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

Question

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

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

BrentGMATPrepNow · Answer

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

Kinshook · Answer

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

ScottTargetTestPrep · Answer

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

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