In January 2023, some boys and 20 girls joined ABC Ltd which trains students for GRE, GMAT, CAT. Some of these students were not planning to take the exams in 2023. Among them 10 were working professionals, 4 of whom were girls. There are 14 undergraduates in the batch, 8 of whom were boys. No undergraduate in the batch is a working professional.
Students preparing for CAT are also preparing for GMAT; those preparing for GMAT are also preparing for GRE.
The following facts are also known:-
(i) 85% and 70% of the boys are preparing for GRE and GMAT respectively. All girls are preparing for GRE.
(ii) No girl is preparing for CAT. All male working professionals, and 2 of the undergraduates, are preparing for CAT.
(iii) Some of the girls are preparing for GRE but not GMAT and some of the girls are preparing both.
(iv) $\frac{5}{7}$ of the boys preparing for GMAT are neither working professionals nor undergraduates. $\frac{3}{4}$ of the girls preparing for GMAT are neither working professionals nor undergraduates.
(v) The number of working professionals preparing for GMAT is one more than the number of undergraduates preparing for GMAT At least one girl working professional is preparing for GMAT.
Question 1:- How many boys are in the batch ?
Question 2 :- How many UG females are preparing for GMAT ?
My attempt so far:-
Setup:-
I assumed the total number of boys to be 100x , and then recorded the data for boys in a venn diagram, and similarly made a seperate venn diagram for girls with each region of the venn diagram further showing how many of them are working professionals, undergraduates or none of them
Have I done it correctly till now, also can't figure out how to proceed from here