How many students were accepted?
Total number of students that were auditioned = 90
Statement 1: 2/3 of the boys and 1/3 of the girls who auditioned were accepted.
Total no. of students = Total no. of boys + Total no. of girls
Total no. of accepted students = Total no. of boys accepted + Total no. of girls accepted
Let boys = b, and girls = g
accepted boys = 2b/3
accepted girls = 1g/3
The exact values of b and g are unknown, hence the target question cannot be answered. Therefore, statement 1 is NOT SUFFICIENT.
Statement 2: 26 of the boys who auditioned were accepted.
Here, the number of accepted girls is unknown, so, we cannot answer the target question based on this information provided. Therefore, statement 2 is NOT SUFFICIENT.
Combining both statements together:
S1: 2/3 of the boys and 1/3 of the girls who auditioned were accepted
S2: 26 of the boys who auditioned were accepted
Therefore, the total number of boys who audited is;
$$\frac{2b}{3}=26$$
$$b=26\cdot\frac{3}{2}=39$$
Total auditioned students = total boys + total girls
90 = 39 + g
g = 90 - 39
g = 51
Therefore, the total number girls who audited = 51
The number of accepted girl = 1/3 of the girls who auditioned.
$$=\frac{1}{3}\cdot51=17$$
Overall, the total no. of accepted students = Total no. of boys accepted + Total no. of girls accepted
= 26 + 17 = 43
Hence, both statements combined together are SUFFICIENT.
Answer = option C
