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Julie wants to be sure that she has enough pies for each of her

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New post 27 Oct 2018, 21:44
2
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A
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C
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E

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Question Stats:

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Julie wants to be sure that she has enough pies for each of her 30 guests to have at least one slice. One pie can be divided into eight slices. If \(⌈x⌉\)represents the least integer greater than \(x\), and \(x\) is greater than \(0\), will \(⌈x⌉\) pies be enough for each guest to have at least one slice?



(1) \(5 < 2x < 12\)

(2) \(x\) is a multiple of \(3\)

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New post Updated on: 28 Oct 2018, 02:21
\(\frac{30}{8}\)=3 r 6
Need 3 pies + 6 slices.
So, we need 4 full pies

1)Note that this is 'x' not ⌈x⌉.
Smallest x is around 2.6. 2x2.6=5.2
2.6=⌈3⌉ isn't enough for 3 pies+ 6 slices
Largest x is around 5.9. 2x5.9=11.8
5.9=⌈6⌉ is enough

Insufficient

2) x=0, 3, 6, 9...
Insufficient
⌈1⌉⌈4⌉⌈7⌉⌈10⌉

Together
x=0, 3, 6, 9...and ⌈x⌉=⌈1⌉⌈4⌉⌈7⌉⌈10⌉
2x>5
x can't be 0
2x<12
Can't be 6 or larger
Only option left is x=3

x=3, therefore ⌈x⌉=4
So we know that number of pies is between 3 and 4. Could be less than, equal to, or greater than 3.6
Insufficient
E

EDIT
I am wrong btw. I wasn't careful about the original condition saying x>0

Originally posted by philipssonicare on 28 Oct 2018, 00:15.
Last edited by philipssonicare on 28 Oct 2018, 02:21, edited 2 times in total.
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New post Updated on: 28 Oct 2018, 17:16
From statement 1:

\(5<2x<12\)
\(2.5<x<6\) x can be 3, 4 or 5.

If 3 pies then 8*3 = 24 slices. Not enough
If 4 or 5 pies then 32 or 40 slices. Enough.
Insufficient.

From statement 2:

x is a multiple of 3.
Already given that x > 0. So, min value of x can be 3. Then [x] is 3. Then 8*3 = 24 pies. Not enough.
If x is 6 then 48 pies. Enough.
InSufficient.

Combining both gives only x as 3. So 24 pies. Not enough.

C is the answer.
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Originally posted by Afc0892 on 28 Oct 2018, 01:48.
Last edited by Afc0892 on 28 Oct 2018, 17:16, edited 1 time in total.
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New post 28 Oct 2018, 07:51
Got my mistake.
X is number of pies means x is integer.
Here I did mistake taking X as positive fractions.
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New post 28 Oct 2018, 12:08
1
I have a silly doubt.

Can someone please clarify if 5.1 would be considered as a multiple of 3 or not (as 3 divides it completely)? If not, please let me know why.

Thanks for the help.
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New post 28 Oct 2018, 12:16
1
1
sssjav
https://www.mathsisfun.com/numbers/fact ... iples.html

"Multiples of Anything
We must multiply by an integer, but the number that is being multiplied can be anything.

Example: Multiples of π
..., −2π, −π, 0, π, 2π, 3π, 4π, ..."

3 is the number being multiplied, so it must be multiplied by an integer
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New post 28 Oct 2018, 17:14
Somebody can explain, why the answer is C?, why the option B is insufficient, if we are told that X is >0 and is a multiple of three, the other X should be 4. Therefore, it has to be sufficient.
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Re: Julie wants to be sure that she has enough pies for each of her  [#permalink]

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New post 28 Oct 2018, 17:20
jorgetomas9 wrote:
Somebody can explain, why the answer is C?, why the option B is insufficient, if we are told that X is >0 and is a multiple of three, the other X should be 4. Therefore, it has to be sufficient.


Hi,

From statement 2: It's given that x is a multiple of 3. If x = 3. then Number of pies = 8*3 = 24 pies. Remember x is the number of pies and each pie has 8 slices. So 24 Slices of pie are not enough for 30 people.

