Jean, Billie and King have $750, $500 and $600 with them, respectively

Question

Jean, Billie and King have $750, $500 and $600 with them, respectively. They want to obtain change for these in terms of smaller denominations. The available denominations are $5, $10, $20, $50 and $100. What is the minimum total number of currency notes that the teller will have to vend out to these three persons to pay them their due, so that all of them have the same denomination of notes?

A. 370
B. 185
C. 92
D. 37
E. 18

A. 370
B. 185
C. 92
D. 37
E. 18

Ishat16189 · Answer

100s notes to Jean,billie and king- 7+5+6 =18.

As the max available notes are of 100s and assuming Jean has 7 100s+1 50s note, billie has 5 100s notes and king has 6 100s notes,
smaller denominations would be, 15- 50's to Jean, 10- 50s to billie, 12- 50s to king
total- 15+10+12 =37.

can someone explain?

Shreshtha55 · Answer

Can someone explain this question?

Arro44 · Answer

I don't get this question to be honest? If 18 is not the answer then I don´t really understand what the question is asking for... or the wording just tripped me up

CrackverbalGMAT · Answer

Hi Ishat, I had missed out the last part of the question. Please look at the revised post and try solving the question once again.

Ishat16189 · Answer

Thanks Arvind. 
15- 50's to Jean, 10- 50s to billie, 12- 50s to king
total- 15+10+12 =37.

CrackverbalGMAT · Answer

This is a question on finding the Highest Common Factor (HCF) of a given set of numbers.

Since we have to minimize the number of notes that the teller has to vend out, we have to make sure that we divide each of the sums by the largest possible number that can divide all of them. Clearly, this has to be their HCF. Now, to calculate their HCF.

750 = 2 * 3 * $5^3$

500 = $2^2$ * $5^3$

600 = $2^3$ * 3 * $5^2$

HCF = 2 * $5^2$ = 50.

Therefore, $750 can be dealt out with 15 notes of $50. $500 as 10 notes of $50 and $600 as 12 notes of $50. The total number of notes dealt is (15 + 12 + 10) i.e. 37.
So, the correct answer option is D.

Clearly, the last part of the question statement (which was missed out when I first posted the question) is a clear clue that the sums 750, 500 and 600 have to be divided by a common value. The first part of the question statement tells us that we need to divide it by the highest such common value because we are trying to minimize the number of notes. This should tell you that the HCF of these numbers has to be the intermediate answer that will eventually help you calculate the final answer.

Had 50 been one of the options, things could have been more interesting

. Hindsight is always beneficial

Hope this helps!

. Hindsight is always beneficial

Hope this helps!

Ishaan2510 · Answer

This question can be solved by observation and then a bit of calculation. 
The key is A. 'Minimum number of total currency notes' & B. 'Same denominations of notes'

Let's start with B.

B. Since all should have same denomination, we narrow down it to one among them and proceed with calculation.

A. For minimum number of notes, higher the denomination, lesser the the number of notes required.

Hence, we start with 100. But since we we have $750 for Jean and since it is not divisble by 100 we cannot give 100s denomination.

So we move to next highest denomination, i.e 50.

This we can use for all 3 as their inital amount is divisible by 50.

So now,

Jean = 750/50 = 15
Billie = 500/50 = 10
King = 600/50 = 12

Total of all three is 37.

Answer: D

Posted from my mobile device

Kinshook · Answer

Given:  Jean, Billie and King have $750, $500 and $600 with them, respectively. They want to obtain change for these in terms of smaller denominations. The available denominations are $5, $10, $20, $50 and $100.

Asked:   What is the minimum total number of currency notes that the teller will have to vend out to these three persons to pay them their due, so that all of them have the same denomination of notes?

For the teller to vend out minimum total number of currency notes, the denomination of notes should be HCF(750,500,600) = $50

$750 = 15 * $50
$500 = 10 * $50
$600 = 12 * $50

The minimum total number of currency notes that the teller will have to vend out to these three persons to pay them their due = 15 + 10 + 12 = 37

IMO D

Jean, Billie and King have $750, $500 and $600 with them, respectively

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Jean, Billie and King have $750, $500 and $600 with them, respectively

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