Data set M consist of distinct negative integers. What is the value of

Question

Data set M consist of distinct negative integers. What is the value of the greatest number in set M?

(1) Every number of set M is the product of -1 and a prime number.
(2) One of the numbers in set M is even.

M36-107

Bunuel · Accepted Answer

Official Solution:

Data set M consist of distinct negative integers. What is the value of the greatest number in set M? 
 
(1) Every number of set M is the product of -1 and a prime number.
 
The set consists of numbers which are of the form  -1*prime . So,  possible  elements of the set are -2, -3, -5, -7, -11, ... Notice that the set can have only one even number, namely -2 because no other negative even number can be written as -1*prime. Not sufficient. 
 
(2) One of the numbers in set M is even. Clearly insufficient.
 
(1)+(2) (2) says that the set contains an even number and from (1) we know that the only even number the set can have is -2. And since all other possible elements of the set are less than -2 (-3, -5, -7, -11, ....), then the greatest number in the set must be -2. Sufficient.

Answer: C

deushyant · Answer

Data set M consist of distinct negative integers. What is the value of the greatest number in set M?

(1) Every number of set M is the product of -1 and a prime number.
 
The set can be {-5,-7,-19} or {-3,-11,-13} i.e. Not sufficient

(2) One of the numbers in set M is even.

The set can be {-8,-9,-11,-15,-18} or {-3,-4,-6,-77} i.e. not sufficient

Combining 1 and 2, we know there is only one even prime number that's 2. and only negative number bigger that -2 is -1 which isn't prime. So -2 is the answer to the question asked, hence Sufficient

Option C

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Bunuel · Answer

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GMATin · Answer

Lets see what we can observe from the question stem.

First, set M can look something like this: M={-1, -2, -3...} but we don't actually know what numbers it will have. Second, if at all the set does look like our example, the greatest number in the set will actually be -1. These two observations are important to keep in mind so that we don't make silly mistakes while actually solving the question.

Statement 1: If every number to be product of -1 and a prime number, we can have set M to look like this: M={-2, -3, -5..}. Notice that we don't include -1 here since 1 is neither prime nor composite and hence -1*1 is not included. Additionally, notice that are not sure if M will in fact contain these numbers because M could also look like this: M={-17, -19, -23..}. Thus, because we cannot necessarily ascertain the greatest number in the set,  this statement is insufficient

Statement 2: This statement again gives us many possibilities of what M could look like. It could be M={-2, -5, -7...} or even M={-17, -20, -21..}. Again,  this statement is insufficient

If we combine statement 1 and 2, we certainly get -2 in the set. This is because -2 satisfies statement 1 (-1*2 (=prime number)) and satisfies statement 2 (-2 is the only even number that will be in the set defined by statement 1.

Thus answer is C

sampad · Answer

i dont agree with the solution. Because nowhere it is mentioned that, the set contains only one even number. So we cant assume that if we combine both the statements, there will be only one even number and that is -2. the answer is really ambiguous and it should not be C.

Bunuel · Answer

That's not correct.

The stem says that "Data set M consist of  distinct  negative integers". Next, (1) says that "Every number of set M is the product of -1 and a prime number", so the set consists of numbers which are of a form of -1*prime. So,  possible  elements of the set are -2, -3, -5, -7, -11, ... Notice that the set can have only one even number, namely -2 because no other negative even number can be written as -1*prime. (2) says that "One of the numbers in set M is even". When combining we know that the even integer of the set must be -2. And since all other possible elements of the set are less than -2 (-3, -5, -7, -11, ....), then the greatest number in the set must be -2.

bumpbot · Answer

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Data set M consist of distinct negative integers. What is the value of

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Data set M consist of distinct negative integers. What is the value of

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