Interesting DS question
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- prateek_guy2004
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Without even solving it one should understand that in 1 st equation its +2 which is a divisible of 4 and second statement too is a div of 4. so answer is D.
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I think the answer is A. because it says x >0
and using the 1st option -> x=4y+4, we have to make sure we put such a value y that makes x >0. So if we put y = -1 then x = -4+4 = 0 so y=-1 is an invalid choice.
Let us try with y = 0, then x = 4 -- divisible by 4. and as in this equation we are adding it with an even number and multiplying by 4 so the result will always be even. Putting x=4 in the main equation
-> 64-48+8 = 24, divisible by 4.
Option 2 - The same rule applies here. We can not assume z to be -1, that will make x as 0. so let us try with 0. that will give us x = 2 and putting it in the main equation - 8-12+4 =0 which is not divisible by 4. So the answer should be A.
Thanks.
Anshul
and using the 1st option -> x=4y+4, we have to make sure we put such a value y that makes x >0. So if we put y = -1 then x = -4+4 = 0 so y=-1 is an invalid choice.
Let us try with y = 0, then x = 4 -- divisible by 4. and as in this equation we are adding it with an even number and multiplying by 4 so the result will always be even. Putting x=4 in the main equation
-> 64-48+8 = 24, divisible by 4.
Option 2 - The same rule applies here. We can not assume z to be -1, that will make x as 0. so let us try with 0. that will give us x = 2 and putting it in the main equation - 8-12+4 =0 which is not divisible by 4. So the answer should be A.
Thanks.
Anshul
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I agree... even though the OA is apparently D, can anyone find fault with anshul's explanation of the problem?
The Fault with Anshul Explanantion is :
Stacey Comment :
FYI: the term divisible, or evenly divisible, means that there is no remainder when solving. Zero divided by anything but zero equals zero. No remainder - so zero is, in fact, divisible by 4 (or anything except zero). Zero divided by zero is undefined.
Stacey Comment :
FYI: the term divisible, or evenly divisible, means that there is no remainder when solving. Zero divided by anything but zero equals zero. No remainder - so zero is, in fact, divisible by 4 (or anything except zero). Zero divided by zero is undefined.
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Its much easier if we factorise the initial expression to x(x-1)(x-2)
A.) Now when x = 4y + 4 , the expression is divisible by 4 as x is divisible by 4.
B.) Now when x = 2z + 2, then the expression is (2z+2)(2z+1)2z
Again this is equal to 4(z+1)(2z+1)(z), which is divisible by 4.
Hence D is the answer.
A.) Now when x = 4y + 4 , the expression is divisible by 4 as x is divisible by 4.
B.) Now when x = 2z + 2, then the expression is (2z+2)(2z+1)2z
Again this is equal to 4(z+1)(2z+1)(z), which is divisible by 4.
Hence D is the answer.
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I agree, answer is D
Both statement 1 and 2 provide us with two factors of 2, which makes it divisible by 4. The original prompt can be simplified as a consecutive product, as, x(x-1)(x-2)
Both statement 1 and 2 provide us with two factors of 2, which makes it divisible by 4. The original prompt can be simplified as a consecutive product, as, x(x-1)(x-2)
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If x > 0, then is x^3 - 3(x^2) + 2x divisible by 4?
1. x = 4y + 4, where y is an integer
2. x = 2z + 2, where z is an integer
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1. x= 4(y+1) implies x is divisible by 4.
x^3 - 3x^2 +2x = x(x^2-3x+2) = 4(y+1)(x^2-3x+2). Statement 1 is sufficient
2. x = 2(z+1)
x^3 - 3x^2 +2x = 2.2.2(z+1)^3 - 3.2.2(z+1)^2 + 2.2(Z+1). Statement 2 is also sufficient
Ans : D
1. x = 4y + 4, where y is an integer
2. x = 2z + 2, where z is an integer
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1. x= 4(y+1) implies x is divisible by 4.
x^3 - 3x^2 +2x = x(x^2-3x+2) = 4(y+1)(x^2-3x+2). Statement 1 is sufficient
2. x = 2(z+1)
x^3 - 3x^2 +2x = 2.2.2(z+1)^3 - 3.2.2(z+1)^2 + 2.2(Z+1). Statement 2 is also sufficient
Ans : D
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0 is divisible by any number except 0 and the result is 0. Not happy with what you see ?codytravers wrote:I agree... even though the OA is apparently D, can anyone find fault with anshul's explanation of the problem?
ok 0/k = 0*(1/k) = 0 * real number = ? 0 !
Anil Gandham
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D it is. Factorize the expression to remove any ambiguity.
You will get (x-2)(x-1)(x)/4
Hence all we need to know is that x is even.
Both statements address the issue.
You will get (x-2)(x-1)(x)/4
Hence all we need to know is that x is even.
Both statements address the issue.
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Guyz according to me the answer is D for this DS quesion.
If x>0, then is x^3-3x^2+2x divisible by 4?
1. x=4y+4 where y is an integer
2. x=2z+2; were z is an integer
So the values for y and z should be > 0 and only intergers, when u put in values you get x divisible by 4.
Hence D...
If x>0, then is x^3-3x^2+2x divisible by 4?
1. x=4y+4 where y is an integer
2. x=2z+2; were z is an integer
So the values for y and z should be > 0 and only intergers, when u put in values you get x divisible by 4.
Hence D...
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