Suppose the number is 149. Then the greatest odd factor is 149> the greatest even factor
Now let x= 148, where the greatest even factor is 148> the greatest odd factor

Shouldn't the answer be D?

Quantity A: We need to find the greatest odd factor for a number between 130 and 150 (exclusive)
The greatest odd factor would be the greatest prime number between 130 and 150, which is 149

Note: How to check if N is a prime number -
Take the square root of N and try dividing N by all prime numbers till \(\sqrt{N}\). If none divide, it is prime

In this case, \(\sqrt{149} = ~ 12...\)
Thus, we try dividing 149 by all primes till 12: 149 is not divisible by 2, 3, 5, 7, 11 => 149 is prime

Thus, the greatest odd factor of x is 149


Quantity B: We need to find the greatest even factor for a number between 130 and 150 (exclusive)
The number, in this case, must be even and the greatest such factor will be 148

Thus, the greatest even factor of x is 148


Thus, Quantity A is greater

Answer A
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X can be any number between 130 and 150, right? So, if we select a number we will have to compare the greatest odd and greatest even numbers of that particular number. So, depending on the number the answers will wary. Why is D not the answer then?

149 is the greatest odd factor because it is a prime number and its factors are 1 and 149 only so clearly 149 is the biggest odd number.
Since we have already found our answer that is 149 which is odd and which is also option A (Answer), there is no need to even check the even number because any number we select would be less than 149, and its factors would be even more less.
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Suppose x is 149.

A= greatest odd factor of x = 149
B= greatest even factor of x = null (since odd number cannot have even factor).

A>B

Suppose x is 148.
A= greatest odd factor of x = 37
B= greatest even factor of x = 148

A<B

Hence, I thought the answer was D. Could you please help me understand why the answer is A and not D? I think we should consider the same x when analyzing both A and B. If not, could you please explain why?

Hey,

So your doubt is valid but see we are given a limit of \(130 < x < 150\), so even if you take \(148\) as the highest even factor, you can have \(149\) as the highest odd factor.

But if you take the highest value of the limit, \(149\) then the highest odd will be greater than, \(148\), the highest even.


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Shouldn't we consider the same particular value of x 'at a time' when analyzing cases A and B? Suppose we consider 148 as x. How can 149 be the odd factor of 148? I got confused here.

Whatever value we consider, we will need the highest value. Either it can be Qt A or B - in this case.

The greatest even no can be 148 only. While the greatest odd will be 149. Hence it is right.


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This question appears to be deliberately misleading. Here is my analysis:

Given: x is a number [integer, because it has factors] between 130 and 150 exclusive; no information is given as to which

Compare: A = greatest odd factor of x; B = greatest even factor of x [note we are considering *all* factors, not just prime factors]

In the case where x is odd, it has no even factors. Therefore B does not exist. Nothing given in the question rules out this possibility. Therefore, the answer must be D.

Several of the answers here compare the greatest odd factor possible for any x with the greatest even factor possible for any x. This is not what the question is asking - to do so it would have to include phrasing (e.g. "possible" or "for any") indicating that we are considering all values of x in our comparison, and no such words are used. As asked, we are comparing the greatest even factor and the greatest odd factor of a single value of x (and we know only that x lies in the range 130 to 150 exclusive).

But we do not know if X is actually 149. It could be anything between 130 and 150, what if X was 142?!
The question does not ask the greatest odd factor of numbers in range 130 to 150, but rather, but rather asks about X itself (which could be ANYTHING between 130 and 150, we only have this much information).


The prescribed answer seems incorrect.

prescribed answer is likely incorrect. Answer should be D, or the question is just incorrect. happens often on this site. Wish there was a better/more consistent site.

It is D, the prescribed answer is likely incorrect. Or more likely, question is incorrect.

We are not told to take the highest value of the limit. WE DO NOT KNOW WHAT X IS! other than the fact that it is ANY number between 130 and 150.

#case 1:
142, highest even factor is 142, highest odd factor is 71.
Quantity A is higher

#case 2:
149, highest odd factor is 149, no even factor.
Since there is no even factor, we cannot even really compare


The question is likely either phrased incorrectly, or the prescribed answer is wrong. Hence, answer is D, there is not enough information to answer this question.

The percentage of INCORRECT questions among 13k just quant questions is meaningless. Moreover, when the OA is incorrect is the book/source that is INcorrect.

We do our best to provide the best GRE experience for the students for FREE. Not only that, if some mistake is made it is unintentionally and fixed swiftly 24 hours round,7 days round, 365 days round. Holidays included.

many Thanks

regards
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You could start with any integer between 130 and 150. Notice you are looking for the greatest factors, not the greatest prime factor, so you should start with the greatest integer which is 149. The largest factor of 149 is 149, which is odd. If you use 148, the largest factor is 148, but that is smaller than 149. If you use 147, the largest factor is 147, still smaller. 149 is the largest factor of the largest number in your set, so you are done. The answer is choice (A).

See also the explanation by the GRE/GMAT tutor here https://gre.myprepclub.com/forum/130-x- ... tml#p44948
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We aren't asked to find the largest factor of the largest number in the range. Rephrase the question if that is what u want to ask.
We are told that x can be anything between 130 and 150.
Based on what x is, either the even factor can be greater, or the even factor may not exist.
Correct answer is not A. We need more information so correct answer is D.

We aren't asked to find the largest factor of the largest number in the range. Rephrase the question if that is what u want to ask.
We are told that x can be anything between 130 and 150.
Based on what x is, either the even factor can be greater, or the even factor may not exist.
Correct answer is not A. We need more information so correct answer is D.

According to the tutor sujoykrdatta

I have edited the question above which is a bit misleading from Princeton



I hope now is fine
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