GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 21 Jan 2020, 20:13

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 25 Aug 2015
Posts: 45
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 21:35
1
The answer is A.

First, start with the largest number.

Try E-47. If you have 2x20s in it, you have a remainder of 7 which can't be filled with 6 or 9. However, if you have 1x20 in it, then you have a remainder of 27 which can be filled with 3 9s. Hence, E is out.

Try D- 46. If you have 2x20s in it, you have a remainder of 6 which can be filled with 6 apples. Hence, 46 is out.

Try C- 45. 45 is a multiple of 9 so it is automatically out.

Try B- 44. If you have 2x20s in it, you have a remainder of 4 which can't be filled with 6 or 9 apples. If you have 1 20 in it, you have a remainder of 24 which is a multiple of 6. So this is out.

Hence the answer is A.

A. 43
B. 44
C. 45
D. 46
E. 47
Manager
Manager
User avatar
G
Joined: 29 May 2019
Posts: 129
CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 22:04
1
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?

Lets use elimination method here.

A. 43 : Correct
B. 44 : 20+24 eliminate
C. 45 : 9* 5 eliminate
D. 46 : 40 + 6 eliminate
E. 47 : 20 + 27 eliminate

_________________
Pick yourself up, dust yourself off, and start again.

Success is the sum of all small efforts.

MAKE IT HAPPEN :)
Senior Manager
Senior Manager
avatar
P
Joined: 25 Jul 2018
Posts: 471
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 22:23
1
A) 43 (no combination of 6,9 and 20 to adds up to get 43)

B) 44=1(20)+4(6)

C) 45=5(9) or 45=3(9)+3(6)

D) 46=2(20)+1(6)

E) 47=1(20)+3(9)

The answer choice is A.

Posted from my mobile device
Manager
Manager
User avatar
G
Joined: 18 Jun 2013
Posts: 140
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35
GPA: 3.2
WE: Information Technology (Consulting)
Reviews Badge CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 23:53
1
Let number of packets of 6 apples be = x
Let number of packets of 9 apples be = y
Let number of packets of 20 apples be = z

Let us go through the options now,

A. 43

No combinations of 6, 9, 20 add up to 43
=> Correct.

B. 44

6*1 + 9*3 + 20*1 = 44
=> Incorrect.

C. 45

6*0 + 9*5 + 20*0 = 45
=> Incorrect.

D. 46

6*1 + 9*0 + 20*2 = 46
=> Incorrect.

E. 47

6*3 + 9*1 + 20+1 = 47
=> Incorrect.

Answer: A
Senior Manager
Senior Manager
avatar
P
Joined: 18 Jan 2018
Posts: 304
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
GMAT ToolKit User
A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 23:54
1
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?

Lets test the answers
45 is a multiple of 9 , ---So eliminate
46 = 2*20 +6-------------Eliminate
47 = 20 + 3*9 ------------Eliminate
44 = 20 +6*4 ------------Eliminate

So left out is Option A ,43
Manager
Manager
avatar
G
Joined: 06 Feb 2019
Posts: 114
CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 26 Jul 2019, 23:58
1
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


So let's check the options:

43 -
44 = 20 + 4*6
45 = 6*6 + 9
46 = 20*2 + 6
47 = 20+3*9


The answer is A
Senior Manager
Senior Manager
User avatar
D
Joined: 05 Jul 2018
Posts: 460
Location: India
Concentration: General Management, Technology
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
GPA: 3.6
WE: Information Technology (Consulting)
Reviews Badge
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 00:16
1
Lets begin from the highest option we have

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

47= 9 *3 + 20*1
46= 20*2 + 6*1
45 = 9*5
44 = 6*4 +20*1
43 = Not POSSIBLE

Hence, IMO, A is the answer
Director
Director
User avatar
P
Joined: 07 Mar 2019
Posts: 582
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 00:34
1
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

Three type of packs are available i.e. 6, 9 and 20. The packs can be sold if following ways:

1. Only one type alone (3 ways – 6 only, 9 only, 20 only )
2. Two types together (3 ways – 6 & 9, 9 & 20, 20 & 6)
3. Three type together (1 ways – all three together)

Total of seven ways are there each of sum lying between 43 and 47 including. Elaborated as per table below in snapshot.

6’s and 20’s don’t result in any of the given numbers. Only option ‘A’ i.e. 43 is false here.

Answer (A).
Attachments

File comment: A store sells apples in pack of 6, 9, or 20.
A store sells apples in pack of 6, 9, or 20.JPG
A store sells apples in pack of 6, 9, or 20.JPG [ 111.46 KiB | Viewed 289 times ]


_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Manager
avatar
S
Joined: 29 Apr 2017
Posts: 56
Location: India
Concentration: Operations, Other
GMAT 1: 660 Q43 V38
GPA: 4
WE: Operations (Transportation)
CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 00:52
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.

Answer: E
Manager
Manager
avatar
S
Joined: 24 Sep 2014
Posts: 51
Concentration: General Management, Technology
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 01:05
1
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, ..
Multiples of 9 = 9, 18, 27, 36, 45, ..
Multiples of 20 = 20, 40, ..

(i) 43, we cannot get this number by any combination of multiples of 6, 9 or 20
(ii) 44, 6x4 + 20x1
(iii) 45, 9x5
(iv) 46, 6+20x2
(v) 47, 20+9x3

Answer is A
Manager
Manager
avatar
G
Joined: 30 May 2019
Posts: 109
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 02:50
1
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?

