If n and P are integers, is p>0?

[plum]

This come from GMAT prep.

If n and P are integers, is p>0?
(1) n+1 > 0
(2) np > 0

I thought the sb E but OA is C.

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1) r/(b+w) > w/(b+r)
(2) b-w > r

OA is A.

thanks!

[Jeff]

Let's consider (1) N+1 >0. This clearly tells you nothing about p, so is insuffienct by itself, ruling out A&D.

Let's look at (2). np >0. This tells us that n,p and either both positive or both negative. Therefore it is insufficient to answer whether p >0, so we can eliminate B.

Now let's consider (1) and (2) together. (1) combined with the fact that N and P are integers tells us that N>= 0. (2) tells us that N and P are either both positive or both negative and that neither are equal to 0. Combined with (1) we therefore know what N is positive, and from (2) P must be positive too. So (1) and (2) together are sufficient and the answer is C.

--------------------------------

Let's consider (1) r/(b+w) > w/(b+r). This statement says that the ratio of the red marbles to the other marbles in the bag is greater than the ratio of the white marbles to the other marbles in the bag. Therefore r>w and (1) is sufficient. If you don't spot the ratios, you can also algebraically manipulate the inequality to r(b+r) > w(b+w). Pick any value of b, and you'll see the only way the inequality can be true is if r>w. Since (1) is sufficient, we can rule out b&e.

Now, let's consider (2): b-w > r. The easiest way to test whether this is sufficient is to pick values. Let's try r=5, w=2. This is true for any b>7. Now let's try r=5, w=2. This is also true for any b>7, so (2) by itself is insufficient and the answer is A.

/Jeff

[Guest]

Thanks! Second one took a little bit to figure out.
-Peter

[dbernst]

Good explanations! Jeff, my only addition pertains to the second question. As we always want to reinforce a consistent approach to any problem type, don't forget to always begin Data Sufficiency questions by considering a rephrase of the question and then attacking the easier statement first.

Rephrase: As the number of black marbles remains constant whether one removes a red or white marble, the rephrase of this question is Is R>W?

Statements: Statement (1) is significantly more difficult than Statement (2). Therefore, you are doing a disservice to yourself (and your score!) by beginning with Statement (1). Instead, start with Statement (2) and use a BD/ACE grid. Since b-w > r can quickly be rewritten as b > r+w, we don't know the relationship between r and w. Eliminate BD, and then move to Statement (1).

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1) r/(b+w) > w/(b+r)
(2) b-w > r

[Guest]

Hi guys,

My question:

For problem 1
I understand how A, D, and B got eliminated, but I don't get why N >= 0 when (1) and (2) are combined.

If N is negative in (2), then N < -1 in (1). Which means that the closest integer N can be is 0.
If N is positive in (2), then N >= 1.
But (2) NP > 0 so N can't be 0. Thus the only integer N can be is greater than 0. So it's positive.

So P has to be positive because 2 positives multiplied is positve.

So I guess in typing out my question I got to the answer.... Does my train of thoughts make sense?

Thanks!

[esledge]

To the last poster: I do believe you ultimately answered your own question, although only if you made a typo where you said "If N is negative in (2), then N < -1 in (1). Which means that the closest integer N can be is 0. " I think you meant N > -1... Also, when you combine (1) and (2), you get n > 0, NOT n>=0.

Just to be certain,

(1)
n + 1 > 0
n > -1
n could be: 0, 1, 2, 3, 4, etc. (these are the integer values allowed by the inequality)

(2)
np > 0
neither n nor p = 0
n & p must have the same sign.
n could be: ...-4, -3, -2, -1, 1, 2, 3, 4,... (any non-zero integer, as long as it has the same sign as p).

(1) and (2)
n could be: 1, 2, 3, 4, etc. (only positive integers are on both lists of possible values for n)
Therefore, p must be positive, too.

[azarmosk]

Emily,

as you said,
(1)
n + 1 > 0
n > -1
n could be: 0, 1, 2, 3, 4, etc. (these are the integer values allowed by the inequality)

sinc n>-1 why cant n be, -0.5, 0, 1, so on...?
when you consider n+1>0 then to create that inequality n has to be somehow above zero
but if n>-1 i thought n can be above -0.9..
Is this wrong?

[gmat_professor]

Emily,

as you said,
(1)
n + 1 > 0
n > -1
n could be: 0, 1, 2, 3, 4, etc. (these are the integer values allowed by the inequality)

sinc n>-1 why cant n be, -0.5, 0, 1, so on...?
when you consider n+1>0 then to create that inequality n has to be somehow above zero
but if n>-1 i thought n can be above -0.9..
Is this wrong?

n has to be an integer. thus n cannot be -0.9, -0.5.

Available options with this inequality are 0, 1, 2, 3......

and since from (2) np>0, n=0 is also ruled out.

Thus n is 1, 2, 3,....and so on. which means that p>0.

Ans. is thus C

[RonPurewal]

n has to be an integer. thus n cannot be -0.9, -0.5.

Available options with this inequality are 0, 1, 2, 3......

yes.

don't ignore the stated conditions!