Posted by **Surya** on Thursday, February 23, 2012 at 10:25am.

Dear Genius,

Good day!

The number of apples in a basket is between 60 and 120. If i put these apples into bags of 5, there will be a remainder of 1 apple. If i put these apples into bags of 8, there will be a remainder of 6 apples. Find the total number of apples in the basket.

I managed to find out the answer using Guess and check method. Please kindly give the solution in other easier methods.

Thank you.

Surya

- Maths -
**MathMate**, Thursday, February 23, 2012 at 11:09am
The other methods are not easier, but can solve more problems. The other method makes use of the "Chinese remainder theorem" (CRT). If you have done modulo arithmetic, you can solve using the CRT. Otherwise you can proceed as follows (also guess & check).

If there is 1 left using bags of 5, the last digit must be 1 or 6.

In bags of 8, there are 6 left, so start with 54 (8*6+6=54) and add 8 until the last digit is 6 (cannot be 1).

Adding 32 will give 54+32=86 is therefore the answer. The next good answer will be 86+40=122>120.

- Maths - erratum -
**MathMate**, Thursday, February 23, 2012 at 11:16am
86+40=126(>120)

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