The given question is a data sufficiency question from Number Theory. A beautiful question to help learn from common mistakes that we tend to make by making unwarranted assumptions about numbers.
This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -
All numbers used are real numbers.
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.
Question 26: Is y an integer?
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" question is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
We know that y3 is an integer.
However, that does not necessarily mean that y is an integer.
Let us say, y3 = 2, then y is not an integer.
However, if y3 = 8, then y = 2 and is an integer.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
We know that 3y is an integer.
Let us say 3y = 2, then y is not an integer.
However, if 3y = 3, then y will be an integer.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Only for integer values of y, will both y3 and 3y be integers simultaneously.
Why? If 3y is an integer and y is not an integer, y3 will not be an integer.
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4. Number Systems | Surds & Conjugates
5. Number Properties | Tests of divisibility
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8. GMAT Number Theory | Prime factorization | Properties of squares & cubes
9. Number Properties | What is HCF? | How to find HCF?
10. Number Properties | What is LCM? | How to find LCM?
11. 3 important properties of LCM & HCF | LCM & HCF of fractions
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