CRE 1 - 2 Sets | LR - Venn Diagram

Answer: 20

Explanation :

Since 15 failed in both subjects there are 150 – 15 = 135 students who passed in at least one subject.

n(M) = number of students who passed in Maths = 90
n(E) = number of students who passed in English = 65
n(M∩E) = number of students who passed in both Maths as well as English.
n(M∪E) = number of students who passed in at least one of Maths or English = 135

∴ n(M ∪ E) = n(M) + n(E) - n(M∩E)
⇒ 135 = 90 + 65 - n(M∩E)
⇒ n(M∩E) = 90 + 65 – 135 = 20

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∴ Number of students who passed in both the subjects = 20

Hence, 20.

Answer: 45

Explanation :

Consider the solution to first question of this set.

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We need to figure out the number of students who passed only in English.

= Number of students who passe in English – Number of students who passed in both.
= 65 – 20 = 45

Hence, 45.

Answer: 115

Explanation :

Consider the solution to first question of this set.

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Number of students who failed in only one subject = Number of students who passed in only one subject

= Number of students who passed only in Maths + Number of students who passed only in English
= (65 - 20) + (90 - 20) = 115

Alternately,
Number of students who failed in only one subject = Number of students who passed in at least one subject – Number of students who passed in both the subjects.

= 135 – 20 = 115

Hence, 115.

Answer: 10

Explanation :

Consider the solution to first question of this set.

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Number of students who failed in Maths = 150 – 90 = 60

Number of students who failed only in English = Number of students who passed only in Maths = 90 – 20 = 70

Difference = 70 – 60 = 10.

Hence, 10.

Answer: Option A

Explanation :

From the given data, we get the following diagram.

Let the total number of guests be x.

⇒ x = 144 + (25% of x) + (25% of x) + (5% of x)

⇒ x - $\frac{x}{4}$ - $\frac{x}{4}$ - $\frac{x}{20}$ = 144

⇒ $\frac{9x}{20}$ = 144

⇒ x = 320.

The total guets at the party = 320.

Hence, option (a).

Answer: Option B

Explanation :

Consider the solution to the first question of this set.

The number of guests who drink only tea or only coffee

= 144 + (25% of 320)

= 144 + 80 = 224.

Hence, option (b).

Answer: Option C

Explanation :

Consider the solution to the first question of this set.

The number of guests who drink neither tea nor coffee

= none = 5% of 320

= 5/100 × 320 = 16.

Hence, option (c).

Answer: Option D

Explanation :

Consider the solution to the first question of this set.

The number of guests who drink only coffee = 25% of 320 = 80.

Hence, option (d).

Answer: Option D

Explanation :

Consider the solution to the first question of this set.

The number of guests who drink at least one of the two

= 144 + (25% of 320) + (25% of 320)

= 144 + 80 + 80 = 304.

Alternately,

The number of guests who drink at least one of the two = Total number of guest – those guests who drink none of tea or coffee.

= 320 – (5% of 320) = 320 – 16 = 304.

Hence, option (d).