Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60646

A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
22 Jun 2018, 23:49
Question Stats:
80% (01:47) correct 20% (01:58) wrong based on 1297 sessions
HideShow timer Statistics
A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order? A. 7 B. 8 C. 9 D. 10 E. 11 NEW question from GMAT® Official Guide 2019 (PS01233)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Aug 2009
Posts: 8336

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
23 Jun 2018, 00:46
Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order? A. 7 B. 8 C. 9 D. 10 E. 11 NEW question from GMAT® Official Guide 2019 (PS01233) W>M and W>R... To minimize W, maximii the other two.. If all three are equal, each would be 25/3=8 1/3 so slightly more than 8.. So let the other two be 8, total =2*8=16 W =2516=9 C
_________________




BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 504
Location: India
GMAT 1: 700 Q49 V36
GPA: 4

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
23 Jun 2018, 00:34
Given : W>M W>R Solution:  so possible combinations are W>M>R or W>R>M or W>R=M Since we want to find out the least possible W , we need to max R and M Go by options If W = 10 then R + M = 15 R or M can be 7 or 8 OR 8 or 7 We need not check W=11 since we know W=10 is possible If W = 9 then R + M = 16 R or M can be 8 each , Hence this possible and we cant discard W=10 as a possibility lets check for W = 8 then R + M = 17 then R or M has to be 9 or 8 which is not possible Hence answer should be C @Experts  looking for a shorter solution. thanks
_________________



Manager
Joined: 10 Jun 2018
Posts: 51
Location: Australia
Concentration: Technology, General Management
GPA: 2.88
WE: Science (Pharmaceuticals and Biotech)

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
23 Jun 2018, 00:45
Winesap = W McIntosh = M Rome = R W>M, W>R So 'best' case scenario is that M = R, and W must be higher than both. Let's just make M = n, then R = n, and W = n + x Total apple crates is 3n + x = 25. n has to be highest possible. In this case n = 8 is highest possible (25/3=8.33...). x = 25  24 = 1. W = 8 + 1 = 9. Answer is C.This stops you from having to test the answer by substituting values into the equation.
_________________
Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.



Intern
Joined: 01 Aug 2016
Posts: 33
Location: Thailand
Concentration: Accounting, Finance
GPA: 3.82
WE: Accounting (Accounting)

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
23 Jun 2018, 01:46
Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?
A. 7 B. 8 C. 9 D. 10 E. 11
(PS01233) The problem given 3 types of apples which are McIntosh(M), Rome(R), and Winesap(W) and the amount of each type of crates are given that W>M and W>R From the problem, total number of ordered crates is 25 crates to minimize the possible number of W means that we have to maximize the number of M and R So I solve this problem by dividing total number of crates by 3 > \(25/3=8.33\) since the number of crates must be integers and W must be more than R and M, so I rounded up the number of W and rounddown the number of M and R. The minimum possible value of W is then 9 with R and M are 8 each (9+8+8=25) so my answer is "C"



Intern
Joined: 26 Apr 2017
Posts: 45

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
26 Jun 2018, 05:04
Let McIntosh = McI ; Rome = R ; Winesap = W Given W > McI ; W > R W + McI + R = 25
To minimize W , McI and R must be maximize ; Therefore McI = R = (W1) Therefore W + R + McI = 25 w + (w1) + (w1) = 25 w = 9



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9143
Location: United States (CA)

