GATE Overflow | General Aptitude | Test 1 | Question: 2

Question

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?

Answer 1

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

Comments

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

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yes..

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

Answer 2

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: $2500- |M \cap D| - (2500-|M \cup D|)$

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