Data Sufficiency

I had a question hopefully someone can help me with.

if 2x (5n) = t, what is the value of t?

1) x = n+3
2) 2x = 32

I realize 1 and 2 by themselves are not sufficient which is obvious. But the approach I took gives me two solutions, making it answer choice E, but the official answer is C.

What i did:
1) x=n+3
10(n+3)n = t
10n^2 + 30n = t

N.S

2) 2x = 32
x=16
t=10(16)n = 160n
N.S

1+2)

10n^2 + 30n = t
t=160n from 2, so
10n^2 + 30n = 160n

10n^2 - 130n = 0
n^2 - 13n = 0
n(n-13) = 0

n = 0 or n = 13

since the problem suggests nothing about n being non zero or positive or negative, i took the two answers to mean this is NS and chose E.

Why is this wrong?
The actual answer is just 13 since 1) since x = n+3, and 2 gives x = 16, so n = 16-3 = 133 and thus C is correct answer. C seems a bit too obvious though, which is another reason I'm now thinking it seems even more obvious.

The answer is C. Just solve for t using the info given in statement 1&2.

Starting with statement 2:

32*(5n) = t

Then:

16 = n + 3
n = 13

So:

t = 32*(5*13)

2x(5n) = t

Value -- what is t? In order for a statement to be sufficient, it must tell us BOTH "x" and "n".

1) x = n + 3. This allows us to rewrite the equation in terms of n or in terms of x, but we cannot solve for t since we will still have two unknowns.

2) 2x = 32. This tells us x = 16, but we still don't know n.

If we combine, we know that x = 16.
16 = n + 3, so n = 13. We can now find t.

For DS, I wouldn't worry about doing so much math, like what you've tried above. We don't actually have to solve, we merely have to determine whether we CAN solve. I sometimes see students get in trouble by over-thinking DS or doing too much unnecessary math. Think of the question in these over-simplified terms:

We have to find t (so we need x AND n).

1) provides a relationship between x and n
2) provides a value for x

Together they will be suff.

Thanks Vivian, I'm certainly guilty of over analyzing gmat questions, but the reason is that i've messed up more than my fair share of questions where I think something is sufficient by looking at the data, but it really isn't because x is a quadratic and thus has two solutions (such as the way I did this question), or where we have to consider not only the positive, but also the negative possibility or that something could be zero if not explicitly mentioned in the question that it isn't. Just from todays practice session I know I messed up 2 questions because i forgot to consider negative possibilities or something along those lines.

I do understand your method, and seems very obvious to do it this way after i look at your explanation. I'm just wondering why is it that mathematically if I do it my way I get two solutions. is there something wrong with my calculations or something i've failed to consider?

VivianKerr wrote:2x(5n) = t

Value -- what is t? In order for a statement to be sufficient, it must tell us BOTH "x" and "n".

1) x = n + 3. This allows us to rewrite the equation in terms of n or in terms of x, but we cannot solve for t since we will still have two unknowns.

2) 2x = 32. This tells us x = 16, but we still don't know n.

If we combine, we know that x = 16.
16 = n + 3, so n = 13. We can now find t.

For DS, I wouldn't worry about doing so much math, like what you've tried above. We don't actually have to solve, we merely have to determine whether we CAN solve. I sometimes see students get in trouble by over-thinking DS or doing too much unnecessary math. Think of the question in these over-simplified terms:

We have to find t (so we need x AND n).

1) provides a relationship between x and n
2) provides a value for x

Together they will be suff.

there are two unknown variables x and n which should be found for giving value of t.
using option 1 - we cannot find value of only one variable. either x or n and not both
using option 2 - we can find value of x. but still n is unknown

Option C is correct. because both options help us in finding x and n

For the follow question, I did exactly the same as Zank did.

if 2x (5n) = t, what is the value of t?

1) x = n+3
2) 2x = 32

I realize 1 and 2 by themselves are not sufficient which is obvious. But the approach I took gives me two solutions, making it answer choice E, but the official answer is C.

What i did:
1) x=n+3
10(n+3)n = t
10n^2 + 30n = t

N.S

2) 2x = 32
x=16
t=10(16)n = 160n
N.S

1+2)

10n^2 + 30n = t
t=160n from 2, so
10n^2 + 30n = 160n

10n^2 - 130n = 0
n^2 - 13n = 0
n(n-13) = 0

n = 0 or n = 13

since the problem suggests nothing about n being non zero or positive or negative, i took the two answers to mean this is NS and chose E.

Why is this wrong?
The actual answer is just 13 since 1) since x = n+3, and 2 gives x = 16, so n = 16-3 = 133 and thus C is correct answer. C seems a bit too obvious though, which is another reason I'm now thinking it seems even more obvious.

Can experts comment on why is this method/calculation wrong?

Thanks a lot in advance
Pooja

Zero is not a possible value because it would invalidate statement 2.

If n=13 and x = n+3, then x=16, which fits statement 2.

If n=0 and x = n+3, then x = 0, which violates statement 2.

zank wrote:I had a question hopefully someone can help me with.

if 2x (5n) = t, what is the value of t?

1) x = n+3
2) 2x = 32

I realize 1 and 2 by themselves are not sufficient which is obvious. But the approach I took gives me two solutions, making it answer choice E, but the official answer is C.

What i did:
1) x=n+3
10(n+3)n = t
10n^2 + 30n = t

N.S

2) 2x = 32
x=16
t=10(16)n = 160n
N.S

1+2)

10n^2 + 30n = t
t=160n from 2, so
10n^2 + 30n = 160n

10n^2 - 130n = 0
n^2 - 13n = 0
n(n-13) = 0

n = 0 or n = 13

since the problem suggests nothing about n being non zero or positive or negative, i took the two answers to mean this is NS and chose E.

Why is this wrong?
The actual answer is just 13 since 1) since x = n+3, and 2 gives x = 16, so n = 16-3 = 133 and thus C is correct answer. C seems a bit too obvious though, which is another reason I'm now thinking it seems even more obvious.

I liked your NS, and I'd definitely use it in future.

You already have the answer of your query. If x is 16 only, then n is 13 only, and t is (10)(16)(13) only. Why worry for the quadratic?