3. Anna, Bianca, Carla, and Diana are four women of different ages (in years). Their ages are prime numbers whose sum is 240. Knowing that none of them is older than 70 years, what is the age of the youngest?
(A) 47
(B) 53
(C) 57
(D) 61
(E) 67
3. The answer is (B). Let $a<b<c<d$ be the four prime numbers corresponding to the ages. Then

$$
60=\frac{a+b+c+d}{4}<\max \{a, b, c, d\}=d<70 .
$$

Therefore, we have only two possibilities: $d=61$ or $d=67$. If $d$ were 61, then $a<b<c<60$ and thus

$$
240=a+b+c+d<3 \cdot 59+61<240
$$

which is impossible. Otherwise, $d=67$ and since $a<b<c<d$, we have $a \leq 53, b \leq 59, c \leq 61$. On the other hand,

$$
240=a+b+c+d \leq 53+59+61+67=240,
$$

so $(a, b, c, d)=(53,59,61,67)$ is the only solution ${ }^{1}$.