A stationery store received a shipment of notebooks. When the manager

Question

A stationery store received a shipment of notebooks. When the manager packs the notebooks into cartons that hold 8 notebooks each, 5 notebooks are left unpacked. If the same shipment is packed into cartons that hold 12 notebooks each, how many notebooks will be left unpacked?

(1) If the notebooks are packed into cartons that hold 6 notebooks each, 5 notebooks are left unpacked.

(2) If the notebooks are packed into cartons that hold 10 notebooks each, 5 notebooks are left unpacked.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A stationery store received a shipment of notebooks. When the manager packs the notebooks into cartons that hold 8 notebooks each, 5 notebooks are left unpacked. If the same shipment is packed into cartons that hold 12 notebooks each, how many notebooks will be left unpacked?

(1) If the notebooks are packed into cartons that hold 6 notebooks each, 5 notebooks are left unpacked.

We are given that the number of notebooks leaves 5 when divided by 8, and statement (1) says it also leaves 5 when divided by 6. So the total must be 5 more than a common multiple of 8 and 6. The least common multiple of 8 and 6 is 24, so the total is of the form

24k + 5

When such a number is divided by 12, the remainder is always 5.

Sufficient.

(2) If the notebooks are packed into cartons that hold 10 notebooks each, 5 notebooks are left unpacked.

Here the total leaves 5 when divided by 8 and also 5 when divided by 10.

That means the total is 5 more than a common multiple of 8 and 10. The least common multiple of 8 and 10 is 40, so the total is of the form

40k + 5

For different values of k, 40k + 5 can leave different remainders when divided by 12. For example:

If k = 1, then 40k + 5 = 45, which leaves remainder 9.
If k = 2, then 40k + 5 = 85, which leaves remainder 1.

Not sufficient.

Answer: A.

Adit_ · Answer

This is quite tricky!

Statement 1:
Always simplify first.

8y+5 = 6x+5
y/x = 3/4

Now notice very carefully.
x is a multiple of 4.
6*4x = 24x and 24x is divisible by 12! Thus No.of notebooks packed = 12z+5 which means remainder is always 5.
SUFFICIENT.

Statement 2:

Similar fashion you get:
8y+5 = 10x+5
y/x = 5/4
Here if you take prime factorization of 8 = 2^3 and 10 = 2*5
2^3*5x not multiple of 12. 2*5*4 is also NOT multiple of 12.
So remainder will vary.
INSUFFICIENT.

Answer:  Option A

KRKfan · Answer

Given: 
# of books in a shipment: __
Original Holding capacity of cartons: 8 books
Remainder when packing books in cartons: 5 books

To find:  # of books remaining unpacked when packed in cartons holding 12 books.

Possible # of books in the shipment will be  8x + 5  where  'x'  is the # of cartons with holding capacity of 8 books.

So the possible shipment can be  13  books with 1 carton used,  21  books with 2 cartons used,  29 ,  37 ,  45 ,  53 ,  61 , and so on...

Statement 1:   If the notebooks are packed into cartons that hold 6 notebooks each, 5 notebooks are left unpacked.

Here, only 6 books can be packed in a carton but still the desired remainder is of 5 books.

Out of the possible book shipments calculated above, the no. of books in a shipment can be:
•  29 books : 29 ÷ 8 = 3 with 5 as remainder and 29 ÷ 6 = 4 with 5 as remainder
•  53 books : 53 ÷ 8 = 6 with 5 as remainder and 53 ÷ 6 = 8 with 5 as remainder
•  77 books : 77 ÷ 8 = 9 with 5 as remainder and 77 ÷ 6 = 12 with 5 as remainder, and so on...

Now, we divide the shipment numbers by 12 to get a consistent remainder i.e. consistent # of books unpacked:
• 29 ÷ 12 = 2 with 5 as remainder
• 53 ÷ 12 = 4 with 5 as remainder
• 77 ÷ 12 = 6 with 5 as remainder

Since the # of books remaining unpacked is  consistent , i.e. # of books remaining unpacked is always 5, Statement (1) is  Sufficent .

Statement 2:   If the notebooks are packed into cartons that hold 10 notebooks each, 5 notebooks are left unpacked.

Here, only 10 books can be packed in a carton but still the desired remainder is of 5 books.

Out of the possible book shipments calculated earlier, the no. of books in a shipment can be:
•  45 books : 45 ÷ 10 = 4 with 5 as remainder and 45 ÷ 8 = 5 with 5 as remainder
•  85 books : 85 ÷ 10 = 8 with 5 as remainder and 85 ÷ 8 = 10 with 5 as remainder
•  125 books : 125 ÷ 10 = 12 with 5 as remainder and 125 ÷ 8 = 15 with 5 as remainder

Now, we divide the shipment numbers by 12 to get a consistent remainder i.e. consistent # of books unpacked:
• 45 ÷ 12 = 3 with 9 as remainder
• 85 ÷ 12 = 7 with 1 as remainder
• 125 ÷ 12 = 10 with 5 as remainder

Here,the # of books remaining unpacked are  inconsistent  with no fixed # of books remaining unpacked, Statement (2) is  Not Sufficent .

Correct answer is  A .

A stationery store received a shipment of notebooks. When the manager

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