The given question is a data sufficiency question in number properties and tests concepts in number of factors of a number and properties of odd and even integers.
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 25: What is the value of X, if X and Y are two distinct integers and their product is 30?
What kind of an answer will the question fetch?
The question is a "What is the value?" question. The answer has to be a value, a number for 'X'.
When is the data sufficient?
The data is sufficient if we are able to get a UNIQUE answer for the value of 'X' from the information in the statements.
Do we have any additional information about 'X' or 'Y' from the question stem?
From the question, we know that both X and Y are distinct integers and their product is 30.
30 can be obtained as a product of two distinct integers in the following ways.
|S No.||Positive X and Y||Negative X and Y|
|1||1 * 30||(-1) * (-30)|
|2||2 * 15||(-2) * (-15)|
|3||3 * 10||(-3) * (-10))|
|4||5 * 6||(-5) * (-6)|
From this statement, we know that the value of X is odd.
Therefore, X can be one of the following values: 1, -1, 3, -3, 5, -5.
So, using information in statement 1 we will not be able to deduce a UNIQUE value for X.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
From this statement, we know that the value of X > Y.
From the combinations listed in the table above, X can take more than one value. Here are two possibilities: X could be 10 and Y could be 3. Or X could be 30 and Y could be 1.
Hence, using information in statement 2, we will not be able to find a UNIQUE value for X.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Values of X and Y that satisfy both the conditions are
|S No.||X is odd and X > Y|
|1||(-1) * (-30)|
|2||(-3) * (-10))|
|3||(-5) * (-6)|
More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using information provided in the two statements together, the given data is NOT sufficient.
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 xn 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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