X and Y are sets of positive integers. Is the greatest integ

[Anaira Mitch]

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?
(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

Please assist with above problem.

[DavidG@VeritasPrep]

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?
(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

Please assist with above problem.

Individually, the statements are clearly not sufficient, as S1 tells us nothing about Y and S2 tells us nothing about X. Together, let's generate some simple sets.

Case 1: x = {1, 3, 5, 7, 9}
y = {2, 4, 6}
The answer here is YES, the greatest integer in x is greater than the greatest integer in y.

Case 2: x = {1, 3, 5, 7, 9}
y = {10, 12, 14}
The answer here is NO, the greatest integer in x is not greater than the greatest integer in y.

Together the statements are not sufficient. The answer is E

[Anaira Mitch]

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?
(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

Please assist with above problem.

Individually, the statements are clearly not sufficient, as S1 tells us nothing about Y and S2 tells us nothing about X. Together, let's generate some simple sets.

Case 1: x = {1, 3, 5, 7, 9}
y = {2, 4, 6}
The answer here is YES, the greatest integer in x is greater than the greatest integer in y.

Case 2: x = {1, 3, 5, 7, 9}
y = {10, 12, 14}
The answer here is NO, the greatest integer in x is not greater than the greatest integer in y.

Together the statements are not sufficient. The answer is E

Thanks for the solution it was helpful.

[Jay@ManhattanReview]

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?
(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

Please assist with above problem.

Since each statement gives information about only one set, the answer to this question would be either C or E.

Let us discuss both the statements.

S1 & S2:

As per S1...

The smallest value of a consecutive odd positive integer would be '1,' thus, X: {1, 3, 5, 7, 9}. The greatest of them is '9.'

Similarly, the greatest value of a consecutive odd positive integer less than '20' would be '19,' thus, X: {11, 13, 15, 17, 19}. The greatest of them is '19.'

So, S1 renders two values: 9 or 19.

As per S2...

The smallest value of a consecutive even positive integer would be '2,' thus, X: {2, 4, 6}. The greatest of them is '6.' Since 6 is less than 9 or 19, the answer YES.

Similarly, the greatest value of a consecutive even positive integer less than '15' would be '14,' thus, X: {10, 12, 14}. The greatest of them is '14.' Since 14 is greater than 9, the answer NO.

No unique answer. Insufficient.

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

The correct answer: E

Hope this helps!

-Jay
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[Jeff@TargetTestPrep]

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?
(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

We are given that X and Y are sets of positive integers, and we need to determine whether the greatest integer in X is greater than the greatest integer in Y.

Statement One Alone:

X is a set of 5 consecutive odd integers, each less than 20.

Since we don't know anything about the integers in Y, statement one alone is not sufficient.

Statement Two Alone:

Y is a set of 3 consecutive even integers, each less than 15.

Since we don't know anything about the integers in X, statement two alone is not sufficient.

Statements One and Two Together:

Even with the two statements, we still don't have enough information to determine whether the greatest integer in X is greater than the greatest integer in Y.

For example, if the 5 consecutive odd integers in X are 11, 13, 15, 17, and 19, and the 3 consecutive even integers in Y are 10, 12, and 14, then the greatest integer in X IS greater than the greatest integer in Y.

However, if the 5 consecutive odd integers in X are 1, 3, 5, 7, and 9, and the 3 consecutive even integers in Y are 10, 12, and 14, then the greatest integer in X IS NOT greater than the greatest integer in Y. The two statements together are still not sufficient.

Answer: E