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Tough and Tricky questions: Word Problems.

Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be

Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be

Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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03 Nov 2014, 20:11

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Bunuel wrote:

Tough and Tricky questions: Word Problems.

Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the age of the boy and the combined ages of the girls will be

A. 1 B. 2 C. 3 D. –2 E. –1

Kudos for a correct solution.

Approach I (Plugin's)

Girl I ............... Girl II ................ Boy

1 ....................... 1 ........................ 3 (Assume the current ages)

1 + 1 < 3 .......... (Satisfies the given condition)

Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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15 Jan 2017, 20:06

Each year, the age of the boy increases by 1. Each year, the sum of the ages of the two girls increases by 2 (as each girl gets older by one year, and there are two of them). Let's say that the age of the boy today is equal to x, while the combined ages of the girls today is equal to y. Then, next year the figures will be x + 1 and y + 2, respectively. The problem states that these two figures will be equal, which yields the following equation:

x + 1 = y + 2 which can be simplified to x = y + 1

(This is consistent with the fact that the sum of the ages of the two girls today is smaller than the age of the boy today.) Three years from now, the combined age of the girls will be y + 3(2) = y + 6. Three years from now, the boy's age will be x + 3. Using the fact (from above) that x = y + 1, the boy's age three years from now can be written as x + 3 = (y + 1) + 3 = y + 4. The problem asks for the difference between the age of the boy three years from today and the combined ages of the girls three years from today. This difference equals y + 4 – (y + 6) = –2. The correct answer is D.

Plug in real numbers to see if this makes sense. Let the girls be 4 and 6 in age. The sum of their ages today is 10. The boy's age today is then (10 + 1) = 11. Three years from today, the girls will be 7 and 9 respectively, so their combined age will be 16. Three years from today, the boy will be 14.
_________________

Roberto has three children: two girls and a boy. All were born on the [#permalink]

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18 Dec 2017, 20:21

anairamitch1804 wrote:

Each year, the age of the boy increases by 1. Each year, the sum of the ages of the two girls increases by 2 (as each girl gets older by one year, and there are two of them). Let's say that the age of the boy today is equal to x, while the combined ages of the girls today is equal to y. Then, next year the figures will be x + 1 and y + 2, respectively. The problem states that these two figures will be equal, which yields the following equation:

x + 1 = y + 2 which can be simplified to x = y + 1

(This is consistent with the fact that the sum of the ages of the two girls today is smaller than the age of the boy today.) Three years from now, the combined age of the girls will be y + 3(2) = y + 6. Three years from now, the boy's age will be x + 3. Using the fact (from above) that x = y + 1, the boy's age three years from now can be written as x + 3 = (y + 1) + 3 = y + 4. The problem asks for the difference between the age of the boy three years from today and the combined ages of the girls three years from today. This difference equals y + 4 – (y + 6) = –2. The correct answer is D.

Plug in real numbers to see if this makes sense. Let the girls be 4 and 6 in age. The sum of their ages today is 10. The boy's age today is then (10 + 1) = 11. Three years from today, the girls will be 7 and 9 respectively, so their combined age will be 16. Three years from today, the boy will be 14.

When it says " Difference" between the boys age and girls age does it necessarily mean Boys age - Girls Age or can it also mean Girls age - Boys age . For example : Difference between A and B does it necessarily mean A-B or can it mean B-A too! Hence if we go (Girl 1 + Girl 2) - Boy = 2 But if we go Boy - ( Girl 1 + Girl 2)= -2 So how are we sure that the latter is being asked here ?
_________________

This question can be solved rather easily by TESTing VALUES. It is oddly-worded though and not written in the 'style' that Official GMAT questions is written in. I'm going to deal with the information in a slightly out-of-order fashion...

We're told that A YEAR FROM NOW the sum of the ages of the two girls will equal the age of the boy...

IF.... in ONE YEAR.... 1st Girl = 2 2nd Girl = 3 Boy = 5

Right NOW... 1st Girl = 1 2nd Girl = 2 Boy = 4

Three years from NOW... 1st Girl = 1+3 = 4 2nd Girl = 2+3 = 5 Boy = 4+3 = 7

Thus, in three years, the difference between the sum of the girls ages (9) and the age of the boy (7) is 2. The author of the prompt wants us to subtract the sum of the girls' ages from the age of the boy, but the author uses the word "difference", which in conventional terms is always considered a positive number (e.g. the difference in points scored by two sports teams is "2 points", not "-2 points"). If this question appeared on the Official GMAT, and we were meant to choose the listed correct answer D, then the prompt would have stated something to the effect of "In three years, the age of the boy minus the sum of the ages of the two girls would be...?"