What is the value of the positive integer n ?

1. The 2 numbers that have 4th power less than 25 are 1 and 2; 1 and 16
2. From this, n is anything but 1;

Both together, clearly, gives the value as 2. Sufficient.

(C).

Statement 1) n^4 < 25, both the values of n = 1 or 2 satisfies the statement. Not Sufficient.
Statement 2) n is not equal to n^2. We cannot determine any value of n from this statement. Not Sufficient.

Combining the two statement, only n = 2 satisfies both the condition. Hence Option C)

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

What is the value of the positive integer n ?

(1) n^4 < 25
(2) n≠n 2

In the original condition there is 1 variable (n) and in order to match the number of variable and equation, we need 1 equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.

in case of 1), n=1,2 the answer is not unique, therefore the condition is NOT sufficient.
in case of 2), n=2,3.4.... and the answer is not unique. therefore the condition is NOT sufficient.
Using both 1) & 2) together, the answer is unique and therefore the conditions are sufficient. Thus the answer is C

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

Hi,
using 1 and 2 separately is true for any of the options... be it A,B,C,D,E..
i do not think the observation of any two equations given would be the same.. equality and inequality of equations will have a great say on the possiblity of that equation giving us the answer so 59% may not be true for eq using < or >...

n^4 < 25

We see that n can be 1 or 2. Statement one is not sufficient.

Statement Two Alone:

n ≠ n^2

We see that if n > 1, then n ≠ n^2. Since n can be an infinite number of values, statement two alone is not sufficient.

Statements One and Two Together:

From statement 1, we know that n can be 1 or 2. Statement 2 says that n ≠ n^2, and so n cannot equal 1 (since 1 = 1^2). Using statements one and two, we see that n must be 2.

Answer: C

S1: there is no unique value of n through this statement. It could be any from= 0,1 and 2. Insufficient. Strike-off AD
S2. this could literally be any positive integer; therefore, no unique value found. Insufficient. Strike-off B

Combining the two, we can cross-off 0 and 1; what remains is 2, which definitely is a unique solution.

Final answer: C

(1) n^4 < 25
Possible values of n are 1 and 2 (Insufficient)

(2) n≠n2
This implies n is not equal to 1 which does not give us the value of n.It tells us what n cannot be.(Insufficient)

Combining both, n=2 (Sufficient)
(option c)

Devmitra Sen
GMAT SME

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