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7) Statement 1 Since both the numbers are even, when one is divided by another the remainder will be even or 0. Since it can't be 0 it will always be even hence>0. Sufficient.

Statement 2

if the numbers are 5&6 the remainder is 1 but if the numbers are 10,15 remainder is 5. Insufficient.

10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket? (1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket. (2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket.

Only true when number of baskets were = 20 Hence B

Question would be a lot more interesting if the Choice 2 it would no longer be possible to distribute the orages evenly This would be true when number of oranges = 4 & 20 and the answer would be E.
_________________

10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket? (1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket. (2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket.

I know it's dangerous to assume, but I interpreted the term "distributed evenly" as basically saying that each basket has to have the same number of oranges.

Statement 1

If so, then based on Statement 1 we can have the following:

# of oranges per basket / # of baskets 10 / 2 2 / 10

INSUFFICIENT

Statement 2

For Statement 2, the same rations would meet the requirement.

INSUFFICIENT

Taken together, they are still insufficient... so

Answer: E?

hi h2polo, i think i can provide u with some explanation for the above problem.

as u assumed, each basket has same number of oranges.

number of oranges=20 and number of baskets= 2/4/5/10/20 (since, only then the number of oranges in each basket will be equal)

1) number of baskets were halved=====> no. of baskets=1/2/5/10 (half of the baskets given before, half of 5 doesn't exist) now for which baskets the oranges are doubled?? Initial no. of baskets || initial no. of oranges per basket || half the number of baskets || oranges in halved baskets 2 || 10 || 1 ||20 4 || 5 || 2 ||10 5 || 4 || - || - 10 || 2 || 5 || 4 20 || 1 ||10 || 2

in all the above cases as the number of baskets halved, the number of oranges doubled. so we cannot conclusively say the total number of baskets and hence the number of oranges each basket contained initially. so data insuff.

2) if the number of baskets were doubled then we can't place at least one orange in every basket. This implies that the number of baskets are more than the number of oranges. This can only happen when the total number of baskets were initially 20. when it is doubled you'll have 40 baskets and just 20 oranges. in any other case, at least one orange can be placed in the baskets. Answer is B.

I think this one was the toughest. I've already given the solution for this one previously, so here it is:

Before considering the statements let's look at the stem: A. Population doubles at constant intervals, but we don't know that intervals. B. Experiment will end in 4 hours from now. C. We don't know when bacteria divided last time, how many minutes ago.

(1) Population divided 2 hours ago and increased by 3750 cells. Note that this statement is talking that bacteria quadrupled during 2 hours before NOW. So, starting point 2 hours ago, end of experiment 4 hours from now. Total 6 hours. This statement gives ONLY the following info: A. population of bacteria TWO hours ago - 1250. B. population of bacteria now - 5000.

But we still don't know the interval of division. It can be 45 min, meaning that bacteria divided second time 30 min ago OR it can be 1 hour, meaning that bacteria just divided. Not sufficient.

(2) An hour before the end of experiment bacteria will double 40.000. Clearly insufficient.

(1)+(2) We can conclude that in 5 hours (2 hours before now+3 hours from now) population of bacteria will increase from 1250 to 40.000, will divide 5 times, so interval is 1 hour. The population will contain 40.000*2=80.000 cells when the bacteria is destroyed. Sufficient.

Answer: C.

The point is that from (1) we can not say what the interval of division is, hence it's not sufficient. Please, tell me if you find this explanation not convincing and I'll try to answer your doubts.

Hi Bunuel... could you please explain the marked text in red? How did you arrive that the bacteria would divide 5 times..?

Thanks, JT
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

First poster here. Many thanks to Bunuel in collecting these tests and answers. I'm particularly stuck in understanding the question below:

Bunuel wrote:

11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912.

From the solutions in this thread, it's suggested that we can count the number of prime numbers between 1 and 3912. However, my understanding is that the statement p is a prime number greater than 2 means that the number of prime numbers between 1 and 3912 must be a prime number as well.

Am I misunderstanding the question, or is the total prime number between 1 and 3912 is actually a prime number?

First poster here. Many thanks to Bunuel in collecting these tests and answers. I'm particularly stuck in understanding the question below:

Bunuel wrote:

11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912.

From the solutions in this thread, it's suggested that we can count the number of prime numbers between 1 and 3912. However, my understanding is that the statement p is a prime number greater than 2 means that the number of prime numbers between 1 and 3912 must be a prime number as well.

Am I misunderstanding the question, or is the total prime number between 1 and 3912 is actually a prime number?

Many thanks.

Welcome to the club.

Yes, your understanding is correct. In data sufficiency questions the stem and the statements are providing us with the TRUE information.

Stem says p is a prime number. Statement (2) says that "here are a total of p prime numbers between 1 and 3912". So yes the # of primes between 1 and 3912 MUST be prime number itself. We don't know what number it is, but we can calculate it, hence we can calculate p, hence (2) is also sufficient.

Yes, your understanding is correct. In data sufficiency questions the stem and the statements are providing us with the TRUE information.

Stem says p is a prime number. Statement (2) says that "here are a total of p prime numbers between 1 and 3912". So yes the # of primes between 1 and 3912 MUST be prime number itself. We don't know what number it is, but we can calculate it, hence we can calculate p, hence (2) is also sufficient.

Hope it's clear.

Thanks Bunuel. I've highlighted part of your reply which clarifies to me that it means we're NOT tasked to evaluate whether that statement itself is correct. Does it mean that it is ALWAYS safe to assume that the stem, and the statements are correct?

This is probably a stupid question, but please humour me, what if the total prime numbers between 1 and 3912 is not a prime number?

Thanks Bunuel. I've highlighted part of your reply which clarifies to me that it means we're NOT tasked to evaluate whether that statement itself is correct. Does it mean that it is ALWAYS safe to assume that the stem, and the statements are correct?

This is probably a stupid question, but please humour me, what if the total prime numbers between 1 and 3912 is not a prime number?

As I stated, stem and the statements are ALWAYS providing us with correct information.

If it turns out that the quantity of primes between 1 and 3912 is not a prime number itself, this will mean that the question is flawed. GMAT wouldn't give us such question then.
_________________

As I stated, stem and the statements are ALWAYS providing us with correct information.

If it turns out that the quantity of primes between 1 and 3912 is not the prime number itself, this will mean that the question is flawed. GMAT wouldn't give us such question then.

9. Is x^2 equal to xy? (1) x^2 - y^2 = (x+5)(y-5) (2) x=y

Answer: B.

Hi Bunuel

I have a problem with this question.

x^2=xy ---> either x=0 or x=y

No doubt that second option is sufficient because it clearly states that x=y. The problem is with the first option.

Now x^2-y^2= (x+5)(y-5) ---> (x+y)(x-y)=(x+5)(y-5)

Case I: x+y = x+5 ---> y=5, now x-y=y-5 put, y=5--->x=5. Therefore, (x,y)=(5,5) Case II: x-y=x+5, ---> y=-5, now x+y=y-5 --->x=-5. Therefore, (x,y)=(-5,-5)

In both the cases, x=y which is nothing but same as the second statement. Hence, answer should be D.

The part highlighted is not to be considered TRUE...... You need to prove that! .. Hence don't use that to solve the question!
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

If \(y=5\) --> \((x+5)(x-5)=(x+5)(5-5)\) --> \((x+5)(x-5)=0\) --> Either \(x=5=y\) and in this case answer to the question is YES OR \(x=-5\), hence \(x\) is not equal to \(y\) (nor to zero) and in this case answer to the question is NO. So two different answers.

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