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A photographer has visited exactly 42 countries, all of which have bee

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A photographer has visited exactly 42 countries, all of which have bee  [#permalink]

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New post 19 Mar 2020, 07:18
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A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia. If the photographer has been to 6 more countries in Europe than in Asia, and twice as many in Africa as in Europe, how many countries in Asia has the photographer visited?

A. 4
B. 6
C. 12
D. 18
E. 24

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A photographer has visited exactly 42 countries, all of which have bee  [#permalink]

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New post 19 Mar 2020, 07:41
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Bunuel wrote:
A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia. If the photographer has been to 6 more countries in Europe than in Asia, and twice as many in Africa as in Europe, how many countries in Asia has the photographer visited?

A. 4
B. 6
C. 12
D. 18
E. 24


Let's solve the question using only one variable

The photographer has been to 6 more countries in Europe than in Asia
Let A = the number of countries visited in Asia
So, A + 6 = the number of countries visited in Europe

The photographer has been to and twice as many in Africa as in Europe
We already know that A + 6 = the number of countries visited in Europe
So, 2(A + 6) = the number of countries visited in Africa

The photographer has visited exactly 42 countries
We can write: A + (A + 6) + 2(A + 6) = 42
Expand and simplify the left side: 4A + 18 = 42
Subtract 18 from both sides: 4A = 24
Solve: A = 6

So, the photographer visited 6 countries in Asia

Answer: B

Cheers,
Brent
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A photographer has visited exactly 42 countries, all of which have bee  [#permalink]

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New post 19 Mar 2020, 08:30
Bunuel wrote:
A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia. If the photographer has been to 6 more countries in Europe than in Asia, and twice as many in Africa as in Europe, how many countries in Asia has the photographer visited?

A. 4
B. 6
C. 12
D. 18
E. 24


Given: A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia.

Asked: If the photographer has been to 6 more countries in Europe than in Asia, and twice as many in Africa as in Europe, how many countries in Asia has the photographer visited?

Let the countries visited in Africa, Europe and Asia be F, E & A respectively

A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia.
F + E + A = 42. (1)

The photographer has been to 6 more countries in Europe than in Asia
E = A + 6. (2)

The photographer has been to twice as many countries in Africa as in Europe
F = 2E. (3)

Putting values of F & E in terms of A in (1)
2(A+6) + (A+6) + A = 42
4A = 42 - 18 = 24
A = 6

IMO B
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Re: A photographer has visited exactly 42 countries, all of which have bee  [#permalink]

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New post 21 Mar 2020, 14:57
Bunuel wrote:
A photographer has visited exactly 42 countries, all of which have been in Africa, Europe, or Asia. If the photographer has been to 6 more countries in Europe than in Asia, and twice as many in Africa as in Europe, how many countries in Asia has the photographer visited?

A. 4
B. 6
C. 12
D. 18
E. 24


We can let F, E and A = the number of countries he visited in Africa, Europe, and Asia, respectively. We can create the 3 equations:

F + E + A = 42

and

E = A + 6

E - 6 = A

and

F = 2E

Substituting, we have:

2E + E + E - 6 = 42

4E = 48

E = 12

Since A = E - 6, then A = 6.

Answer: B
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Re: A photographer has visited exactly 42 countries, all of which have bee   [#permalink] 21 Mar 2020, 14:57

A photographer has visited exactly 42 countries, all of which have bee

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