Three years from today..

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abhi332: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member; Location: India; Thanked: 4 times

by abhi332 » Thu Feb 25, 2010 12:41 pm

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

[spoiler]OA:D[/spoiler]

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Source: Beat The GMAT — Problem Solving | Thu Feb 25, 2010 12:41 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Thu Feb 25, 2010 1:12 pm

G=age of girl 1
G1=age of girl 2
B=age of boy

G+G1<B This info is not relevant

G+G1+2=B+1

G+G1+1=B

In 3 years, difference in boys age and the combined ages of the two girls will be:B+3-G-3-G1-3

B-(G+G1+3)=B-B-2=-2

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Anaira Mitch: Master | Next Rank: 500 Posts; Posts: 235; Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members; Thanked: 3 times

by Anaira Mitch » Sun Jan 15, 2017 8:06 pm

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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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Jan 15, 2017 8:43 pm

abhi332 wrote: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

[spoiler]OA:D[/spoiler]

Say the ages of two girls and a boy are x, y, and z, respectively, and TODAY falls after p years.

Then as per the first condition,

(x+p) + (y+p) < z+p
=> x+y+p < z ----(1)

As per the second condition,

(x+p+1) + (y+p+1) = z+p+1
=> x+y+p+1 = z ----(2)

As per the third condition,

We need to find out the value of (z+p+3) - [(x+p+3)+(y+p+3)]

(z+p+3) - [(x+p+3)+(y+p+3)] = z - (x+y)-p-3 ----(3)

By plugging in the value of z from equation (2) in (3), we get

z - (x+y)-p-3 = (x+y)+p+1- (x+y)-p-3 = -2

Answer: D

Hope this helps!

-Jay
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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Jan 16, 2017 5:51 am

abhi332 wrote: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

[spoiler]OA:D[/spoiler]

Let the combined age of girls be X and age of boy be Y
so X<Y

Also X+1+1 = Y+1 -> Y-X = 1

After 3 year, difference = (Y+3)- (X+3+3) = Y-X - 3 = 1-3 = -2 . [spoiler](D) is correct.[/spoiler]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 16, 2017 9:06 am

abhi332 wrote: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

[spoiler]OA:D[/spoiler]

Side note: The word difference is used unconventionally in this question. The GMAT typically treats the difference between two values as a positive difference.
For example, the difference between 2 and 5 is 3, just as the difference between 5 and 2 is 3.

An official example:

Is the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3?
(1) The variance for the set of measurements is 4.
(2) For each measurement, the difference between the mean and that measurement is 2

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Jan 16, 2017 11:06 am

Hi All,

While this is an old question, it can be solved rather easily by TESTing VALUES. It is poorly-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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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Jan 18, 2017 7:13 pm

Brent@GMATPrepNow wrote:The word difference is used unconventionally

Brent is such a nice guy that he put this charitably, but I'm a grump, so I'll put it more directly: the word difference is used DANGEROUSLY in this problem, and that makes the authorship suspect. Beyond elementary school, the difference between a and b is typically |a - b|, not (a - b), leading to difference â‰¥Â 0 in all cases. The GMAT takes this interpretation, so be sure to remember it: it will be necessary on many math problems, PS and DS alike.

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