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Bunuel
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Marco is making z pizzas and will distribute x slices of pepperoni to 01 Nov 2024, 01:30
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95% (hard)

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33% (02:44) correct 67% (02:55) wrong based on 156 sessions

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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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Marco is making z pizzas and will distribute x slices of pepperoni to 10 Jan 2025, 10:05
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KarishmaB Magoosh
Please provide explanation.
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GauravMathur2507
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Marco is making z pizzas and will distribute x slices of pepperoni to 11 Jan 2025, 02:05
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Bunuel
Are we assuming the number of Pizzas to some number and then proceeding to solve the question?
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coolsies
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Marco is making z pizzas and will distribute x slices of pepperoni to 13 Jan 2025, 08:25
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Bunuel
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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Can someone please explain the solution for this.
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Marco is making z pizzas and will distribute x slices of pepperoni to 16 Jan 2025, 12:18
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Bunuel
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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No. of pepperoni slices for each pizza = x/z (x must be divisible by z)
We know: 3z < x < 8z
z > or = 4
We need to find x

S1: x is divisible by (z - 2) - clearly not enough information to determine x or z
S2: x is divisible by (z + 5) - clearly not enough information to determine x or z

Combining: x is divisible by (z-2), z and (z+5)

case 1: z = 4: x is divisible by 2, 4 and 9 i.e. 36 - but 36 does not lie between 3z and 8z - not possible

case 2: z = 5: x is divisible by 3, 5 and 10 i.e. 30, which lies between 3z = 15 and 8z = 40

case 3: z = 6: x is divisible by 4, 6 and 11 i.e. 132 - but 132 does not lie between 3z and 8z - not possible
case 3: z = 7: x is divisible by 5, 7 and 12 i.e. 420 - but 420 does not lie between 3z and 8z - not possible

With higher values of z, the value of x will not lie between 3z and 8z
Thus, only z = 5 is possible - Sufficient

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Marco is making z pizzas and will distribute x slices of pepperoni to 17 Jan 2025, 08:26
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Bunuel
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.
Show more
Alternate approach:

Since the total number of pepperoni slices must be more than 3 times but less than 8 times the number of pizzas -- and each pizza must have the same number of slices -- each pizza has 4, 5, 6 or 7 pepperoni slices.

Case 1: 4 pizzas --> total number of pepperoni slices = 4*4=16, 5*4=20, 6*4=24, or 7*4=28
Case 2: 5 pizzas --> total number of pepperoni slices = 4*5=20, 5*5=25, 6*5=30, or 7*5=35
Case 3: 6 pizzas --> total number of pepperoni slices = 4*6=24, 5*6=30, 6*6=36, or 7*6=42
Case 4: 7 pizzas --> total number of pepperoni slices = 4*7=28, 5*7=35, 6*7=42, or 7*7=49

Stateement 1:
Given the 4 pizzas in Case 1, any of the totals -- 16, 20, 24, 28 -- could be evenly distributed among 2 pizzas (2 fewer).
Since the number of pepperoni slices can be different values, INSUFFICIENT.

Statement 2:
Given the 5 pizzas in Case 2, two totals -- 20 and 30 -- could be evenly distributed among 10 pizzas (5 more).
Since the number of pepperoni slices can be different values, INSUFFICIENT.

Statements combined:
Only one of the listed scenarios satisfies both statements.
Given the 5 pizzas in Case 2, one total -- 30 -- could be evenly distributed among 3 pizzas (2 fewer) or 10 pizzas (5 more)

An extreme case can serve to illustrate that no other scenario will work.
Case 5: 100 pizzas --> total number of pepperoni slices = 4*100=400, 5*100=500, 6*100=600, or 7*100=700
None of the four totals could be evenly distritubed among 98 pizzas (2 fewer) or 105 pizzas (5 more).

Implication:
The number of pizzas = 5 and the number of pepperoni slices = 30, as listed under Case 2.
SUFFICIENT.

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