A tourist purchased a total of $1,500 worth of traveler’s

Question

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

(A) $1,430 
(B) $1,310 
(C) $1,290 
(D) $1,270 
(E) $1,150

carlosamq · Accepted Answer

Since you are looking for the minimum possible value of checks lost, you have to maximize the value of the 7 cashed checks. To maximize: out of the 7 cashed checks, 3 have to be 10$ and 4 need to be $50.
3($10) + 4(50) = 230

$1500 - 230 = 1270

fluke · Answer

The right forum for problem solving question is:  https://gmatclub.com/forum/gmat-problem-solving-ps-140/ . Please post your PS questions there.

Sol:

Let the number of $10 checks cashed be "T"
Let the number of $50 checks cashed be "F"

7 checks cashed;
T+F=7

Now; T can be F+1 OR T can be F-1

Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190

Let's check the other condition as well;

T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230

The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.

Value cashed = $230
Value lost = 1500-230 = $1270

Ans: "D"

vyassaptarashi · Answer

since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3

using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost

Therfore 1500 - 230 = 1270 hence answer is D

jamifahad · Answer

Thank you guys. Guess i got confused with wordings.

Banterninja · Answer

Its more of a trick question than anything else. To tackle such stuff, It will he helpful to read the question probably again and then make a note on the work sheet on what exactly is needed. In this,m "Minimum loss" or "Find least loss outcome?" etc , just a remainder for you to check before submitting an answer.

qweert · Answer

For such kind of questions, i always write stuff down.

deepthit · Answer

10 x + 15 y = 1500 
50 and 10 denominations can be either 4 and 3 or 3 and 4 
to minimise the lost money, we have to maximize the money used

so 4 - 50$ and 3 10$ are used which equates to 230

subtracting 230 from 1500 = 1270 answer

09173140521 · Answer

I do not understand this question why ? I am non native . could anyone explain what is meaning ? 
why we say= "To MINIMIZE the value of the LOST checks, we must MAXIMIZE the value of the CASHED checks. "
I go for B but is not true !

BrentGMATPrepNow · Answer

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

arbazfatmi1994 · Answer

Don't get scared after reading the question... It's very basic

To get the minimum value of checks lost you just have to maximize the value of the 7 cashed checks. You have 7 checks that are cashed and... The number of $10 checks cashed was one more OR one less than the number of $50 checks cashed Hence... 3($10) + 4($50) = $230 $1500 - $230 = $1270

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A tourist purchased a total of $1,500 worth of traveler’s

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