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# A certain store will order 25 crates of apples. The apples will be of

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A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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22 Jun 2018, 23:49
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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)

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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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23 Jun 2018, 00:46
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9
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 =25-16=9

C
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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23 Jun 2018, 00:34
1
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

@Experts - looking for a shorter solution. thanks
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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23 Jun 2018, 00:45
1
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.

This stops you from having to test the answer by substituting values into the equation.
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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 round-down 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)
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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 = (W-1)
Therefore
W + R + McI = 25
w + (w-1) + (w-1) = 25
w = 9
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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.

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A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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07 Jul 2018, 05:37
1
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
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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15 Aug 2018, 11:56
1
[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
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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.
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A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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.

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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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09 Dec 2018, 11:53
1
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.

Hi nust2017 ,

what is the LEAST POSSIBLE number of crates of Winesap that the store will order?

Regards,
Fabio.
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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

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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.
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A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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Updated on: 04 Apr 2019, 03:29
1) W+M+R=25;
2) W>M;
3) W>R;
2)+3) => 2W>M+R=25-W
=> 2W>25-W
=> 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.
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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03 Apr 2019, 22:33
We need not check W=11 since we know W=10 is possible

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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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.

This stops you from having to test the answer by substituting values into the equation.

SO GLAD SAME SOLUTION FOLLOWED BY ME TOO
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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 =25-16=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!
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Re: A certain store will order 25 crates of apples. The apples will be of  [#permalink]

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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.

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

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