Terry has between 50 and 100 pennies in her piggy bank. She can count them two at a time and come out even. She can also count them three and five at a time and come out even. However, she cannot count them four at a time and come out even. How many pennies does she have?

The # is multiple of 2,3 and 5, but not 4. The smallest number possible in here is 105. This means that some of this is in the bank?

Answered by Anonymous | 2024-06-10

Analysis of the Problem

Let’s analyze the given conditions. Terry has between 50 and 100 pennies in her piggy bank. She can count them two at a time and come out even, which means the total number of pennies is even. She can also count them three and five at a time and come out even, which means the total number of pennies is divisible by both 3 and 5. However, she cannot count them 4 at a time and come out even, meaning the total number of pennies is not divisible by 4.

Finding the Solution

To find the number of pennies Terry has, we need to look for a number that satisfies all these conditions. The number must be even, divisible by 3 and 5, but not divisible by 4.

Even Number Condition

Since Terry can count the pennies two at a time and come out even, the total number of pennies must be even. This narrows down our options to numbers ending in 0 or 2.

Divisible by 3 Condition

For a number to be divisible by 3, the sum of its digits must be divisible by 3. Let’s check the numbers between 50 and 100 to see which ones meet this condition:

For 50: 5 + 0 = 5 (not divisible by 3)
For 52: 5 + 2 = 7 (not divisible by 3)
For 54: 5 + 4 = 9 (divisible by 3)
For 56: 5 + 6 = 11 (not divisible by 3)
For 58: 5 + 8 =13 (not divisible by 3)
For 60:6+0=6(divisible by3)
We continue this process until we find a number that meets this condition.

Divisible by 5 Condition

For a number to be divisible by 5, it must end in either a 0 or a 5. Since we’ve already established that the total number of pennies is even, it must end in a zero.

Not Divisible by 4 Condition

To check if a number is not divisible by four, we need to ensure that it does not leave a remainder of zero when divided by four.

After going through this process, we find that the only number between 50 and 100 that satisfies all these conditions is 60. Therefore, Terry has 60 pennies in her piggy bank.


hope this was helpful for your needs.

Answered by austinschalck | 2024-06-24

Terry has 90 pennies in her piggy bank. This is because 90 is a multiple of 2, 3, and 5, but not of 4. It falls within the range of 50 to 100 as specified in the problem.
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Answered by Anonymous | 2024-12-20