IMO C:
Question asks whether n is a factor of t or t/n = integer
A: n=3^(n-2)
=> n = 3^n / 9 => 3^n = 9n
This doesn't give any information about t. Hence insufficient
B: t = 3^n
t/n = 3^n / n. If n = 2, t/n is not an integer
if n = 3, t/n is an integer. Hence insufficient
Combining A and B
t = 9n. t/n = 9 (integer). Hence sufficient.
Hope this helps
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factor of integer
Source: Beat The GMAT — Data Sufficiency |
thanks, the OA is the same but the official explanation is slightly different. this is where I'm a bit confused.
OA: Combining (1) and (2) provides the information that t=3^n where n=3^(n-2). thus, t=3^3^(n-2), which in turn yields t=3^(3n-6) or
3n^(n-2). this bit is rather unclear...where does 6 come from??
this can be restated as 3^3*3^(n-2) or 27*3^(n-2). since n=3^(n-2), then t = 27n.
BTW what does abbreviation IMO stand for?
OA: Combining (1) and (2) provides the information that t=3^n where n=3^(n-2). thus, t=3^3^(n-2), which in turn yields t=3^(3n-6) or
3n^(n-2). this bit is rather unclear...where does 6 come from??
this can be restated as 3^3*3^(n-2) or 27*3^(n-2). since n=3^(n-2), then t = 27n.
BTW what does abbreviation IMO stand for?
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That solution is simply incorrect. When they substitute for n, to get:LevelOne wrote:thanks, the OA is the same but the official explanation is slightly different. this is where I'm a bit confused.
OA: Combining (1) and (2) provides the information that t=3^n where n=3^(n-2). thus, t=3^3^(n-2), which in turn yields t=3^(3n-6) or
3n^(n-2). this bit is rather unclear...where does 6 come from??
this can be restated as 3^3*3^(n-2) or 27*3^(n-2). since n=3^(n-2), then t = 27n.
BTW what does abbreviation IMO stand for?
t = 3^(3^(n-2))
they've clearly misunderstood where the brackets are supposed to be. They seem to think that
t = (3^3)^(n-2)
which is wrong, and they've then rewritten that (correctly), using the exponent rule (x^a)^b = x^ab, as:
t = 3^(3n - 6)
It's more or less coincidental that they've arrived at the correct solution.
_______
When you do use both statements together, we know that n = 3^(n-2) and that t = 3^n. The question "is t divisible by n" then becomes "is 3^n divisible by 3^(n-2)?" The answer to that question is clearly yes, since the exponent in 3^(n-2) is smaller than the exponent in 3^n.
In fact, 3^n = (3^2)*(3^(n-2)) = 9*3^(n-2), so t = 9n (and not 27n, as the original solution contends).
You could look at the question in another way: the equation in Statement 1 has only one solution for n; n must be equal to 3. So using both statements we can find exact values for both n and t, and since that's the case, the question can certainly be answered using both statements together.
The questions in GMATFocus are great, but unfortunately there are problems with a few of the solutions.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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