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in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

if x is a +ve integer, is x³ - 3x² + 2x divisible by 4? (1) x = 4y + 4, where y is an integer (2) x = 2z + 2, where z is an integer

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

If x is a positive integer , is x^3 - 3x^2+2x divisible by 4?

(1) x=4y+4, where y is an integer --> since x itself is divisible by 4 then x^3-3x^2+2x is divisible by 4. Sufficient.

(2) x=2z+2, where z is an integer --> x^3-3x^2+2x=x(x^2-3x+2)=(2z+2)(4z^2+8z+4-6z-6+2)=4(z+1)(2z^2+z) --> hence this expression is divisible by 4. Sufficient.

Answer: D.

As for your question: if x=2 then x^3-3x^2+2x=0. Now, zero is divisible by EVERY integer except zero itself, as 0/integer=integer.

if x is a +ve integer, is x³ - 3x² + 2x divisible by 4? (1) x = 4y + 4, where y is an integer (2) x = 2z + 2, where z is an integer

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

If x is a positive integer , is x^3 - 3x^2+2x divisible by 4?

(1) x=4y+4, where y is an integer --> since x itself is divisible by 4 then x^3-3x^2+2x is divisible by 4. Sufficient.

(2) x=2z+2, where z is an integer --> x^3-3x^2+2x=x(x^2-3x+2)=(2z+2)(4z^2+8z+4-6z-6+2)=4(z+1)(2z^2+z) --> hence this expression is divisible by 4. Sufficient.

Answer: D.

As for your question: if x=2 then x^3-3x^2+2x=0. Now, zero is divisible by EVERY integer except zero itself, as 0/integer=integer.

For the second statement could one only say that since x is a multiple of 2 and thus even then x-2 will also be even and that means that E*E = E and multiple of 4?

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

Bunuel - could we have solved/approached the question this way?

Given the question stem - x^3-3x^2+2x - factor out an "x" and apply the FOIL method --> therefore we are left with x(x^2 - 3x +2x) = 0 --> x(x - 2)(x - 1) Therefore, x must equal 0, 1, or 2

With that said, plug in the values of 0, 1, and 2 into each of statement one and two to determine if they are sufficient Statement 1 --> only 0 works Statement 2 --> both 0 and 2 work (due to the value being an integer)

Therefore, OA is D because we can determine what exact values of of the question stems can be valid.

Let me know what you think, just trying to help out with different ways to approach this question.

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

Bunuel - could we have solved/approached the question this way?

Given the question stem - x^3-3x^2+2x - factor out an "x" and apply the FOIL method --> therefore we are left with x(x^2 - 3x +2x) = 0 --> x(x - 2)(x - 1) Therefore, x must equal 0, 1, or 2

With that said, plug in the values of 0, 1, and 2 into each of statement one and two to determine if they are sufficient Statement 1 --> only 0 works Statement 2 --> both 0 and 2 work (due to the value being an integer)

Therefore, OA is D because we can determine what exact values of of the question stems can be valid.

Let me know what you think, just trying to help out with different ways to approach this question.

Your approach is not correct. Notice that we are NOT told that x^3-3x^2+2x is 0, thus your derivation that x is 0, 1, or 2 is not right.
_________________

if x is a +ve integer, is x³ - 3x² + 2x divisible by 4? (1) x = 4y + 4, where y is an integer (2) x = 2z + 2, where z is an integer

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

If x is a positive integer , is x^3 - 3x^2+2x divisible by 4?

(1) x=4y+4, where y is an integer --> since x itself is divisible by 4 then x^3-3x^2+2x is divisible by 4. Sufficient.

(2) x=2z+2, where z is an integer --> x^3-3x^2+2x=x(x^2-3x+2)=(2z+2)(4z^2+8z+4-6z-6+2)=4(z+1)(2z^2+z) --> hence this expression is divisible by 4. Sufficient.

Answer: D.

As for your question: if x=2 then x^3-3x^2+2x=0. Now, zero is divisible by EVERY integer except zero itself, as 0/integer=integer.

if x is a +ve integer, is x³ - 3x² + 2x divisible by 4? (1) x = 4y + 4, where y is an integer (2) x = 2z + 2, where z is an integer

in the above (1) is exactly a multiple for 4, so sufficient BUT in (2) if z = 0 , then x = 2, which when substituted in quest will not be divisible by 4. right? but the answer is D, both alone sufieicient

can anyone guide. do i have a wrong approach towards DS??

If x is a positive integer , is x^3 - 3x^2+2x divisible by 4?

(1) x=4y+4, where y is an integer --> since x itself is divisible by 4 then x^3-3x^2+2x is divisible by 4. Sufficient.

(2) x=2z+2, where z is an integer --> x^3-3x^2+2x=x(x^2-3x+2)=(2z+2)(4z^2+8z+4-6z-6+2)=4(z+1)(2z^2+z) --> hence this expression is divisible by 4. Sufficient.

Answer: D.

As for your question: if x=2 then x^3-3x^2+2x=0. Now, zero is divisible by EVERY integer except zero itself, as 0/integer=integer.

Re: If x is a positive integer, is x^3-3x^2+2x divisible by 4? [#permalink]

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31 Mar 2015, 07:16

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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.

If x is a positive integer, is x^3-3x^2+2x divisible by 4?

(1) x=4y+4, where y is an integer (2) x=2z+2, where z is an integer

If we modify the question, x^3-3x^2+2x=4t? (t is an integer), --> x(x^2-3x+2)=4t? and we ultimately want to know whether x(x-1)(x-2)=4t, which is the same as whether x-2 is even For condition 1, from x=4y+4, x-2=4y+2=2(2y+1). This is even and the condition is sufficient For condition 2, from x=2z+2, x-2=2z. This is also even and the condition sufficiently answers the question 'yes' The answer becomes (D).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If x is a positive integer, is x^3-3x^2+2x divisible by 4? [#permalink]

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26 Aug 2016, 05:43

I simplified the prompt to is x(x-2)(x-1)/4.?

In S1: Any value of y would satisfy the equation, hence it is sufficient In S2: All the values of z above integer 0 would satisfy the condition, and if I consider z=0, then the numerator becomes 0, and 0 divided by any integer will yield 0. Hence it should be sufficient.

I always pick numbers for testing cases in DS problems. Is that a good practice.?

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