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

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

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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

A. 1
B. 2
C. 3
D. –2
E. –1

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

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New post 03 Nov 2014, 09:44
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.


Check other Age Problems HERE.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 03 Nov 2014, 15:08
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girl1: g1, girl2: g2, boy:b, these are the symbols for their ages today.

g1+g2<b

(1 year from now): (g1+1)+(g2+1) = b+1 ; g1+g2 = b-1

The difference between the girls's age and the boy's age is one today:

Assume ages, g1:20, g2:25, b:46 (notice the difference is currently 1); in 3 years the ages will be g1:23, g2:28, b:49 ; 49-(23+28) = -2

The Answer should be D.

or b-g1-g2=1; in 3 years the eqn should be (b+3)-(g1+3)-(g2+3)=1-3=-2 (subtracted -3 from the RHS to balance both sides of the eqn)

Bunuel, can you please confirm the soln :)
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Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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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)

1 Year later there ages are

2 ....................... 2 ......................... 4

2 + 2 = 4 ............ (Satisfies the given condition)


After 3 years there ages are


4 ....................... 4 ............................ 6


Difference = 6 - (4+4) = 6 - 8 = -2

Answer = D

Approach II (Arithmetic)

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

a ........................ b ...................... c (Assume there current ages; a+b < c)

a+1 ................... b+1 ................... c+1 (Ages after 1 year)

Given that a+1 + b+1 = c+1

a+b = c - 1 ................... (1)

a+3 .................... b+3 .................. c+3 (Ages 3 years later from today)

Difference = c+3 - (a+3+b+3)

= c + 3 - (c-1+6) ............ Substitute from (1)

= 3 - 5 = -2

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

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New post 26 Jun 2016, 13:51
one year from now, G+g=b
two years after that, G+2+g+2=b+2
➡G+g-b=2-4=-2
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Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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New post 27 Jun 2016, 00:00
let g1 and g2 denote age of the girls
now,
as per the question
g1+g2 < b1 --- now
g1+g2+2 = b1+1 (one year from today) ---1

3 years from today the combined age of the girls is
g1+g2+6
or,
g1+g2+6 = b1+1+4 (substituting the value from 1)

difference = b1+3 - (b1+5) = -2
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Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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New post 15 Jan 2017, 21:06
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.
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Roberto has three children: two girls and a boy. All were born on the [#permalink]

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New post 18 Dec 2017, 21:21
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 ?
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Re: Roberto has three children: two girls and a boy. All were born on the [#permalink]

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New post 20 Jan 2018, 15:16
Hi All,

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...?"

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Re: Roberto has three children: two girls and a boy. All were born on the   [#permalink] 20 Jan 2018, 15:16
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