If x is 6 or above then the number of slices for 30 would be enough. So both yes or no from statement 2. Hence insufficient.

But on combining both. we get x as 3. only 24 slices. not enough. Hence c is the answer.
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New post 28 Oct 2018, 17:27
Afc0892 wrote:
jorgetomas9 wrote:
Somebody can explain, why the answer is C?, why the option B is insufficient, if we are told that X is >0 and is a multiple of three, the other X should be 4. Therefore, it has to be sufficient.


Hi,

From statement 2: It's given that x is a multiple of 3. If x = 3. then Number of pies = 8*3 = 24 pies. Remember x is the number of pies and each pie has 8 slices. So 24 Slices of pie are not enough for 30 people.

If x is 6 or above then the number of slices for 30 would be enough. So both yes or no from statement 2. Hence insufficient.

But on combining both. we get x as 3. only 24 slices. not enough. Hence c is the answer.


But ⌈x⌉ is not least greater than X?, if X equals 3, therefore ⌈x⌉ should be 4 and 4 * 8 =32 , maybe I am wrong in my interpretation.

Is ⌈x⌉>X?
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New post 28 Oct 2018, 22:55
2
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.
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New post 29 Oct 2018, 06:36
sssjav wrote:
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.

Ok, I get it, thank you very much.
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New post 01 Nov 2018, 22:49
In simple words, we need to check whether x is 4 or greater.

1. x is between 2.5 and 6. It could be 3 or 4 so the answer could be yes or no.
2. Insufficient, easily.
Combining, in the range of 2.5<x<6, x=3 is the only case possible for x to be a multiple of 3.
Hence, she has 3 pies and can get only 24 slices. So we get NO.
Sufficient.
C.
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New post 09 Nov 2018, 10:04
1
sssjav wrote:
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.


Thank you for the explanation, however I think that the question is poorly worded since it provides an insufficient explanation of the function ⌈x⌉

I would suggest to amend the text of the question. " If ⌈x⌉ represents the least integer greater than x "
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New post 09 Nov 2018, 13:05
Manfo wrote:
sssjav wrote:
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.


Thank you for the explanation, however I think that the question is poorly worded since it provides an insufficient explanation of the function ⌈x⌉

I would suggest to amend the text of the question. " If ⌈x⌉ represents the least integer greater than x "



I agree, based on the current wording if x = 3 then [x] = 4
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Re: Julie wants to be sure that she has enough pies for each of her  [#permalink]

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New post 09 Nov 2018, 21:58
Manfo wrote:
sssjav wrote:
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.


Thank you for the explanation, however I think that the question is poorly worded since it provides an insufficient explanation of the function ⌈x⌉

I would suggest to amend the text of the question. " If ⌈x⌉ represents the least integer greater than x "



Hello

Yes, I think there could be some doubt in the wording: instead of symbolising ⌈x⌉ as 'least integer greater than x', question could have symbolised ⌈x⌉ as 'least integer greater than or equal to x'.

But in either case, answer would still be C only. If we assume ⌈x⌉ to be 'least integer greater than x', then after combining the two statements, x=3 and thus ⌈x⌉ = 4. 4 pies will be sufficient for 30 guests. Answer to the question is a clear YES, and together the two statements are sufficient.

If however, we change the wording of the question to be that ⌈x⌉ means 'least integer greater than or equal to x', then after combining the statements, x=3 and thus ⌈x⌉ is also = 3. 3 pies will NOT be sufficient for 30 guests. Answer to the question is a clear NO, and still together the two statements are sufficient.

So in any case, answer would be C only.
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Re: Julie wants to be sure that she has enough pies for each of her  [#permalink]

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New post 09 Nov 2018, 22:11
sssjav wrote:
I have a silly doubt.

Can someone please clarify if 5.1 would be considered as a multiple of 3 or not (as 3 divides it completely)? If not, please let me know why.

Thanks for the help.


