Mona and Donald fly to Rome for the weekend. They take cash

AAPL wrote:Economist GMAT

Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 40 notes (of either $10 or €10) then what is the total number of notes (of either $10 or €10) they take?

A. 70
B. 80
C. 100
D. 120
E. 150

We can PLUG IN THE ANSWERS, which represent the total number of notes.

The number of €10 notes they take is double the number of $10 notes they take.
Thus, the ratio of €10 notes to $10 notes = 2:1.
Since the sum of the parts of this ratio = 2+1 = 3, the total number of notes must be a MULTIPLE OF 3.
Eliminate A, B and C.

D: 120 notes
Here, the total number of notes (120) is 40 times as great as the sum of the parts of the ratio above (2+1=3), implying that the two values in the ratio must each be multiplied by 40:
€10 notes = 2*40 = €80.
$10 notes = 1*40 = $40.

Mona carries as many dollars as Donald carries.
Since they have a total of $40, Mona = $20 and Donald = $20.

Donald carries a total of 40 notes.
Since Donald has $20, he must have €20, for a total of 40 notes.
Since they have a total of €80, and Donald has €20, Mona must have €60.

Only one condition remains:
Mona carries three times the amount of euros Donald carries.
Success!
According to the green portions above, Mona's amount in Euros (€60) is 3 times Donald's amount in Euros (€20).

The correct answer is D.

AAPL wrote:Economist GMAT

Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 40 notes (of either $10 or €10) then what is the total number of notes (of either $10 or €10) they take?

A. 70
B. 80
C. 100
D. 120
E. 150

We can let the number of $10 notes Mona and Donald each carries = d since they each carry the same number of dollars.

We can let the number of €10 notes Donald carries = e, and thus the number of €10 notes Mona carries is 3e, since she carries three times the amount of euros Donald carries.

We need to determine the total number of notes they both take, i.e., the value of (d + e) + (d + 3e) = 2d + 4e.

From this we can see that 2d is the total number of $10 notes they both take, and 4e is the total number of €10 notes they both take.

We are given that the number of €10 notes they take is double the number of $10 notes. That is:

4e = 2(2d)

4e = 4d

e = d

We are also given that Donald carries a total of 40 notes (of either $10 or €10), which means that d + e = 40. However, since e = d, e and d must be each = 20. Therefore, the total number of notes they both take (or carry) is:

2d + 4e = 2(20) + 4(20) = 40 + 80 = 120

Answer: D