For which of the following 6a+9b+20c cannot equal to an integer (a,b, and c are all positive integers)

A. 43 = 20+23 - can 6a+9b equal to 23. No, because 6*4 is 24, 2*9+6=24, 20+6=26, 6*3+9=27, 3*9=27 OR 23-6=17 (prime number cannot be divided by composite number), 23-9=14(not divisible by 6 or 9), 23-12=11(prime number cannot be divided by a composite number), 23-18=5(prime number cannot be divided by a coposite number). As we see, from 6a+9b+20c we cannot get 43. Keep A

B. 44 = 20+6+2*9 - works
C. 45 = 5*9 - works
D. 46 = 20*2+6 - works
E. 47=20+3*9 - works

A is answer
Senior Manager
Senior Manager
User avatar
P
Joined: 12 Dec 2015
Posts: 474
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 03:11
2
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--> correct :can't be bought: 43 can be make w/ any combination of 6,9 & 20
B. 44--> can be bought: 44=20+4*6
C. 45--> can be bought: 45 = 5*9
D. 46--> can be bought: 46=2*20+6
E. 47--> can be bought: 47=20 + 3*9
Manager
Manager
avatar
S
Joined: 10 Aug 2016
Posts: 68
Location: India
GMAT ToolKit User
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 03:50
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.
Hence, answer = 46.


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

Answer Choice: D
Manager
Manager
avatar
S
Joined: 17 Jan 2017
Posts: 87
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 04:08
1
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?

Here, the combination is 6x+9y+20z

A. 43 it is not possible in any combination
B. 44 is possible when x= 4 and z= 1
C. 45 is possible when x= 6 and y= 1
D. 46 is possible when x= 1 and z= 2
E. 47 is possible when y = 3 and z = 1

so, the correct answer choice is A
Manager
Manager
avatar
S
Joined: 01 Oct 2018
Posts: 112
CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 04:44
1
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?

So, the question is the greatest:
!= not equal
6*x+9*y+20*z != a

Let's input variants (start from the greatest):
E. 47
6*x+9*y+20*z = 47
x - y - z - 47
any - any - 2 - not 47
0 - 3 - 1 - 47
D. 46
6*x+9*y+20*z = 46
x - y - z - 46
1 - 0 - 2 - 46
C. 45
6*x+9*y+20*z = 45
x - y - z - 45
0 - 5 - 0 - 45
B. 44
6*x+9*y+20*z = 44
x - y - z - 44
4 - 0 - 1 - 44
A. 43
6*x+9*y+20*z = 43
x - y - z - 43
any - any - any != 43

ANSWER A


A. 43
B. 44
C. 45
D. 46
E. 47
Manager
Manager
avatar
B
Joined: 27 Mar 2016
Posts: 115
GMAT 1: 590 Q44 V22
GMAT ToolKit User
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 05:16
1
Lets start from the greatest number from the option
47 = (20 + 9*3i.e 27 =47) hence NO
46 = (20*2 + 6) hence No
45 = (9*5) hence No
44 = (20+6*4)hence No
43 Not possible
Hence answer is A
Manager
Manager
avatar
S
Joined: 22 Oct 2018
Posts: 73
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 05:23
1
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

Solution:
I tried this question by hit and trial.
By picking up the various answer options i tried to see if the combination of various packs of apples is possible or not .Also we need to find the greatest number of apples which cannot be bought.


44 is possible to buy with 1 pack of 6+2 pack of 9+1 pack of 20=6+18+20=44
45 is possible to buy 5 pack of 9=45
46 is possible to buy with 1 pack of 6 and 2 pack of 20=6+40=46
47 is possible to buy with 3 pack of 9 and 1 pack of 20=27+20=47
No combination would buy us 43


Hence A IMO
Manager
Manager
avatar
S
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)
Premium Member
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 05:36
A. 43 --
B. 44--6*4 +20
C. 45--9*5
D. 46
E. 47 --20+9*3
SC Moderator
User avatar
V
Joined: 25 Sep 2018
Posts: 605
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Premium Member Reviews Badge CAT Tests
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 05:44
1
Solution:

In this question, it is easier to start with the answer choices and try out various combinations to fit into that particular answer choice.
According to the Stem, we can use any combinations of 6,,9, 20 or maybe just a single number

A. 43 = Now 43 cannot be obtained by any combinations we try. Hence lets keep this one.
B .44 = 6 + (9 X 2) + 20 Here we use 1 pack of 6, 2 packs of 9 & one pack of 20. Hence we can buy apples in this combination so this option is out.
C .45 = 5 X 9 . we can straightaway use 5 packs of 9 and get 45 apples. Hence this option is out.
D. 46 = we can obtain this by using 2 packs of 20 and one pack of 6. Hence this is out.
E. 47 = If we use a larger pack of 20. we have 27 remaining for which we can use 3 packs of 9 apples and hence this combination is possible. Rule out this choice

So the answer must be A
_________________
Why do we fall?...So we can learn to pick ourselves up again
Manager
Manager
User avatar
G
Joined: 12 Jan 2018
Posts: 117
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6  [#permalink]

Show Tags

New post 27 Jul 2019, 06:04
1
Lets check each of the choices in descending order of their value
E. 47; 47 can be expressed as 9+9+9+20 =>Incorrect
D. 46; 46 can be expressed as 6+20+20 =>Incorrect
C.45; 45 can be expressed as 9+9+9+9+9 =>Incorrect
B.44; 44 can be expressed as 6+6+6+6+20 =>Incorrect
A. 43; Must be correct

Ans: A
_________________
"Remember that guy that gave up?
Neither does anybody else"
GMAT Club Bot
Re: A store sells apples in pack of 6, 9, or 20. By ordering 2 packs of 6   [#permalink] 27 Jul 2019, 06:04

Go to page   Previous    1   2   3   4   5    Next  [ 85 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne