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
I saw this quesiton in Manhattan guide, but i am not convinced with its answer.
Interesting DS question
- thankont
- Senior | Next Rank: 100 Posts
- Posts: 41
- Joined: Fri Dec 15, 2006 9:23 am
- Location: Greece
- Followed by:1 members
statement 1
x^3 -3x^2+2x = x(x^2-3x+2) (1) and since x=4(y+1) then it is divisible by 4
statement 2
from (1) if x =2(z+1) we have 2(z+1)(4(..)-6(..)+2)=4(z+1)(2(..)-3(..)+1)divisible by 4
so I would go for --d-- here.
Do you know the OA
x^3 -3x^2+2x = x(x^2-3x+2) (1) and since x=4(y+1) then it is divisible by 4
statement 2
from (1) if x =2(z+1) we have 2(z+1)(4(..)-6(..)+2)=4(z+1)(2(..)-3(..)+1)divisible by 4
so I would go for --d-- here.
Do you know the OA
1. x=4y+4, where is an integer. Now put -1 for y. then x becomes 0. so is 0 divisible by 4. I think it is no. So u cant answer with 1.
Similar reasoning occurs for 2.
So i felt the answer to be E.
But Manhattan guide says the answer to be D.
Similar reasoning occurs for 2.
So i felt the answer to be E.
But Manhattan guide says the answer to be D.
-
- Senior | Next Rank: 100 Posts
- Posts: 76
- Joined: Tue Dec 26, 2006 11:26 am
- Followed by:3 members
But the problem states that X > 0 so you can't use -1. You have to use 0 or greater.venkb wrote:1. x=4y+4, where is an integer. Now put -1 for y. then x becomes 0. so is 0 divisible by 4. I think it is no. So u cant answer with 1.
I guess the trick here is to factor out the problem which makes the problem a whole easier (than putting in numbers).
Thankont, can we explain how you solved statement 2? Thanks!!
GMAT/MBA Expert
- Stacey Koprince
- GMAT Instructor
- Posts: 2228
- Joined: Wed Dec 27, 2006 3:28 pm
- Location: Montreal, Canada
- Thanked: 639 times
- Followed by:694 members
- GMAT Score:780
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.
As maxim points out, that doesn't matter for this problem, since we're given x>0, but I just wanted to clarify the concept.
As maxim points out, that doesn't matter for this problem, since we're given x>0, but I just wanted to clarify the concept.
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Fri Nov 24, 2006 5:38 pm
x^3-3*X^2+2X
X(X-1)(X-2)
So a number (number-1) (number-2)
If number odd then odd*even*odd; May or may not be devisible
Number even definitely divisible
Now A -> X devisible by 4 so Yes
B -> X even so Yes
Hence D :
X(X-1)(X-2)
So a number (number-1) (number-2)
If number odd then odd*even*odd; May or may not be devisible
Number even definitely divisible
Now A -> X devisible by 4 so Yes
B -> X even so Yes
Hence D :
GMAT/MBA Expert
- Stacey Koprince
- GMAT Instructor
- Posts: 2228
- Joined: Wed Dec 27, 2006 3:28 pm
- Location: Montreal, Canada
- Thanked: 639 times
- Followed by:694 members
- GMAT Score:780
Yep, definitely want to factor the initial statement before doing anything else. Just wanted to add a little clarification.
Why do we know that even*odd*even is div. by 4, when we don't know if odd*even*odd is?
The only thing we do know is that an even number is divisible by 2. We know nothing universal about div. of odd numbers. If we have two even numbers in the group, then we have two 2's, or (2x2) = 4, so the product of the three numbers is definitely div. by 4. If we have only one even number in the group, then we know the product of the three numbers is definitely div. by 2, but it may or may not be div. by 4.
Also, how do we know statement 1 tells us x is div. by 4? If you add or subtract any numbers which share the same factor(s), then the sum or difference will also have that same factor. So, for statement 1: 4y+4 (and y is integer), the two numbers have 4 as a factor. Therefore, the sum of the two numbers will also have 4 as a factor. That sum, of course, equals x, so x has 4 as a factor.
