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# A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6

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Manager
Joined: 29 Apr 2017
Posts: 56
Location: India
Concentration: Operations, Other
GMAT 1: 660 Q43 V38
GPA: 4
WE: Operations (Transportation)
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

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26 Jul 2019, 23:52
To find: which option is the greatest no. of apples that can't be bought in packs of 6, 9 or 20?
Solution: A) 43- we can't buy 43 apples as its not divisible by either 6, 9,20 or combination of any
43/6=7 packs +1 apple
43/9=4 packs of 9+7 apples=4 packs of 9+1 pack of 6+1 apple
43/20=2 packs of 20+3 apples
B) 44- we can't buy 45 apples as well
44/6=7 packs of 6+2 apples
44/9=4 packs of 9 + 8 apples=4 packs of 9+1 pack of 6+2 apples
44/20=2 packs of 20+4 apples
C) 45- we can buy 45 apples as 45/9=5 packs of 9
D) 46-we can buy 46 apples as 46/20=2 packs of 20 + 6 apples=2 packs of 20+1 pack of 6
E) 47- we can't buy 47 apples as well
47/6=7 packs of 6+5 apples
47/9=5 packs of 9+2 apples
47/20=2 packs of 20+7 apples=2 packs of 20+1 pack of 6+1 apple

So, greatest no. of apples that can't be bought is 47.

Alternatively, one may start with the biggest number in the options and will find that option to be the answer.

Manager
Joined: 10 Aug 2016
Posts: 68
Location: India
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

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27 Jul 2019, 02:50
A store sells apples in pack of 6, 9, or 20. By buying 2 packs of 6, you can get 12. But you cannot buy 13 apples, since no combination of 6, 9, and 20 adds up to 13. What is the greatest number of apples that you CANNOT buy in the store?

By looking at answer choices we need to find the greatest number which does not satisfy the eq.
N = 6a+9b+20c (where a, b, c >=0).

Now,
44 = 6*4 + 20*1
45 = 9*5
47 = 9*3 + 20*1

Both, 43 and 46 doesn't fit the combination of 6, 9 and 20.
and greatest of both is 46.

A. 43
B. 44
C. 45
D. 46
E. 47

Manager
Joined: 30 Aug 2018
Posts: 104
Location: India
Concentration: Finance, Accounting
GMAT 1: 600 Q49 V23
GMAT 2: 650 Q49 V29
GPA: 3.36
WE: Consulting (Computer Software)
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

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27 Jul 2019, 04:36
A. 43 --
B. 44--6*4 +20
C. 45--9*5
D. 46
E. 47 --20+9*3
Manager
Joined: 29 Nov 2018
Posts: 154
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

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27 Jul 2019, 06:44
A store sells apples in pack of 6, 9, or 20. By buying 2 packs of 6, you can get 12. But you cannot buy 13 apples, since no combination of 6, 9, and 20 adds up to 13. What is the greatest number of apples that you CANNOT buy in the store?

A. 43
B. 44
C. 45
D. 46
E. 47

Lets start with highest number in the option 47. It can be bought. 1 pack of 20 and 3 packs of 9.
46 cannot be bought - hence answer is D
Intern
Joined: 23 May 2019
Posts: 18
GMAT 1: 710 Q50 V37
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

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04 Dec 2019, 04:06
Prasannathawait wrote:
we cannot have 43 and 47. 47 is the largest.

E option is not correct as:

47=20*1+9*3
Among the given numbers, only 43 is not possible to be obtained from any combination
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6   [#permalink] 04 Dec 2019, 04:06

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