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 -

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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?

- y
^{3}is an integer - 3y is 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.

Evaluate Statement (1) ALONE: y

We know that y^{3} is an integer.

However, that does not necessarily mean that y is an integer.

Let us say, y^{3} = 2, then y is not an integer.

However, if y^{3} = 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.

Evaluate Statement (2) ALONE: 3y is an integer

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.

Evaluate Statements (1) & (2) Together: y

Only for integer values of y, will both y^{3} and 3y be integers simultaneously.

**Why?** If 3y is an integer and y is not an integer, y^{3} will not be an integer.

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1. Number Systems | Types of Numbers | Chart

2. Number Properties | Rational & Irrational Numbers

3. GMAT Number Properties | Indices & Rule of Exponents

4. Number Systems | Surds & Conjugates

5. Number Properties | Tests of divisibility

6. Number Properties | How to check whether a number is prime?

7. Number Properties | How to prime factorize a number?

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

12. Number Properties | When to use LCM and HCF?

13. Number Theory | How to find number of factors?

14. Number Theory | Number of ways to express as a product of 2 factors

15. Number Theory | Sum of all factors of a number

16. Number Theory | Product of all factors of a number

17. Number Theory | Remainders of sum & product

18. Number Theory | Remainder of dividing x^{n} by 'd'

19. Polynomials | Remainder when a monomial divides it

20. Number Theory | Highest power of a prime that divides factorial of 'n'

21. Number Theory | Highest power of a composite number that divides factorial of 'n'

22. Number Theory | Number of trailing zeroes in a number

23. Number Theory | Unit digit of higher powers of numbers

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