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## Comment on

Precious Metals## On the question about 8

## Your counter-example assumes

Your counter-example assumes that the data values are rounded to the nearest integer. However, there is nothing in the question that confirms this assumption.

So, we must assume that the given percentages are exact values. So, for example, Country B produced 30% of the Rhenium (and not 30.4% as you suggest)

## Hello,

for the second statement how we concluded that total production of Country B&C will be 150 since when they doubled production we can consider only doubled amount not the sum of doubled+normal production.

## Sorry for the confusion. We

Sorry for the confusion. We aren't saying that the total production from countries B and C is 150; we're saying that the NEW total for ALL of the counties (after B and C doubled their production) is 150 units.

We started by seeing what would happen if the original total volume of Rhenium is 100 units.

So, we can calculate the production of each country:

Country A: 4 units

Country B: 30 units

Country C: 20 units

Country D: 15 units

Country E: 8 units

Country F: 2 units

All other countries: 21 units

TOTAL = 100 units

If countries B and C DOUBLED their production, we get:

Country A: 4 units

Country B: 60 units

Country C: 40 units

Country D: 15 units

Country E: 8 units

Country F: 2 units

All other countries: 21 units

As we can see, the NEW production total = 150 units

Of these 150 units, Country D produced 15 units (i.e., 10% of the NEW production total.

## Thank you Brent,

What I do not understand is that sum of all volume altogether is 79 before doubling the production and after doubled it is 119, Now I am confusing how it happens to be 100 and 150 when D=15 units. I mean when we consider D=15 then how we can calculate other countries more units than they are.

## Sorry, I forgot to add in the

Sorry, I forgot to add in the row representing all OTHER countries (who produce the remaining 21% of rhenium).

I've edited my response above.

## Therefore by the current

## The answer to the middle

The answer to the middle question is YES.

If countries B and C had DOUBLED their production, the NEW production total = 150 units (see my calculations above)

Country D produced 15 of those 150 (hypothetical) units, which means country D produced 10% of the total.

## Thanks a lot for the very

## for a) can you just check

so that 17% + 6% + 8% is less than 50%+ required to answer the question?

## That is perfectly sound

That is perfectly sound reasoning - nice work!

Cheers,

Brent

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