Statement 2 only tells us that 2 is a factor of x, so we have to take it one more step. If 2 is a factor of x, then x is even. If x is even, then our product is even*odd*even, which we know works b/c of our initial analysis, above.
Why do we know that even*odd*even is div. by 4, when we don't know if odd*even*odd is?
The only thing we do know is that an even number is divisible by 2. We know nothing universal about div. of odd numbers. If we have two even numbers in the group, then we have two 2's, or (2x2) = 4, so the product of the three numbers is definitely div. by 4. If we have only one even number in the group, then we know the product of the three numbers is definitely div. by 2, but it may or may not be div. by 4.
Also, how do we know statement 1 tells us x is div. by 4? If you add or subtract any numbers which share the same factor(s), then the sum or difference will also have that same factor. So, for statement 1: 4y+4 (and y is integer), the two numbers have 4 as a factor. Therefore, the sum of the two numbers will also have 4 as a factor. That sum, of course, equals x, so x has 4 as a factor.
Statement 2 only tells us that 2 is a factor of x, so we have to take it one more step. If 2 is a factor of x, then x is even. If x is even, then our product is even*odd*even, which we know works b/c of our initial analysis, above.
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
hi i am sarika from delhi
need help on these ds qs
Ques 1: each employee on a certain task is either a manager or director. What % of employees on taskforce are directors.
1.the avg salary of managers on task force is $5000 less than avg salary of all employees on task force.
2.the avg salary of directors on task force is $150000 greater than avg salary of all employees on task force
Ques2: last month 15 homes were sold in town x. the avg sale price of homes was $150,000 and median sale price was $130,000
which of following must be true.
1. at least one of homes was sold for more than $165,000
2. at least one of homes was sold for more than $130,000 and less than $150,000
3. at least one of homes was sold for less than $130,000
Ques3: IS z equal to median of 3 positive integers x, y and z
1. x < y+z
2. y=z
Ques 4: a construction co was paid a total of $500,000 for a construction project. The cos only costs for the project were for labor and materials . was the cos profit for the project greater than $150,000
1.the co’s total cost as 3 times its cost for materials
2.the co’s profit was greater than its cost for labor
thannx
sarika
need help on these ds qs
Ques 1: each employee on a certain task is either a manager or director. What % of employees on taskforce are directors.
1.the avg salary of managers on task force is $5000 less than avg salary of all employees on task force.
2.the avg salary of directors on task force is $150000 greater than avg salary of all employees on task force
Ques2: last month 15 homes were sold in town x. the avg sale price of homes was $150,000 and median sale price was $130,000
which of following must be true.
1. at least one of homes was sold for more than $165,000
2. at least one of homes was sold for more than $130,000 and less than $150,000
3. at least one of homes was sold for less than $130,000
Ques3: IS z equal to median of 3 positive integers x, y and z
1. x < y+z
2. y=z
Ques 4: a construction co was paid a total of $500,000 for a construction project. The cos only costs for the project were for labor and materials . was the cos profit for the project greater than $150,000
1.the co’s total cost as 3 times its cost for materials
2.the co’s profit was greater than its cost for labor
thannx
sarika
GMAT/MBA Expert
- Stacey Koprince
- GMAT Instructor
- Posts: 2228
- Joined: Wed Dec 27, 2006 3:28 pm
- Location: Montreal, Canada
- Thanked: 639 times
- Followed by:694 members
- GMAT Score:780
Hi, Sarika, welcome! If you want to post new questions, you should generally start an entirely new thread so that people will notice your new questions and try them!
Also, please don't forget to post the source for any questions you post.
Thanks!
Edited to add: I saw you just did add a new thread and you posted the source - thanks so much!
Also, please don't forget to post the source for any questions you post.
Thanks!
