Interesting DS question

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venkb: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Fri Dec 22, 2006 3:01 pm

by venkb » Tue Dec 26, 2006 7:16 pm

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.

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Source: Beat The GMAT — Data Sufficiency | Tue Dec 26, 2006 7:16 pm

thankont: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Fri Dec 15, 2006 9:23 amFollowed by: 1 member; Location: Greece

by thankont » Wed Dec 27, 2006 7:48 am

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

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venkb: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Fri Dec 22, 2006 3:01 pm

by venkb » Wed Dec 27, 2006 11:30 am

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.

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maxim730: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Tue Dec 26, 2006 11:26 amFollowed by: 3 members

by maxim730 » Thu Dec 28, 2006 7:05 am

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.

But the problem states that X > 0 so you can't use -1. You have to use 0 or greater.

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!!

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Stacey Koprince: GMAT Instructor; Posts: 2228; Joined: Wed Dec 27, 2006 3:28 pmFollowed by: 694 members; Location: Montreal, Canada; Thanked: 639 times; GMAT Score:780

by Stacey Koprince » Sat Jan 06, 2007 4:07 pm

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.

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coolrahulin: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Fri Nov 24, 2006 5:38 pm

Why not this ...

by coolrahulin » Tue Jan 09, 2007 5:52 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

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Stacey Koprince: GMAT Instructor; Posts: 2228; Joined: Wed Dec 27, 2006 3:28 pmFollowed by: 694 members; Location: Montreal, Canada; Thanked: 639 times; GMAT Score:780

by Stacey Koprince » Tue Jan 09, 2007 6:16 pm

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.

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sarika.k: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Dec 26, 2006 10:41 pm

need help on ds q's

by sarika.k » Mon Jan 15, 2007 12:52 am

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

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Stacey Koprince: GMAT Instructor; Posts: 2228; Joined: Wed Dec 27, 2006 3:28 pmFollowed by: 694 members; Location: Montreal, Canada; Thanked: 639 times; GMAT Score:780

by Stacey Koprince » Wed Jan 17, 2007 7:14 pm

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!

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alimirmustafa: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Jan 24, 2007 10:05 pm

by alimirmustafa » Sat Jan 27, 2007 1:05 am

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.

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tgou008: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Jan 15, 2011 11:26 am; Thanked: 9 times

by tgou008 » Tue Mar 15, 2011 7:06 am

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

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sushantgupta: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun Mar 27, 2011 9:54 am; Thanked: 2 times

by sushantgupta » Sat May 07, 2011 11:47 pm

Answer is D

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smishrajec: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Wed May 18, 2011 9:07 pm; Location: Pune, India; GMAT Score:410

by smishrajec » Sun Jun 26, 2011 5:23 am

I think its Option A

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Sanjay2706: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue May 31, 2011 7:52 pmFollowed by: 2 members; Location: Bangalore, India; Thanked: 2 times

by Sanjay2706 » Sun Jun 26, 2011 10:17 pm

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.

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tailoc: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Jun 15, 2011 11:38 am; Thanked: 1 times

by tailoc » Mon Jul 25, 2011 3:14 am

venkb 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 1: x=4(y+1) => x^3 ,x^2, 2x divisible by 4 with any integers of y
statement 2: x=2(z+1) => x^3 ,x^2, 2x divisible by 4 with any integers of z

thus, OA is D

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