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
04 Jul 2018, 19:10
Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?
A. 7 B. 8 C. 9 D. 10 E. 11 On average, each variety of apple is approximately 25/3 ≈ 8 crates. So we can have 9 crates of Winesap and 8 crates of Rome and 8 crates of McIntosh, for a total of 25 crates. Since 9 is the closest number to the average, it’s the least possible number of crates for the variety of apples  Winesap  that has the greatest number of crates. Alternate Solution: Let’s try each answer choice, starting from the smallest. Answer Choice A: 7 McIntosh crates If there are 7 McIntosh crates, then there are 25  7 = 18 crates of Winesap and Rome crates. If there are 18 crates of Winesap and Rome crates combined, then either one of these crates has to be more than the number of McIntosh crates (which is 7). This is because, if both the number of Winesap and Rome crates are less than 7, then there can be at most 12 remaining crates, but we have 18. Answer Choice B: 8 McIntosh crates Similar to the above discussion, there are 25  8 = 17 crates of Winesap and Rome crates. Again, if one of these crates is less than 8, then the other one will definitely be greater than 8. Answer Choice C: 9 McIntosh crates In this case, there are 25  9 = 16 crates of Winesap and Rome crates. In this case, we observe that the store could have ordered 8 crates of the Winesap and Rome apples each, so it is possible for the store to have ordered 9 McIntosh crates. Since we are looking for the smallest value, this is the value we are looking for. Answer: 9 (C)
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



VP
Joined: 09 Mar 2016
Posts: 1223

A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
07 Jul 2018, 05:37
Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order? A. 7 B. 8 C. 9 D. 10 E. 11 NEW question from GMAT® Official Guide 2019 (PS01233) here is a shortcut to problem but first of all forget the math Distrubue simply values proprtionally yet keep in mind W must be bigger let M, R and W be respectively 8+8+9 = 25 i think in all MAX/MIN the best approach is at first to distribute value proportionally initially if possible, if is it not possible then the remainder add to the value we need to maximize From there you can easily see a bigger picture quickly



Intern
Joined: 08 Jul 2018
Posts: 39

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
15 Aug 2018, 08:34
just use the options, if w=7, at max m and r can be 6...but 7+6+6 is not equal to 25. Keep going until you get C as the answer
_________________
“Pain + Reflection = Progress” ― Ray Dalio



VP
Joined: 07 Dec 2014
Posts: 1230

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
15 Aug 2018, 11:56
[quote="Bunuel"]A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?
A. 7 B. 8 C. 9 D. 10 E. 11
let x=number of M let x=number of R let x+1=number of W 2x+(x+1)=25 x=8 x+1=9 C



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
15 Nov 2018, 10:16
Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order?
A. 7 B. 8 C. 9 D. 10 E. 11
\(?\,\,\, = \,\,\,\min \left( W \right)\,\,\) \(M + R + W = 25\,\,\left( * \right)\) \(\left\{ \matrix{ \,W > M \ge 1\,\,\,{\rm{ints}} \hfill \cr \,W > R \ge 1\,\,\,{\rm{ints}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,W = M + k\,,\,\,\,\,\,M,k\,\, \ge 1\,\,\,{\rm{ints}} \hfill \cr \,W = R + j\,,\,\,\,\,\,R,j\,\, \ge 1\,\,\,{\rm{ints}} \hfill \cr} \right.\,\,\,\,\,\left( {**} \right)\) \(\left( * \right) \cap \left( {**} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,M + R + {{\left( {M + R + k + j} \right)} \over 2} = 25\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{3 \over 2}\left( {M + R} \right) + {{k + j} \over 2} = 25\) \(\min \left( W \right)\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\min \left( {k + j} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,k + j = 1 + 1 = 2\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,M + R = {2 \over 3}\left( {24} \right) = 16\) \(?\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,\,{{\left( {M + R} \right) + \left( {k + j} \right)} \over 2}\,\,\, = \,\,\,{{16 + 2} \over 2}\,\,\, = \,\,\,9\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 04 Sep 2018
Posts: 27
GPA: 3.33

A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
09 Dec 2018, 11:26
Hi everyone. Would be really glad if someone can help on this. Why did we not consider option D or E? I get that we choose C, because 9 perfectly fits in for W, and we divided R and M to be 8 each, but my question, and the point that I want clarity on is why didn't we choose option D or E, since in both the options, it does tick the boxes for the main criteria of the question which W> M, and W> R, so assuming W is 10, M can be 8, and R can be 7, or assuming W is 11, then M can be and 7, and R can be 7. Just puzzled about this, and would really appreciate clarity. Thanks in advance



