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In a Mock test series 35% candidates failed in Math  and 42% failed in Digital while 15% failed in both the subjects. If 2500 candidates appeared in the test, how many passed in either subject but not in both?

No. of people who have passed in either subject but not both = No. of people who have failed in exactly one subject

= (35% + 42% - 15%) (Those who have failed at least one subject)
(- 15%) (Those who have failed both subject)

= 47%

= 0.47 * 2500

= 1175

sir... it just as we subtracting intersection from both side of circle and adding individual probablity ??
yes..

https://gateoverflow.in/1846/gate2006-68 sir  plz see this question als... so much confused

Let |M| = students that failed in Maths, and |D| = students that failed in Digital.

$|M| = 875$

$|D| = 1050$

$|M \cap D| = 375$

To find: $| \overline{M}\cup \overline{D}| - | \overline{M} \cap \overline{D}|$

which is equivalent to finding: $| \overline{M \cap D}| - | \overline{M \cup D}|$

which is equivalent to finding: $2500- |M \cap D| - (2500-|M \cup D|)$

We know, $|M \cap D|$ = 375.

Now, $|M \cup D|$ = $875+1050-375=1550$

So, finally we have: $2500- |M \cap D| - (2500-|M \cup D|)$

=> $2500- 375 - (2500-1550)=1175$