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If Sara's age is exactly twice Bill's age, what is Sara's ag

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If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 18 Dec 2012, 06:43
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If Sara's age is exactly twice Bill's age, what is Sara's age?

(1) Four years ago, Sara's age was exactly 3 times Bill's age.
(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 18 Dec 2012, 06:47
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If Sara's age is exactly twice Bill's age, what is Sara's age?

Given: S = 2B.

(1) Four years ago, Sara's age was exactly 3 times Bill's age --> S - 4 = 3(B-4). We have two distinct linear equations (S - 4 = 3(B-4) and S = 2B) with two unknowns, thus we can solve for both. Sufficient.

(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age --> S + 8 =1.5(B + 8). The same here: we have two distinct linear equations with two unknowns, thus we can solve for both. Sufficient.

Answer: D.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 19 Mar 2013, 13:00
I solved this correctly via solving simultaneous equations ... but I could not understand the other approach the OG mentioned in the answer explanation : " another way to conclude that we can determine the value of s is to note that the pair of equations represents 2 non - parallel lines in the coordinate plane"
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 06 Apr 2013, 03:48
TheNona wrote:
I solved this correctly via solving simultaneous equations ... but I could not understand the other approach the OG mentioned in the answer explanation : " another way to conclude that we can determine the value of s is to note that the pair of equations represents 2 non - parallel lines in the coordinate plane"


What they try to say is that the equations can be considered linear functions with different slopes. Therefore they will intersect at a certain point leading to one solution.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 10 Jan 2014, 09:31
Walkabout wrote:
If Sara's age is exactly twice Bill's age, what is Sara's age?

(1) Four years ago, Sara's age was exactly 3 times Bill's age.
(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age.



We're given the equation S = 2B


1) S - 4 = 3(B - 4), we now have two equations and two unknowns, that's enough. Sufficient
2) S + 8 = 1.5(B + 8), again two equations and two unknowns, sufficient.

So, D.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 12 Oct 2014, 00:59
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I thought the answer would be A because

2) S=2B
and S+8 = 1.5(B+8); solve this we have B=4/3.5 => B is not an integer => insufficient

Should B and S be integers because they are years of age?
Could someone help to explain when integers should be considered and when not?
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 12 Oct 2014, 01:21
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trambn wrote:
I thought the answer would be A because

2) S=2B
and S+8 = 1.5(B+8); solve this we have B=4/3.5 => B is not an integer => insufficient

Should B and S be integers because they are years of age?
Could someone help to explain when integers should be considered and when not?


When you solve S + 8 =1.5(B + 8) and S = 2B you get B = 8 and S = 16.

Also, why should a statement be insufficient if the result is not an integer?

And finally, I haven't seen a single official question where age is not an integer.

Check other Age Problems in our Speial Questions Directory.

Hope it helps
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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: If Sara's age is exactly twice Bill's age, what is Sara's ag   [#permalink] 12 Oct 2014, 01:21
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