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DS from Gurome blog

by rahulvsd » Tue Aug 23, 2011 8:50 am
The total age of the father, brother, and sister was 64. How old was the sister?

(1) When the age of the father was three times of the age of the brother, the sister was nine years old.

(2) When the brother was twice as old as his sister, the father was 34 years old.

Experts the answer given in the blog says b.[spoiler] Please help me out with the explanation provided for the question in the link,for statement1. https://www.gurome.com/Blog/21151 [/spoiler]
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by arashyazdiha » Tue Aug 23, 2011 9:43 am
f:father
b:brother
s:sister

if f+b+s = 64 what is s?
1)(f-(s-9))=3*(b-(s-9))----------->f-s+9 = 3b-3s+27------>f-3b+2s = 18
(s-9) is the difference between the current age and the age given in the 1st statement because they are all (s-9) years older.
We now have f-3b+2s=18 and f+b+s=64 altogether, but we can not solve it.

2)b-(f-34) = 2*(s-(f-34))-------->b-f+34 = 2s-2f+68------>b+f-2s = 34
now we have b+f-2s = 34 and b+f+s = 64, if we subtract these two statements. we will have 3s = 30, so s is 10, and this one alone is sufficient.

bests
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by GMATGuruNY » Tue Aug 23, 2011 7:39 pm
rahulvsd wrote:The total age of the father, brother, and sister was 64. How old was the sister?

(1) When the age of the father was three times of the age of the brother, the sister was nine years old.

(2) When the brother was twice as old as his sister, the father was 34 years old.

Experts the answer given in the blog says b.[spoiler] Please help me out with the explanation provided for the question in the link,for statement1. https://www.gurome.com/Blog/21151 [/spoiler]
Let F = current age of the father.
Let B = current age of the brother.
Let S = current age of the sister.
F+B+S = 64.

Statement 1: When the age of the father was three times of the age of the brother, the sister was nine years old.
Number of years ago that the sister was 9 = S-9.
S-9 years ago, the age of the father = F - (S-9) = F-S+9
S-9 years ago, the age of the brother = B - (S-9) = B-S+9

Since the age of the father was 3 times the age of the brother, we get:
F-S+9 = 3(B-S+9)
F-S+9 = 3B-3S+27
F+2S-3B = 18.
No way to solve for S.
Insufficient.

Statement 2: When the brother was twice as old as his sister, the father was 34 years old.
Number of years ago that the father was 34 = F-34.
F-34 years ago, the age of the brother = B - (F-34) = B-F+34.
F-34 years ago, the age of the sister = S - (F-34) = S-F+34.

Since the age of the brother was 2 times the age of the sister, we get:
B-F+34 = 2(S-F+34)
B-F+34 = 2S-2F+68
B+F = 2S+34

The equation in the question stem implies that B+F = 64-S.
Since B+F = 2S+34 and B+F = 64-S:
2S+34 = 64-S
3S=30
S=10.
Sufficient.

The correct answer is B.
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by gmatdriller » Wed Aug 24, 2011 9:24 am
that was an interesting one.
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by winniethepooh » Wed Aug 24, 2011 4:58 pm
GMATGuruNY wrote:
rahulvsd wrote:The total age of the father, brother, and sister was 64. How old was the sister?

(1) When the age of the father was three times of the age of the brother, the sister was nine years old.

(2) When the brother was twice as old as his sister, the father was 34 years old.

Experts the answer given in the blog says b.[spoiler] Please help me out with the explanation provided for the question in the link,for statement1. https://www.gurome.com/Blog/21151 [/spoiler]
Let F = current age of the father.
Let B = current age of the brother.
Let S = current age of the sister.
F+B+S = 64.

Statement 1: When the age of the father was three times of the age of the brother, the sister was nine years old.
Number of years ago that the sister was 9 = S-9.
S-9 years ago, the age of the father = F - (S-9) = F-S+9
S-9 years ago, the age of the brother = B - (S-9) = B-S+9

Since the age of the father was 3 times the age of the brother, we get:
F-S+9 = 3(B-S+9)
F-S+9 = 3B-3S+27
F+2S-3B = 18.
No way to solve for S.
Insufficient.

Statement 2: When the brother was twice as old as his sister, the father was 34 years old.
Number of years ago that the father was 34 = F-34
F-34 years ago, the age of the brother = B - (F-34) = B-F+34.
F-34 years ago, the age of the sister = S - (F-34) = S-F+34.

