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Marco is making z pizzas and will distribute x slices of pepperoni to

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rohitgm
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Marco is making z pizzas and will distribute x slices of pepperoni to [#permalink] Marco is making z pizzas and will distribute x slices of pepperoni to   07 Jul 2023, 04:00
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Marco is making z pizzas and will distribute x slices of pepperoni to the pizzas so that every pizza has the same number of slices of pepperoni. If the number of slices of pepperoni is more than three times the number of pizzas but less than eight times the number of pizzas, and Marco will make at least four pizzas, what is the number of slices of pepperoni Marco uses?

1. If Marco makes 2 fewer pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
2. If Marco makes 5 more pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
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C
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Marco is making z pizzas and will distribute x slices of pepperoni to [#permalink] Marco is making z pizzas and will distribute x slices of pepperoni to   07 Jul 2023, 22:37
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Given: Marco is making z pizzas and will distribute x slices of pepperoni to the pizzas so that every pizza has the same number of slices of pepperoni.

Asked: If the number of slices of pepperoni is more than three times the number of pizzas but less than eight times the number of pizzas, and Marco will make at least four pizzas, what is the number of slices of pepperoni Marco uses?

x is a multiple of z.
x = kz; where k is the number of pepperoni slice in each pizza.

3z < x=kz < 8z
3<k<8; k={4,5,6,7}
z >=4
x = kz = ?

1. If Marco makes 2 fewer pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
x=kz is also a multiple of (z-2)
kz/(z-2) is an integer.
If k=4; 4z/(z-2) is an integer; z= {4,6,10,...}
If k=5; 5z/(z-2) is an integer; z= {7,12,...}
If k=6; 6z/(z-2) is an integer: z = {4, 5, 6, 8, ..}
If k=7; 7z/(z-2) is an integer: z = {4,9,...}
NOT SUFFICIENT

2. If Marco makes 5 more pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
x = kz is also a multiple of z+5
kz/(z+5) is an integer
If k=4; 4z/(z+5) is an integer; z= {5,..}
If k=5; 5z/(z+5) is an integer; z= {}
If k=6; 6z/(z+5) is an integer: z = {5,}
If k=7; 7z/(z+5) is an integer: z = {5,...}
NOT SUFFICIENT

(1) + (2)
1. If Marco makes 2 fewer pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
x=kz is also a multiple of (z-2)
kz/(z-2) is an integer.
2. If Marco makes 5 more pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
x = kz is also a multiple of z+5
kz/(z+5) is an integer
z = 5; k = 6; x=kz = 30
SUFFICIENT

IMO C
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Re: Marco is making z pizzas and will distribute x slices of pepperoni to [#permalink] Marco is making z pizzas and will distribute x slices of pepperoni to   09 Jul 2023, 09:54
Found this to be a great question. Following

rohitgm wrote:
Marco is making z pizzas and will distribute x slices of pepperoni to the pizzas so that every pizza has the same number of slices of pepperoni. If the number of slices of pepperoni is more than three times the number of pizzas but less than eight times the number of pizzas, and Marco will make at least four pizzas, what is the number of slices of pepperoni Marco uses?

1. If Marco makes 2 fewer pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
2. If Marco makes 5 more pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
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walterwhite756
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Re: Marco is making z pizzas and will distribute x slices of pepperoni to [#permalink] Marco is making z pizzas and will distribute x slices of pepperoni to   14 Jul 2023, 23:46
Question: In simple words, it is saying that z pizzas, x slices and x/z = integer. Also we are provided with range of x which is 3z< x < 8z so x can take values = 4z, 5z, 6z and 7z. Also z >= 4.

Stmt (1): In simple words, if z be z-2 then also x/(z-2) = integer.
We have to check if only one such case exists for z and x in provided constraints. If it doesn't then it is insufficient by itself.
Let z = 4, then z-2 = 2. Assume x = 4z = 16. In this case x/z and x/(z-2) are both integers.
Let z = 4, then z-2 = 2. Assume z = 6z = 24. In this case too, x/z and x/(z-2) are both integers. Hence insufficient.

Stmt (2): In simple words, if z be z+5 then also x/(z+5) = integer.
We have to check if only one such case exists for z and x in provided constraints. If it doesn't then it is insufficient by itself.
Let z = 5, then z+5 = 10. Assume x = 4z = 20. In this case x/z and x/(z+5) are both integers.
Let z = 5, then z+5 = 10. Assume z = 6z = 30. In this case too, x/z and x/(z+5) are both integers. Hence insufficient.

Stmt (1) and Stmt (2): In simple words, if z be z-2 then also x/(z-2) = integer ALSO if z be z+5 then also x/(z+5) = integer.
This time instead of making cases, see if already taken values of x satisfy both these conditions.
Let z = 5, z-2 = 3 and z+5 = 10. Assume z = 6z = 30. In this case, x/z, x/(z-2) and x/(z+5) are all integers. Hence sufficient.

Therefore answer is C.

A good question indeed. Hope it helped. :)
rohitgm wrote:
Marco is making z pizzas and will distribute x slices of pepperoni to the pizzas so that every pizza has the same number of slices of pepperoni. If the number of slices of pepperoni is more than three times the number of pizzas but less than eight times the number of pizzas, and Marco will make at least four pizzas, what is the number of slices of pepperoni Marco uses?

1. If Marco makes 2 fewer pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
2. If Marco makes 5 more pizzas than he does, he would be able to distribute the x pepperoni slices evenly among them.
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Re: Marco is making z pizzas and will distribute x slices of pepperoni to [#permalink]
14 Jul 2023, 23:46
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