Andrew was asked by his friend to count all the numbers from 1 to 90 that are divisible by two and three but not by five. Andrew made a mistake in the process and counted the result as 10.What is the difference between the actual result and the result that Andrew got ?

Options

A. 2
B. 4
C. 6
D. 10

Answer

To solve the problem step by step, we need to find the numbers from 1 to 90 that are divisible by both 2 and 3, but not by 5.

### Step 1: Identify the numbers divisible by both 2 and 3
Since a number divisible by both 2 and 3 is also divisible by 6, we will find the multiples of 6 between 1 and 90.

**Calculation:**
The multiples of 6 from 1 to 90 are:
- 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90.

### Step 2: Count the multiples of 6
Now, we will count how many multiples of 6 are there from 1 to 90.

**Calculation:**
The multiples of 6 are:
- 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90.

There are a total of 15 multiples of 6.

### Step 3: Exclude the numbers that are divisible by 5
Next, we need to exclude the numbers from the list that are also divisible by 5.

**Calculation:**
The multiples of 6 that are also divisible by 5 are:
- 30 (6 x 5)
- 60 (6 x 10)
- 90 (6 x 15)

So, we will remove 30, 60, and 90 from our list of multiples of 6.

### Step 4: Count the remaining numbers
After removing the numbers divisible by 5, we will count the remaining numbers.

**Remaining multiples of 6:**
- 6, 12, 18, 24, 36, 42, 48, 54, 66, 72, 78, 84.

There are 12 numbers left after excluding those divisible by 5.

### Step 5: Calculate the difference between the actual result and Andrew's result
Andrew counted the result as 10, but the actual result is 12.

**Calculation:**
Difference = Actual Result - Andrew's Result = 12 - 10 = 2.

### Final Answer
The difference between the actual result and the result that Andrew got is **2**.

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