The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the value of the positive integer n ?

(1) n^4 < 25
(2) \(n\neq{n^2}\)


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Its C..

STATEMENT 1===== n4<25.. n can 1 AND 2.. 1^4=1 that is less than 25. N2=16 that is less than 25.

Statement 2====== n is not equal to n2 .. from this we can say this n is not 1..bt we dont knw n cud be 2 ,3 or 4 not sufficient.

Both statement togather are sufficient. n is 2 because from statement 1 we got that n cud be 2 or 1 ..and from statement 2 we got that n can not 1..so n is 2..sufficient.
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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.
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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
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