sud21 wrote:For positive integer n, is the product (n)(n+1)(n+2) divisible by 24?
1. n is even
2. n + 2 = 6

24 could be rewritten as 2x3x4

1. n= even
if n= 2; 2x3x4 / 2x3x4 = 1 satisfied
if n= 6; 6x7x8 / 2x3x4 = 14 satisfied
any even number we use for n will always satisfy the equation
statement is sufficent

2. n+2=6; n= 4
4x5x6 / 2x3x4 = 5
statement is sufficent

ans = d

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.

For positive integer n, is the product (n)(n+1)(n+2) divisible by 24?
1. n is even
2. n + 2 = 6

Transforming the original condition and the question, for n(n+1)(n+2) to be divisible by 24 it means n = even. Therefore the question is practically asking whether n is even or not. Since 1) =2), the answer is D.

Once we transform and check the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

And for 95% of questions where 1)=2), the answer is usually D

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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.

Is ab odd?
1. a is even
2. a is an integer

In the original condition there are 2 variables (a,b), thus we need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C has high probability of being the answer. Using both 1) & 2) together, the answer is no if a=2,b=1, while the answer is yes if a=2, b=1/2. Therefore the conditions are not sufficient and the answer is E.

) Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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See our Youtube demo (https://www.youtube.com/watch?v=R_Fki3_2vO8)

Since n, (n + 1), and (n + 2) are three consecutive integers, one of them MUST be a multiple of 3. So the number will always divide by 3. We need it to divide by 24, or 3*8, so the question becomes "Is n * (n + 1) * (n + 2) divisible by 8?"

S1:: n is even.

Since n is even, (n + 2) must also be even. This gives us two CONSECUTIVE evens, so one is divisible by 2 and the other is divisible by 4. This gives us n * (n + 2) divisible by 2*4, or 8, so we DO have a multiple of 8 after all; SUFFICIENT.

S2:: This gives the unique value of n and hence must be SUFFICIENT.

Max wrote:And for 95% of questions where 1)=2), the answer is usually D

Nah. If #1 = #2, then the answer is either D or E, and it's E fairly often in my experience.

Of course in this question, #1 ≠ #2, as #2 restricts n to a single value while #1 allows for an infinite number of possibilities, all with a governing condition.