Question

If% means 'is less than', $ means' is greater than and# means 'is equal to' and given that a%b, c#d and c$b then which is true?

• A. a > b
• B. a < c
• C. c > d > a
• D. d < b

Answer 1

The Correct Option is B

Let's decipher the given symbols in the question:

• % means "is less than"
• $ means "is greater than"
• # means "is equal to"

We are given the following relationships based on these symbols: 

1. a % b, which translates to a is less than b.
2. c # d, which translates to c is equal to d.
3. c $ b, which translates to c is greater than b.

We need to determine which of the given options is true.

Let's break down each option:

1. a > b: This contradicts a % b, which means a is less than b. Thus, this statement is false.
2. a < c: From a % b, we have a < b and from c $ b, we have c > b. This implies a < b < c, so a < c is true.
3. c > d > a: Since c # d means c = d, the statement c > d is false (as they are equal). Hence, this statement cannot be true.
4. d < b: Since c # d means c = d and c > b, this implies d = c > b or d > b. Hence, d < b is false.

Only option (a < c) is valid based on the given symbols and relationships. Hence, the correct answer is:
a < c.