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# Josie's land is to be divided into three parcels. If the larger parcel

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Math Expert
Joined: 02 Sep 2009
Posts: 64248
Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 01:27
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Difficulty:

25% (medium)

Question Stats:

84% (01:16) correct 16% (01:14) wrong based on 45 sessions

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Competition Mode Question

Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.

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Director
Joined: 30 Sep 2017
Posts: 922
GMAT 1: 720 Q49 V40
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Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 02:23
1
Large parcel (L) = 60% area
Small parcel (S1) = 20% area
Small parcel (S2) = 20% area
L:S1:S2 = 3:1:1

(1) L+ (S1 or S2) = 416 acre
L = 3/4*416 = 312 acre
S1 = S2 = 1/4*416 = 104 acre
Area of the smaller parcel = 104 acre
SUFFICIENT

(2) L = 312 acre
L: (S1 or S2) = 3:1
S1 = S2 = 1/3*312 = 104 acre
Area of the smaller parcel = 104 acre
SUFFICIENT

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Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 03:54
1
Quote:
Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.

L=3/5T
2S=2/5T
S=1/5T

(1) sufic
L+S=416, 4T/5=416, T=416*6/4

(2) sufic
L=3/5T=312, T=312*5/3

ans (D)
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Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 09:21
Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.
large part is 60 % so other two parts must be 20 % each
so
#1
The combined size of the larger parcel and one of the smaller parcels is 416 acres.
.6x+.2x = 416
.8x = 416
x= 520 ; we can find large ; 312 so balance 104 each is small part
sufficient
#2
The size of the larger parcel is 312 acres
.6x = 312
x= 520
sufficient
OPTION D
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Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 10:19
1
From the question stem we know if Josie's land comprised of x acres
Then bigger parcel = 0.6x
Each Smaller parcel = 0.2x

(1) 0.8x = 416,
or, x = 520 acres
Therefore, 0.2x = 104 acres
Sufficient

(2) 0.6x = 312
or, x=520 acres
Therefore, 0.2x = 104 acres
Sufficient

Director
Joined: 25 Jul 2018
Posts: 712
Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 14:57
1
$$0.6x +0.2x+ 0.2x=x$$
--> $$0.2x = ???$$

(Statement1): 0.6x + 0.2x = 416
0.8x = 416
--> $$x = \frac{426}{8}*10= 520$$
Sufficient

(Statement2): 0.6x = 312
--> $$x = \frac{312}{6}*10 = 520$$
Sufficient

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Posts: 108
Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 18:38
1
Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.
60% larger, 20% two smaller
1) 80% of total=416
sufficient
2) 60% of total=312
sufficient
Ans D
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Joined: 24 Sep 2014
Posts: 65
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Re: Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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04 May 2020, 19:21
1
Given:
Largest parcel = p1 = 0.6T (T is the total land)
Two smaller = p2 = p3 = 0.2T (since p1+p2+p3 = T)

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
0.6T+0.2T = 416
0.8T = 416 --> T = 520, we can find out p2.

(2) The size of the larger parcel is 312 acres.
0.6T = 312 --> T = 520, we can find out p2.

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Josie's land is to be divided into three parcels. If the larger parcel  [#permalink]

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05 May 2020, 19:24
Bunuel wrote:

Competition Mode Question

Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.

Given:
1. Josie's land is to be divided into three parcels.
2. The larger parcel is 60 percent of the total and the smaller parcels are the same size.

Let the total land size be x,
Larger parcel size = .6x
Smaller parcel size = (x - .6x)/2 = .2x

Asked: What is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
.6x+ .2x = .8x = 416 acres
Number of acres in one of the smaller parcel = .2x = .8x/4 = 416/4= 104 acres
SUFFICIENT

(2) The size of the larger parcel is 312 acres.
Size of larger parcel = 312 acres = .6x
Number of acres in one of the smaller parcel = .2x = .6x/3 = 312/3 = 104 acres
SUFFICIENT

IMO D
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Josie's land is to be divided into three parcels. If the larger parcel   [#permalink] 05 May 2020, 19:24