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# Lou has three daughters: Wen, Mildred, and Tyla. Three years

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2912 [0], given: 394

Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  14 Jun 2018, 14:25
Expert's post
00:00

Question Stats:

68% (04:37) correct 31% (00:44) wrong based on 16 sessions
Lou has three daughters: Wen, Mildred, and Tyla. Three years ago, when Lou was twice as old as Tyla, he was 30 years older than Mildred. Now, he is 47 years older than Wen. In 4 years, Wen will be half as old as Tyla. What is the sum of the current ages of Lou and his three daughters?

(A) 138
(B) 144
(C) 154
(D) 166
(E) 181
[Reveal] Spoiler: OA

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2912 [0], given: 394

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  05 Jul 2018, 03:21
Expert's post
Explanation

The key to this tricky-sounding problem is setting up variables correctly and ensuring that you subtract or add appropriately for these variables when representing their ages at different points in time:

L = Lou’s age now
W = Wen’s age now
M = Mildred’s age now
T = Tyla’s age now

Two equations come from the second sentence of the problem:

Equation 1: $$(L - 3) = 2(T - 3)$$
Equation 2: $$(L - 3) = (M - 3) + 30$$

Another two equations come from the third sentence of the problem:

Equation 3: $$L = W + 47$$
Equation 4: $$(W + 4) =\frac{T+4}{2}$$

In order to solve this problem effectively, look for ways to get two of the equations to have the same two variables in them. If you have two equations with only two variables, you can solve for both of those variables. Equation 4 has a W and a T; the only other equation with a T is Equation 1. If you substitute the L in Equation 1 with the W from Equation 3, you will have two equations with just W’s and T’s.

Equation 1: $$(L - 3) = 2(T - 3)$$

$$(W + 47) – 3 = 2(T - 3)$$

$$W + 44 = 2T - 6$$

$$W + 50 = 2T$$

Equation 4: $$(W + 4) =\frac{T+4}{2}$$

$$2W + 8 = T + 4$$

$$2W + 4 = T$$

Now combine the equations to solve for W.

$$W + 50 = 2(2W + 4)$$

$$W + 50 = 4W + 8$$

$$W + 42 = 4W$$

$$42 = 3W$$

$$14 = W$$

Now that you know Wen’s age, you can solve for the rest.

Equation 3: $$L = W + 47$$
$$L = 14 + 47$$
$$L = 61$$

Equation 1: $$(L - 3) = 2(T - 3)$$

$$(61 - 3) = 2(T - 3)$$

$$58 = 2T - 6$$

$$64 = 2T$$

$$32 = T$$

Equation 2: $$(L - 3) = (M - 3) + 30$$

$$(61 - 3) = (M - 3) + 30$$

$$58 = M + 27$$

$$31 = M$$

Now that you know that L = 61, W = 14, M = 31, and T = 32, sum them to find the answer:

$$61 + 14 + 31 + 32 = 138$$
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Director
Joined: 22 Jun 2019
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Kudos [?]: 103 [0], given: 161

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  09 Jul 2019, 02:05
sandy wrote:
Lou has three daughters: Wen, Mildred, and Tyla. Three years ago, when Lou was twice as old as Tyla, he was 30 years older than Mildred. Now, he is 47 years older than Wen. In 4 years, Wen will be half as old as Tyla. What is the sum of the current ages of Lou and his three daughters?

(A) 138
(B) 144
(C) 154
(D) 166
(E) 181

Is this really a REAL GRE type question where as GRE do not concern about long tedious calculation rather than mathematical logic.
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Manager
Joined: 01 Jan 2020
Posts: 112
Concentration: Marketing
Schools: Copenhagen Business School - Class of 2022
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Kudos [?]: 57 [0], given: 46

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  02 Mar 2020, 10:25
Had exactly the same thinking as huda while I was doing this exercise, yet it is a good exercise for writing the formulas correctly out!
Intern
Joined: 09 Jan 2020
Posts: 20
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Kudos [?]: 10 [0], given: 8

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  04 Mar 2020, 09:03
My method is attached.
Attachments

Screenshot 2020-03-04 at 17.01.59.png [ 388.32 KiB | Viewed 915 times ]

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years   [#permalink] 04 Mar 2020, 09:03
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