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# A certain wooded lot contains 56 oak trees. How many pine trees does

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A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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12 Oct 2015, 21:06
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Difficulty:

5% (low)

Question Stats:

86% (01:03) correct 14% (01:14) wrong based on 171 sessions

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A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain?

(1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.

(2) If the number of oak trees were increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.

Kudos for a correct solution.

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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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12 Oct 2015, 21:48
Given:
Oak = 56
Pine = ?

S1:
$$\frac{Oak}{Pine} = \frac{8k}{5k}$$
=> $$\frac{56}{P} = \frac{8}{5}$$ ($$Oak = 56$$)
=> $$p = 37$$
Sufficient

S2:
Oak = 56 + 4 = 60
Pine = ?
$$\frac{Oak}{Pine} = \frac{12k}{7k}$$
Similar info as in S1
Sufficient

D

(Please correct me if i have gone wrong anywhere)
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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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12 Oct 2015, 22:41
Bunuel wrote:
A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain?

(1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.

(2) If the number of oak trees were increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.

Kudos for a correct solution.

Question : No. of Pine Trees = ?

Statement 1: Oak : Pine = 8:5
i.e. Oak = 56 then Pine = 35
SUFFICIENT

Statement 2: (Oak+4):Pine = 12:7
i.e. (56+4):Pine = 12:7
i.e. Pine = 35
SUFFICIENT

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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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13 Oct 2015, 04:51
1

Statement: gives the ratio of oak to pine: Sufficient

Statement 2: gives the new ratio as K+4/p=12/7: Sufficient
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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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14 Oct 2015, 05:18
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain?

(1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5.

(2) If the number of oak trees were increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.

We only need to know the number of pine trees, so there is only one variable in this question, whereas we are given 2 equations from the conditions. Therefore, there is high chance that (D) is going to be our answer.
From condition 1, oak=8k=56, k=7 therefore the no. of pine=5k= 5(7)=35. This condition is sufficient.
From condition 2, 56+4=60, 60:pine=12:7, 12pine=60 x 7. Pine=25. This condition is also sufficient, and the answer is therefore D.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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30 Mar 2016, 23:51
Attached is a visual that should help.
Attachments

Screen Shot 2016-03-31 at 12.51.05 AM.png [ 106.63 KiB | Viewed 2137 times ]

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Re: A certain wooded lot contains 56 oak trees. How many pine trees does  [#permalink]

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04 Sep 2018, 10:18
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Re: A certain wooded lot contains 56 oak trees. How many pine trees does &nbs [#permalink] 04 Sep 2018, 10:18
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