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A tourist purchased a total of $1,500

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by guerrero » Sun Sep 08, 2013 9:11 am
A tourist purchased a total of $1,500 worth of traveler's checks in $10 and $50 denominations, During the trip the tourist cashed 7 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) $1,430
(B) $1,310
(C) $1,290
(D) $1,270
(E) $1,150

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by GMATGuruNY » Sun Sep 08, 2013 9:34 am
guerrero wrote:A tourist purchased a total of $1,500 worth of traveler's checks in $10 and $50 denominations, During the trip the tourist cashed 7 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) $1,430
(B) $1,310
(C) $1,290
(D) $1,270
(E) $1,150

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To MINIMIZE the value of the LOST checks, we must MAXIMIZE the value of the CASHED checks.
Thus, the number of $50 checks that are cashed must be one MORE than the number of $10 checks that are cashed.
Let the number of $50 checks that are cashed = 4 and the number of $10 checks that are cashed = 3, for a total of 7 cashed checks.
Thus:
Maximum possible value of the cashed checks = 5*40 + 3*10 = 230.
Minimum possible value of the lost checks = 1500-230 = 1270.

The correct answer is D.
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Re: A tourist purchased a total of $1,500

by Brent@GMATPrepNow » Sat Mar 19, 2022 9:20 am
guerrero wrote: ↑
Sun Sep 08, 2013 9:11 am
 A tourist purchased a total of $1,500 worth of traveler's checks in $10 and $50 denominations, During the trip the tourist cashed 7 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) $1,430
(B) $1,310
(C) $1,290
(D) $1,270
(E) $1,150

OAD
The tourist cashed 7 checks. The number of $10 checks cashed was one more OR one less than the number of $50 checks cashed
There are two possible cases:
case i: The tourist cashed 4 10-dollar checks and 3 50-dollar checks
case ii: The tourist cashed 3 10-dollar checks and 4 50-dollar checks

What is the minimum possible value of the checks that were lost?
To minimize the value of the lost checks, we must MAXIMIZE the value of the checks that were cashed.

Case ii (above) maximizes the value of the checks that were cashed.
Value of 3 10-dollar checks and 4 50-dollar checks = (3)($10) + (4)($50) = $230

Value of checks that were LOST = $1,500 - $230 = $1270

Answer: D
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