It cannot be as x represents the number of pies. Re-read the first sentence of the question.
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New post 11 Nov 2018, 02:00
amanvermagmat wrote:
Manfo wrote:
sssjav wrote:
jorgetomas9
https://www.mathsisfun.com/sets/functio ... iling.html

⌈x⌉ : This function of x essentially means that x takes the value of the least integer CLOSEST to x, and greater than (or equal to) x: greater only if x is not an integer itself. (I agree that this info is not given very clearly in the question, but I'd suggest to you to learn it anyway)

Note: This is known as the ceiling function of x. The FLOOR function for x, where the brackets are inverted in the shape of an "L" and a mirrored L, would represent the greatest integer less than or equal to x.


Thank you for the explanation, however I think that the question is poorly worded since it provides an insufficient explanation of the function ⌈x⌉

I would suggest to amend the text of the question. " If ⌈x⌉ represents the least integer greater than x "



Hello

Yes, I think there could be some doubt in the wording: instead of symbolising ⌈x⌉ as 'least integer greater than x', question could have symbolised ⌈x⌉ as 'least integer greater than or equal to x'.

But in either case, answer would still be C only. If we assume ⌈x⌉ to be 'least integer greater than x', then after combining the two statements, x=3 and thus ⌈x⌉ = 4. 4 pies will be sufficient for 30 guests. Answer to the question is a clear YES, and together the two statements are sufficient.

If however, we change the wording of the question to be that ⌈x⌉ means 'least integer greater than or equal to x', then after combining the statements, x=3 and thus ⌈x⌉ is also = 3. 3 pies will NOT be sufficient for 30 guests. Answer to the question is a clear NO, and still together the two statements are sufficient.

So in any case, answer would be C only.


Hi,

I don't agree, if " ⌈x⌉ represents the least integer greater than x, and x is greater than 0 " and if (2) " x is a multiple of 3 " this means that x is 3, 6, 9, etc.. and ⌈x⌉ will then be 4 , 7, 10, etc..

So ⌈x⌉ * 8 > 30 , hence (2) is sufficient. We don't need the first statement. Ans = B

Please re-edit the text since statistics on this question are clearly flawed because of the bad wording..
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Re: Julie wants to be sure that she has enough pies for each of her  [#permalink]

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New post 12 Nov 2018, 15:00
XavierAlexander wrote:
Julie wants to be sure that she has enough pies for each of her 30 guests to have at least one slice. One pie can be divided into eight slices. If \(⌈x⌉\)represents the least integer greater than \(x\), and \(x\) is greater than \(0\), will \(⌈x⌉\) pies be enough for each guest to have at least one slice?



(1) \(5 < 2x < 12\)

(2) \(x\) is a multiple of \(3\)


Guys, the official answer is: E

Here is the explanation from Manhattan:

Each pie produces 8 slices and Julie needs to feed 30 guests. ⌈x⌉
is defined as an integer, so the question is asking about an integer value of pies. 3 pies would only produce 24 slices, which is not enough. 4 pies will produce 32 slices. Julie will need at least 4 pies to feed all her guests

(1) INSUFFICIENT: Simplify the inequality.

5 < 2x < 12

2.5 < x < 6

x can be anything between 2.5 and 6, giving multiple possible values for ⌈x⌉
. Test Cases to determine whether all values of ⌈x⌉
are at least 4. Keep in mind that x does not have to be an integer, even though ⌈x⌉
does.

Case 1: x = 5.99, ⌈x⌉
= 6. Yes, there are enough pies.

Case 2: x = 2.51, ⌈x⌉
= 3. No, there are not enough pies.

Since there is at least one Yes case and at least one No case, this statement is not sufficient. Eliminate choices (A) and (D).



(2) SUFFICIENT: The question specifies that x is greater than 0. Therefore, x can be any positive multiple of 3. All of these produce enough pies for Julie.

Case 1: x = 3, ⌈x⌉
= 4. Yes, there are enough pies.

Case 2: x = 6, ⌈x⌉
= 7. Yes, there are enough pies.

Eliminate choices (C) and (E).



The correct answer is (B).
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