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
09 Dec 2018, 11:53
nust2017 wrote: Hi everyone. Would be really glad if someone can help on this. Why did we not consider option D or E? I get that we choose C, because 9 perfectly fits in for W, and we divided R and M to be 8 each, but my question, and the point that I want clarity on is why didn't we choose option D or E, since in both the options, it does tick the boxes for the main criteria of the question which W> M, and W> R, so assuming W is 10, M can be 8, and R can be 7, or assuming W is 11, then M can be and 7, and R can be 7. Just puzzled about this, and would really appreciate clarity. Thanks in advance Hi nust2017 , what is the LEAST POSSIBLE number of crates of Winesap that the store will order? Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 04 Sep 2018
Posts: 27
GPA: 3.33

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
09 Dec 2018, 21:47
Thanks a lot. That really helps. Appreciate it mate.



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
10 Dec 2018, 04:30
nust2017 wrote: Thanks a lot. That really helps. Appreciate it mate. I am glad I could help. See you in other posts! Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 30 Mar 2019
Posts: 1
Location: France
Concentration: Strategy, International Business

A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
Updated on: 04 Apr 2019, 03:29
1) W+M+R=25; 2) W>M; 3) W>R; 2)+3) => 2W>M+R=25W => 2W>25W => W>25/3, Wmin=9
Originally posted by ShiqiangHAN on 03 Apr 2019, 14:13.
Last edited by ShiqiangHAN on 04 Apr 2019, 03:29, edited 1 time in total.



Intern
Joined: 29 Mar 2019
Posts: 7

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
03 Apr 2019, 22:33
We need not check W=11 since we know W=10 is possible
Posted from my mobile device



Intern
Joined: 18 Oct 2017
Posts: 19
Location: India

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
09 Apr 2019, 11:09
Azedenkae wrote: Winesap = W McIntosh = M Rome = R
W>M, W>R
So 'best' case scenario is that M = R, and W must be higher than both.
Let's just make M = n, then R = n, and W = n + x
Total apple crates is 3n + x = 25. n has to be highest possible. In this case n = 8 is highest possible (25/3=8.33...). x = 25  24 = 1. W = 8 + 1 = 9.
Answer is C.
This stops you from having to test the answer by substituting values into the equation. SO GLAD SAME SOLUTION FOLLOWED BY ME TOO



Intern
Joined: 23 Mar 2018
Posts: 1

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
28 May 2019, 00:09
chetan2u wrote: Bunuel wrote: A certain store will order 25 crates of apples. The apples will be of three different varieties—McIntosh, Rome, and Winesap—and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, what is the least possible number of crates of Winesap that the store will order? A. 7 B. 8 C. 9 D. 10 E. 11 NEW question from GMAT® Official Guide 2019 (PS01233) W>M and W>R... To minimize W, maximii the other two.. If all three are equal, each would be 25/3=8 1/3 so slightly more than 8.. So let the other two be 8, total =2*8=16 W =2516=9 C I get that the answer is option C. But why should we consider that M and R would be not 0? Why cannot we assume that R could be 0 (which still makes W>R), and both W and M should equal the 25 crates? In that case, the least number of crates of W would be 13 (since M could be 12). Thanks!



Intern
Joined: 24 Oct 2016
Posts: 7

Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
Show Tags
08 Jun 2019, 14:57
Hi,
I have a doubt here. Let's say we have least possible number of W as 9 according to the given answer so remaining distribution would be between R and M, since there is no explicit relation given among them or any constraint of on their quantity we can say that M can be 10 and R would be 6 in that case W<M and hence violates the law of question.
My answer would be 13 for least W as in that case remaining would be 11 and hence one cannot violate the equation of W>M and W>R. Also you can have any value greater than 13 for W and hence maximum possible would be 23 and 1 for each R and M.I am confused here it would be helpful if someone would throw light on this or in case I have misunderstood the question.
Posted from my mobile device




Re: A certain store will order 25 crates of apples. The apples will be of
[#permalink]
08 Jun 2019, 14:57



Go to page
1 2
Next
[ 22 posts ]



