Open-ended - With worked solutions · SET 10

One pair of socks costs 3.50 dollars. A pack of 6 pairs costs 19.50 dollars. By what percentage are the socks cheaper per pair when you buy a pack of 6?

What number should replace the question mark? 1.5, 4.5, 13.5, 16.5, ?

The first two figures follow the same rule. What numbers should replace the question marks in the third figure?

Which number should replace the question mark? 16, 21, 16 7/8, 20 1/4, 17 3/4, 19 1/2, ?

Each of the nine squares in the grid marked A1 to C3 should incorporate all the lines and symbols shown in the squares of the same letter and number immediately above and to the left. For example, B2 should incorporate all the lines and symbols that are in 2 and B. One of the squares is incorrect. Which one is it?

EHL is to VSO as JKS is to ? Write the three missing letters and explain the rule (use A=1, …, Z=26).

Tanya can swim faster than Jack but slower than Sally. Harry usually swims faster than Jack, sometimes swims faster than Tanya, but never swims faster than Sally. Who is the slowest swimmer? Explain.

Josie has £600 to spend. She spends 3/5 of the £600 on clothes, 0.45 of the remainder at a beauty salon, and writes a cheque for £150 for a new watch. What is her financial situation at the end of the day? Show your working.

Write the numbers 1, 2, 3, 4 and 5 into the five circles (each once) so that, for each number, the sum of the numbers in the circles directly connected to it equals the total given in the list: 1=8, 2=12, 3=7, 4=5, 5=3. The small boxed diagram is an example of how the list works.

What numbers should replace the three question marks in the last column (top, middle, bottom)?

Each of the nine squares A1 to C3 should contain all the lines and symbols shown in the square with the same letter (above) and the same number (to the left). For example, B2 should contain everything that is in 2 and B. One of the squares is incorrect. Which one is it, and what is wrong with it?

The combined ages are: Alan + Bertie = 43, Alan + Charlie = 55, Bertie + Charlie = 66. How old are Alan, Bertie and Charlie?

Simplify: 46/27 ÷ 92/9. Give the answer as a fraction in lowest terms.

A crate holds 100 eggs, 6 of which are bad. If you draw out 2 eggs at random, what is the probability that both are bad? Give the answer as a fraction in lowest terms.

In the top row, HF – 86 – SU follow a rule linking letters and numbers. What should replace the two question marks in the bottom row ? – ? – TX? (A=1, …, Z=26; the reverse alphabet Z=1, …, A=26 may be needed.) Give both the letters and the number.

Each of the 11 figures A–K is made of a line of 4 dots and a perpendicular line of 4 dots sharing one dot. Which figure is the odd one out? Explain the rule.

Each square tells you how to move (1N 2W = 1 North, 2 West). Find the starting square from which you visit every square exactly once and finish on the treasure T. Describe the start square and the route.

Follow the zigzag 1, 10, 2.25, 7.25, 3.5, 4.5, 4.75, ?. What number comes next? Explain the rule.

Each of the nine squares A1 to C3 should contain all the lines and symbols shown in the square of the same letter directly above and the square of the same number to the left. For example, B2 should contain everything in 2 and in B. One of the nine squares is incorrect. Which one is it, and what is wrong?

Which two words mean the opposite? CORPULENT, DAZED, MERITORIOUS, VIRULENT, STANDARD, LEAN, UNCONCIOUS, END