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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??

Re: data sufficiency [#permalink]
06 Feb 2012, 12:44

Expert's post

kashishh wrote:

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: data sufficiency [#permalink]
11 Jan 2014, 16:37

Bunuel wrote:

kashishh wrote:

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. _________________

Re: data sufficiency [#permalink]
29 Jan 2014, 14:47

Bunuel wrote:

kashishh wrote:

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: data sufficiency [#permalink]
29 Jan 2014, 21:52

Expert's post

jlgdr wrote:

Bunuel wrote:

kashishh wrote:

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.