Question

A clerk in a sportswear department was asked to arrange T-shirts in a display in stacks of equal size. When she separated the T-shirts into stacks of 4, there was 1 left over. When she tried stacks of 5, there was still 1 left over. The same was true for stacks of 6. However, she was able to arrange the shirts evenly in stacks of 7. How many T-shirts were in the display that she was arranging?

Answer 1

Answer: 301

(43 stacks of 7 t-shirts)

This is kind of a long process, so stay with me!

Since the shirts could be stacked evenly in stacks of 7, it must be a multiple of 7. We know the total number of shirts will be one of the following:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, etc

Now, we need to narrow it down. Stacks of 5 + 1 is equal to 6, so the total number of shirts will need to end in a 1 or a 6.

This leaves us with the following:

21, 56, 91, 126, 161, 196, 266, 301, 336, etc

This list is much more manageable. Now, with the remaining options, we will narrow it down even more. First, we will divide by 4 and see which ones give us a reminder of one.

[✓] 21 / 4 = 5 and a remainder of 1

[✗] 56 / 4 = 14 with no remainder

[✗] 91 / 4 = 22 with a remainder of 3

[✗] 126 / 4 = 31 with a remainder of 2

[✓] 161 / 4 = 40 with a remainder of 1

[✗] 196 / 4 = 49 with no remainder

[✗] 266 / 4 = 66 with a remainder of 2

[✓] 301 / 4 = 75 with a remainder of 1

[✗] 336 / 4 = 84 with no remainder

Lastly, we will do the same for the number 6.

[✗] 21 / 6 = 3 with a remainder of 3

[✗] 161 / 6 = 26 with a remainder of 5

[✓] 301 / 6 = 50 with a remainder of 1

The only number that works for all scenarios is 301, leaving us with our answer!