A Small Party

At the party the speaker made following 6 statements

[1] There were 9 men and children.

[2] There were 2 more women than children.

[3] The number of different man – woman couples possible was 24. ( If there were 10 men and 5 women at the party, then there would have been 10 x 5 or 50 man – woman couples possible.)

Of the three categories – men, women, and children – at the party:
[4] There were 4 people in one of the categories

[5] There were 6 people in one of the categories
[6] There were 8 people in one of the categories 

 Exactly one of the 6 statements made by speaker is false

Which of [1] through [6] is false?

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House Number 


My house has a number.

(1) If my house number is a multiple of 3, then it is a number from 50 through 59. 
(2) If my house number is not a multiple of 4, then it is a number from 60 through 69. 
(3) If my house number is not a multiple of 6, then it is a number from 70 through 79.”

What is my house number?

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Alma, Bess, Cleo, and Dina visited Edna. 

[1] The time of each visit was as follows: 
Alma at 8 o’clock 
Bess at 9 o’clock 
Cleo at 10 o’clock 
Dina at 11 o’clock. 
[2] At least one woman visited Edna between Alma and Bess. 
[3] Alma did not visit Edna before both Cleo and Dina. 
[4] Cleo did not visit Edna between Bess and Dina.

Who visited Edna last?

Source: The Great Book of PUZZLES & TEASERS

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Numbers 

What is the largest integer that is a divisor of (n+1) (n+3) (n+5) (n+7) (n+9) for all even integers n?

1. 33
2. 15
3. 21
4. 11
5. 165


See our previous ‘Questions of the Day’: 


Quant Question Of The Day: 164

Quant Question Of The Day: 163

Algebra – Geometry 

The perimeter of an equilateral triangle exceeds the perimeter of a square by 1989 cm. The length of each side of the triangle exceeds the length of each side of the square by d cm. The square has perimeter greater than zero. How many positive integers are not possible values for d?

See our previous ‘Questions of the Day’: 

Quant Question Of The Day: 163
Quant Question Of The Day: 162

After-Dinner Drink

Abigail, Bridget and Claudia often eat dinner out.

1. Each orders either coffee or tea after dinner.

2. If Abigail orders coffee, then Bridget orders the drink that Claudia orders.

3. If Bridget orders coffee, then Abigail orders the drink that Claudia doesn’t order.

4. If Claudia orders tea, then Abigail orders the drink that Bridget orders.

Who always orders the same drink after dinner?


Source: The Great Book of PUZZLES & TEASERS

See our previous ‘Puzzles of the Day’:

Puzzle of the Day: 82
Puzzle of the Day: 81

 

Geometry

An ice-cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice-cream occupies 75% of the volume of frozen ice-cream. What is the ratio of the cone’s height to its radius?

1. 2 : 1
2. 4 : 1
3. 16 : 3
4. 3 : 1
5. 6 : 1

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