princeton DS

[bblast]

If Brian's age is exactly one-third of Tanya's age, what is Brian's age?

(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age now.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age now.

OA-D

can someone solve this by the matrix method ?

[clock60]

hi, my try
if b=1/3*t find b-?
(1)(b-6)=1/5*(t-6), solving together with t=3*b, results in b=12
(2)(b+12)=1/2*(t+12), also results in b=12

[Stuart@KaplanGMAT]

If Brian's age is exactly one-third of Tanya's age, what is Brian's age?

(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age now.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age now.

OA-D

can someone solve this by the matrix method ?

Hi,

by far, the most powerful rule to remember in DS is the "number of equations/number of unknowns rule".

Here's the basic rule:

If you have the same number of distinct, linear, equations as you have unknowns, you can answer any question about the system.

Understanding this rule and when it's applicable will allow you to answer many DS questions without doing any math. Let's apply it to this question!

Q: If Brian's age is exactly one-third of Tanya's age, what is Brian's age?

We see: 1 linear equation, 2 variables. We're asked to solve for 1 of the variables.
We need: 1 more distinct and linear equation.

(1) Another equation. Go through a quick checklist:

- no new variables;
- different from our original equation (original one was just a multiplier, this one also has a -6); and
- linear (no squares or products of variables).

We now have 2 distinct linear equations for our 2 unknowns - sufficient!

(2) Another equation. Go through a quick checklist:

- no new variables;
- different from our original equation (original one was just a multiplier, this one also has a +12); and
- linear (no squares or products of variables).

We now have 2 distinct linear equations for our 2 unknowns - sufficient!

Each statement is sufficient alone, choose (D).

Remember: your goal in DS is not to actually solve the question; rather, your goal is to determine whether it's possible to solve the question. The better you understand the concepts underlying GMAT math the fewer calculations you'll have to make.

[Whitney Garner]

If Brian's age is exactly one-third of Tanya's age, what is Brian's age?

(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age now.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age now.

OA-D

can someone solve this by the matrix method ?

Hi bblast!

Can you please check the wording of this problem with the original source, because currently it is incorrect (the two statements do not agree). [See matrix method below]

Statement (1):
This compares Brian's age 6 years ago with Tanya's age NOW (See below, I believe the NOW is incorrect). So Brian 6 years ago was (1/5)T. But if Brian = (1/3)T now, then 6 years ago, he will be (1/3)T - 6, so we can set them equal and solve:

(1/5)T = (1/3)T - 6
6 = (2/15)T
T = 45
B = T/3 = 15

Statement (2);
This compares Brian's age IN 12 YEARS with Tanya's age NOW (see below, I believe the NOW is incorrect)
Now we see that in 12 years Brian is 1/2 T. But if Brian = (1/3)T now, then in 12 years he will be (1/3)T - 6, so we can set them equal and solve:

(1/2)T = (1/3)T + 12
(1/6)T = 12
T = 72
B = T/3 = 24

Notice that the Statements DO NOT MATCH. @Clock60, your intuition below was exactly right and I suspect that you worked the math for the correct question:

hi, my try
if b=1/3*t find b-?
(1)(b-6)=1/5*(t-6), solving together with t=3*b, results in b=12
(2)(b+12)=1/2*(t+12), also results in b=12

The work you are showing would be correct if the question were written as follows:

If Brian's age is exactly one-third of Tanya's age, what is Brian's age?

(1) Six years ago, Brian's age was exactly one-fifth of Tanya's age.
(2) Twelve years from now, Brian's age will be exactly one-half of Tanya's age.

Note that the difference between this version and that posted by the OP is the deletion of the word "now" at the end of each sentence.

Completing the version above with the box would be as follows:

Start with a blank box, with dates from the problem (Now, 6 years ago, 12 years from now), and fill in the info from the stem ONLY: Now, Brian is (1/3)T.



Statement (1):
6 years ago, Brian was (1/5) of Tanya's age (then). Because the Table is in T, move T into the past 6 years (T-6). Then set up Brian as (1/5) of that.



We also know that if Brian is (1/3)T now, 6 years ago he was (1/3)T - 6, so we can set that equal to what we have in the box:

(1/5)(T-6) = (1/3)T - 6
(1/5)T - 6/5 = (1/3)T - 6
6 - 6/5 = (1/3)T - (1/5)T
24/5 = (2/15)T
T = 36
B = (1/3)T = 12


Statement (2);
12 years from now, Brian will be (1/2) of Tanya's age (then). Because the Table is in T, move T into the future 12 years (T+12). Then set up Brian as (1/2) of that.



We also know that if Brian is (1/3)T now, in 12 years ago he will be (1/3)T + 12, so we can set that equal to what we have in the box:

(1/2)*(T+12) = (1/3)T + 12
(1/2)T + 6 = (1/3)T + 12
(1/2)T - (1/3)T = 6
(1/6)T = 6
T = 36
B = (1/3)T = 12

Hope this helps!!


Whit

[bblast]

The question is indeed ambiguous and wrongly worded. I have copied it as it was from the cat. even I reached different answers through 2 statements(15 and 24). Any princeton review rep here ?

[clock60]

to be honest when i solved this problem for the first time, i also got two different answers 15 and 24, but in gmat two st never contradict ech other, so i decided that my intial thinking was wrong, and resolved it obtaining 12 as an answer, perhaps this problem is poorly worded

[Whitney Garner]

to be honest when i solved this problem for the first time, i also got two different answers 15 and 24, but in gmat two st never contradict ech other, so i decided that my intial thinking was wrong, and resolved it obtaining 12 as an answer, perhaps this problem is poorly worded

You are EXACTLY right - in the universe of the GMAT, the statements:

(1) Are your friends (they are there to help)
(2) DO NOT LIE (which therefore means...)
(3) They do not contradict each other!

If this problem was copied exactly from the CAT, then I would contact someone to include this in their Errata list.


Whit