Edited to add: I saw you just did add a new thread and you posted the source - thanks so much!
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
-
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Wed Jan 24, 2007 10:05 pm
Hi Guys...
The ideal way to solve this is by factoring the given polynomic expression into linear terms. After which using the options for the values of x we will be able to make the expression a multiple of 4.....which states that it is divisible by both option 1 and 2.
The ideal way to solve this is by factoring the given polynomic expression into linear terms. After which using the options for the values of x we will be able to make the expression a multiple of 4.....which states that it is divisible by both option 1 and 2.
This took me a bit longer than two minutes, but this is how I approached the problem.
1. I took the quadratic eqn in the question and factored it to get x(x^2 - 3x +2), which equals x(x-1)(x-2)
From this we know that x = 0, x = 1, and x=2
However, the question explicitly states that x does not equal 0, so we can eliminate that possibility.
2. In order for the equation to be divisible by 4, we need another 2 OR a 4. As we only currently have a 2 and a 1, as shown above.
3. I now turn to the stmts.
Statement 1:
x = 4y +4 Factor this to get
x = 4 (y+1)
Then plug in values for y.
If y = -1, then X = 0. We can disregard this bc the q states that x>0
If y = 0, then x =4. This is sufficient, we can stop here
[Cross out B, C, E]
Statement 2:
x = 2z +2 Factor this to get
x = 2(z+1)
Then plug in values for z.
If z = -1, then x = 0. Again disregard
If z = 0, then z = 2
If z = 1, then x = 4
Therefore, statemetn 2 is also sufficient. Cross out A, correct answer is D.
I'm not sure if that was the correct approach, so if someone could confirm I'd be grateful.
Thanks
Tessa
1. I took the quadratic eqn in the question and factored it to get x(x^2 - 3x +2), which equals x(x-1)(x-2)
From this we know that x = 0, x = 1, and x=2
However, the question explicitly states that x does not equal 0, so we can eliminate that possibility.
2. In order for the equation to be divisible by 4, we need another 2 OR a 4. As we only currently have a 2 and a 1, as shown above.
3. I now turn to the stmts.
Statement 1:
x = 4y +4 Factor this to get
x = 4 (y+1)
Then plug in values for y.
If y = -1, then X = 0. We can disregard this bc the q states that x>0
If y = 0, then x =4. This is sufficient, we can stop here
[Cross out B, C, E]
Statement 2:
x = 2z +2 Factor this to get
x = 2(z+1)
Then plug in values for z.
If z = -1, then x = 0. Again disregard
If z = 0, then z = 2
If z = 1, then x = 4
Therefore, statemetn 2 is also sufficient. Cross out A, correct answer is D.
I'm not sure if that was the correct approach, so if someone could confirm I'd be grateful.
Thanks
Tessa
-
- Senior | Next Rank: 100 Posts
- Posts: 40
- Joined: Sun Mar 27, 2011 9:54 am
- Thanked: 2 times
- smishrajec
- Junior | Next Rank: 30 Posts
- Posts: 16
- Joined: Wed May 18, 2011 9:07 pm
- Location: Pune, India
- GMAT Score:410
-
- Master | Next Rank: 500 Posts
- Posts: 116
- Joined: Tue May 31, 2011 7:52 pm
- Location: Bangalore, India
- Thanked: 2 times
- Followed by:2 members
Answer is D.
Split the equation into quadratic.
Substitute x/4 with value given in statements 1 and 2.
You will find that both the statements are alone sufficient.
Split the equation into quadratic.
Substitute x/4 with value given in statements 1 and 2.
You will find that both the statements are alone sufficient.
statement 1: x=4(y+1) => x^3 ,x^2, 2x divisible by 4 with any integers of yvenkb wrote: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
I saw this quesiton in Manhattan guide, but i am not convinced with its answer.
statement 2: x=2(z+1) => x^3 ,x^2, 2x divisible by 4 with any integers of z
thus, OA is D