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Micheal purchased a total of $1,200 worth of traveler’s chec 26 Jul 2013, 23:52
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fameatop
Micheal purchased a total of $1,200 worth of traveler’s checks in $10 and $50 denominations. During the trip he cashed 15 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $830
(B) $800
(C) $770
(D) $730
(E) $700
Show more

Nice question!
It is given that the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, so why don't we take the number of $10 checks cashed be \(x\).
Then as per the above statement number of $50 checks can either be \(x-1\) or \(x+1\).
Let us solve for both.
\(x\)+\(x-1\)=\(15\) 1)

\(x\)+\(x+1\)=\(15\) 2)

From 1) we get #$10 checks cashed as 8 and #$50 checks cashed as 7
From 2) we get #$10 checks cashed as 7 and #$50 checks cashed as 8.

We must go with the second solution as we are supposed to maximize the value of the checks that were lost.
Hence forth, \(50*8\)+\(10*7\)=\(470\).

So 1200-470=730.

+1D
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Micheal purchased a total of $1,200 worth of traveler’s chec 27 Jul 2013, 02:59
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fameatop
Micheal purchased a total of $1,200 worth of traveler’s checks in $10 and $50 denominations. During the trip he cashed 15 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $830
(B) $800
(C) $770
(D) $730
(E) $700
Show more

Similar question to practice: a-tourist-purchased-a-total-of-1-500-worth-of-traveler-s-111369.html
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Micheal purchased a total of $1,200 worth of traveler’s chec 28 Jul 2013, 20:52
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Hi Macrab,

Can you please help explain why we need to maximize when the question says minimize. I am missing something here

1. 50*7 + 10*8 = 430 loss 770

2. 50*8 + 10*7 = 470 loss 730

How should i look at this? or since the loss should be minimum we need to pick the higher denominations values....

Thanks
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Micheal purchased a total of $1,200 worth of traveler’s chec 28 Jul 2013, 23:08
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GMAT40
Hi Macrab,

Can you please help explain why we need to maximize when the question says minimize. I am missing something here

1. 50*7 + 10*8 = 430 loss 770

2. 50*8 + 10*7 = 470 loss 730

How should i look at this? or since the loss should be minimum we need to pick the higher denominations values....

Thanks
Show more

Hi GMAT40, I'll jump in here since this is a Veritas-type question and there's a good takeaway here: Minimizing vs maximizing.

When you're minimizing, you're trying to make the value as small as possible (obvious, right?): So if I could lose 730$ or lose 770$, which one is smaller? Obviously 730$, but that's dependent on the fact that you solve for both possible situations and pick the smaller of the two. Obviously that's not an optimized solution.

The most logical way to think about it is I have some amount of money. If I want to minimize the amount I lost, then I need to maximize the amount I spend. It's a zero-sum game, so if I can spend more, I will lose less. If I'm minimizing loss, I must then maximize gain. Classic GMAT trap here is that the question is asking you to minimize what's lost, but what you have to do is calculate what's spent.

A fair number of people will read a question like this too quickly and maximize the amount left over. This is why 770$ is there as a trap answer, just waiting for someone to pick it because they are going too fast. Beware the common trap of asking for X but needing to calculate Y. Be sure to reread the question to make sure you're answering the problem asked of you.

As I say: I'd rather spend two minutes and fifteen seconds getting a question right than spend 2 minutes and get it wrong.

Hope this helps!
-Ron
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Micheal purchased a total of $1,200 worth of traveler’s chec 04 Jul 2025, 09:31
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