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

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

by VJesus12 » Mon Apr 08, 2019 5:08 am

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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

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT
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Source: — Data Sufficiency |
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by deloitte247 » Wed Apr 17, 2019 6:46 am

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If the number of pies will be enough for the guest to have at least one slice.
Guest=3; x>0 and 1 pie = 8 slices
Statement 1=> 5<2x<12
Dividing through by 2 gives;
$$2.5<x<6$$
Thus, x cab be either 3,4 or 5.
1 pie = 8 slices if x=3, then 8 * 3=24 => not enough
If x=4, then 8 * 4 = 32 => enough
If x=5, then 8 * 5 = 40 => enough
The information is not enough to arrive at a definite conclusion. Hence, statement 1 is INSUFFICIENT

Statement 2=> x is a multiple of 3
Since x>0, then x can be 3,6,9,12,15 etc.
If x=3, then 8 * 3 = 24 => not enough
If x=4, then 8 * 12 = 96 => enough
The information given is not enough to arrive at a definite conclusion. Hence, statement 2 is INSUFFICIENT

Combining both statement together;
From statement 1, x=3,4,5
From statement 2, x is a multiple of 3. The only multiple of 3 between 3,4 and 5 is 3. So, x=3
However, if one guest must have at least one slice of pie, then the pie will only be enough for 24 guests. Therefore, both statement combined together are SUFFICIENT.

Answer is option C
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