Since the age of the brother was 2 times the age of the sister, we get:
B-F+34 = 2(S-F+34)
B-F+34 = 2S-2F+68
B+F = 2S+34

The equation in the question stem implies that B+F = 64-S.
Since B+F = 2S+34 and B+F = 64-S:
2S+34 = 64-S
3S=30
S=10.
Sufficient.

The correct answer is B.
Hi Mitch, in your post above, how did you get the statements in dark red?
I am a bit comfused.
Isn't the wordings of the problem very ambiguous?
Your help is really appreciated.
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by GMATGuruNY » Thu Aug 25, 2011 3:24 am
winniethepooh wrote:
GMATGuruNY wrote:
rahulvsd wrote:The total age of the father, brother, and sister was 64. How old was the sister?

(1) When the age of the father was three times of the age of the brother, the sister was nine years old.

(2) When the brother was twice as old as his sister, the father was 34 years old.

Statement 2: When the brother was twice as old as his sister, the father was 34 years old.
Number of years ago that the father was 34 = F-34
F-34 years ago, the age of the brother = B - (F-34) = B-F+34.
F-34 years ago, the age of the sister = S - (F-34) = S-F+34.

Since the age of the brother was 2 times the age of the sister, we get:
B-F+34 = 2(S-F+34)
B-F+34 = 2S-2F+68
B+F = 2S+34

The equation in the question stem implies that B+F = 64-S.
Since B+F = 2S+34 and B+F = 64-S:
2S+34 = 64-S
3S=30
S=10.
Sufficient.

The correct answer is B.
Hi Mitch, in your post above, how did you get the statements in dark red?
I am a bit comfused.
Isn't the wordings of the problem very ambiguous?
Your help is really appreciated.
First red statement:

F = the age of the father now.
34 = the age of the father when he was 34.
F-34 = the difference between the father's age now and his age when he was 34.
In other words, F-34 = the number of years ago the father was 34.

To illustrate:
If the father is 60 now, 60-34=26 years ago he was 34.
If the father is 70 now, 70-34=36 years ago he was 34.

Second red statement:
The question stem indicates that F+B+S = 64.
Thus, B+F = 64-S.

Statement 2 indicates that B+F = 2S+34. (See my post above.)

B+F = 2S+34
B+F = 64-S

Subtracting the second equation from the first, we get:
0 = 3S-30
S=10.
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by navami » Thu Aug 25, 2011 4:01 am
Interesting problem
This time no looking back!!!
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by [email protected] » Wed Sep 07, 2011 12:41 pm
GMATGuruNY wrote:
rahulvsd wrote:The total age of the father, brother, and sister was 64. How old was the sister?

(1) When the age of the father was three times of the age of the brother, the sister was nine years old.

(2) When the brother was twice as old as his sister, the father was 34 years old.

Experts the answer given in the blog says b.[spoiler] Please help me out with the explanation provided for the question in the link,for statement1. https://www.gurome.com/Blog/21151 [/spoiler]
Let F = current age of the father.
Let B = current age of the brother.
Let S = current age of the sister.
F+B+S = 64.

Statement 1: When the age of the father was three times of the age of the brother, the sister was nine years old.
Number of years ago that the sister was 9 = S-9.
S-9 years ago, the age of the father = F - (S-9) = F-S+9
S-9 years ago, the age of the brother = B - (S-9) = B-S+9

Since the age of the father was 3 times the age of the brother, we get:
F-S+9 = 3(B-S+9)
F-S+9 = 3B-3S+27
F+2S-3B = 18.
No way to solve for S.
Insufficient.

Statement 2: When the brother was twice as old as his sister, the father was 34 years old.
Number of years ago that the father was 34 = F-34.
F-34 years ago, the age of the brother = B - (F-34) = B-F+34.
F-34 years ago, the age of the sister = S - (F-34) = S-F+34.

Since the age of the brother was 2 times the age of the sister, we get:
B-F+34 = 2(S-F+34)
B-F+34 = 2S-2F+68
B+F = 2S+34

The equation in the question stem implies that B+F = 64-S.
Since B+F = 2S+34 and B+F = 64-S:
2S+34 = 64-S
3S=30
S=10.
Sufficient.

The correct answer is B.
THANKS FOR YOUR REPLY
BUT SIR CAN YOU TELL ME HOW YOU ASSUME (IN BOTH STATEMENT A AND B)THAT
A: When the age of the father was three times of the age of the brother, the sister was nine years old.[/b]
Number of years ago that the sister was 9 = S-9.
B: When the brother was twice as old as his sister, the father was 34 years old.[/b]
Number of years ago that the father was 34 = F-34.
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