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Family 1 comprising mother, father and son are to be seated at a table with family 2 comprising mother, father and daughter. The layout of the table is shown in the diagram. F represents one of the fathers and M represents one of the mothers. X represents any family member. If a male family member must sit opposite a female of the other family, how many different seating plans are possible?

Solution

Correct Answer: 16

Explanation:

Assume Father 1 and Mother 2 are seated as shown. Now select one of the remaining four people for the first vacant seat. We can only choose one of the two people from the other family to sit opposite them (to ensure that the person is of the opposite sex). For the one vacant seat on the same side of the table we have a choice of one out of two, and the final person will have to sit opposite. This give us 4 x 2 = 8 arrangements. But we could also have started with Father 2 and Mother 1 which, following the same logic, will give us another 8 arrangements. Hence, the total number of seating plans is 8 + 8 = 16.

(2+3) / X = (2 + X)/3

What one value for x can be correctly entered into the answer grid?

Solution

Correct Answer: 3

Explanation:

To make both sides equal, the obvious thing to do is to substitute 3 for x

♣ ♥ ¥ ♠ ¤
How many different 3-symbol arrangements of the symbols above are possible if the symbol ¤ must be in the last position, and the symbol ♣ can be used in only one arrangement. The other symbols can be used more than once in an arrangement.

Solution

Correct Answer: 10

Explanation:

There is one 3-symbol arrangement allowed using the first symbol.
Further arrangements can be made with the last symbol in the third place, and choosing any of the remaining three symbols for the first place and any of the same three symbols for the second place. This give 3 x 3 arrangements = 9
Along with the first possibility, this makes 10

2 cars travel from the same point along parallel lanes of a highway for a distance of 10 miles. When car M, travelling at 60 miles an hour reaches the end of the distance, how much further will car N have to travel if it is travelling at 48 miles an hour?

Solution

Correct Answer: 2

Explanation:

Speed = distance/time; time = distance/speed
Car M traveling at 60mph covers 10 miles in 10/60 hours.
In the same time, car N traveling at 48mph will cover 48 x 10/60 miles= 8
Car N will therefore still have 2 miles to travel.

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Points A and B are on the top and bottom edges of a cylindrical roll of paper of height 8 and circumference 12. A and B are diagonally opposite each other. The paper is cut along line C and opened out. How far apart are A and B on the flat surface?

Solution

Correct Answer: 10

Explanation:

When opened out, the cylinder forms a rectangle of 12 x 8.
The straight line distance between A and B will be from a point on the long edge to a point on the opposite edge, such that the line forms the hypotenuse of a triangle height 8, and base half the circumference (=6). This is a 3-4-5 triangle, and the hypotenuse will be 10.

What is the largest odd-numbered factor of 4500 ?

Solution

Correct Answer: 1125

Explanation:

Factorize the number
4500 = 2 x 2250 = 2 x 2 x 1125
No need to go any further because 1125 is odd.

The sum of three numbers is 6. Each number is increased by 20 and the new numbers are multiplied by 10. What is the sum of the resulting numbers?

Solution

Correct Answer: 660

Explanation:

Let the numbers be x,y, and z
Follow the directions for each number: increase by 20 and multiply the result by 10. Then add the terms:
10(x + 20) + 10(y + 20) + 10(z + 20) = required sum
10x + 200 + 10y + 200 + 10z + 200 = 600 + 10(x + y + z)
Since x + y + z = 6; the sum = 600 + 60 = 660

If a sack of dried dog food feeds 4 dogs or 5 puppies for one week, then 5 sacks of the food will feed 15 puppies and how many dogs ?

Solution

Correct Answer: 8

Explanation:

Since five puppies require one sack per week, 15 puppies require 3 sacks. So out of the five available, the puppies will use 3, leaving 2 for the dogs. One sack feeds four dogs, so 2 sacks will feed 8.

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Triangle ABC is equilateral. What is the degree measure of angle y ? (Ignore the degree sign when gridding your answer)

Solution

Correct Answer: 80

Explanation:

Since the big triangle is equilateral, angle BAC = 60, and x = 60/3 = 20
Now, since the angles of measure X divide the angle equally, the line segments from A to BC are also equal. This makes y the measure of one of a pair of equal angles of an isosceles triangle. So y = (180 - x)/2; y = 80

A time lapse camera takes pictures once every 40 seconds. How many pictures does it take in a 24 hour period? (Assume that it takes its first picture 40 seconds after the start of the time period.)

Solution

Correct Answer: 2160

Explanation:

First calculate how many seconds there are in a 24 hour period.
24 x 60 x 60 = 86400
Divide by 40 to find how many pictures = 2160

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