Question

A survey was conducted at a coaching institution and it was found that there were 34 students who appeared in MAT. There were 37 students who appeared in CAT of which 17 students appeared in MAT. 30 students appeared in XAT of which 13 students appeared in MAT. Among the XAT applications (i.e., appeared students) 14 appeared in CAT and these 6 appeared in MAT. How many students appeared in CAT but not in MAT or XAT?

• A. 9
• B. 10
• C. 12
• D. none of these

Answer 1

The correct option is C 12

Given, $I{I}_{CM}+II{I}_{CMX}$ = 17 - - - (i)
$I{I}_{MX}+II{I}_{CMX}$ = 13 - - - (ii)
$I{I}_{CX}+II{I}_{CMX}$ = 14 .- - - (iii)
$II{I}_{CMX}$ = 6 - - - (iv)
$\therefore I{I}_{CM}$ = 17 - 6 = 11
$I{I}_{MX}$ = 13 - 6 = 7
$I{I}_{CX}$ = 14 - 6 = 8
Now, $I_C+I{I}_{CX}+I{I}_{CM}+II{I}_{CMX}=37$
$I_C+8+11+6=37\Rightarrow$
Number of students appeared in CAT but not in MAT or XAT = $I_C=12$

Alternatively


Hence there are 12 students who appeared in CAT but not in MAT or XAT