T his GMAT Data Sufficiency question is from Number Properties.Concept: Positive and negative numbers - number line basics. A very interesting question.

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 15: How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

- x + y + z = 20
- x + y = 14

**What kind of an answer will the question fetch?**

The question is a "How many?" question. For questions asking "how many", the answer should be a number.

**When is the data sufficient?**

The data is sufficient if we are able to get a UNIQUE answer for the number of positive numbers from the information in the statements.

If the statements do not have adequate data to uniquely determine how many among the three numbers are positive, the data is NOT sufficient.

**Key data from the question stem**

Each of the three numbers x, y, and z are less than 10.

Evaluate Statement (1) ALONE: x + y + z = 20

From the question stem we know that each number is less than 10.

So, x < 10, y < 10 and z < 10.

Therefore, the __maximum sum__ of any two of these numbers, say x + y < 20.

However, statement 1 states x + y + z = 20.

Unless the third number, z in this case, is also positive x + y + z cannot be 20.

Hence, we can conclude that all 3 numbers x, y and z are positive.

**Statement 1 ALONE is sufficient.**

Eliminate choices B, C and E. Choices narrow down to A or D.

Evaluate Statement (2) ALONE: x + y = 14

As each of x and y is less than 10, both x and y have to be positive for the sum to be 14.

However, z could also be positive or z could be negative.

So, there could be either 2 or 3 positive numbers among the three numbers.

We are not able to find a unique answer from the information in statement 2.

**Statement 2 ALONE is NOT sufficient.**

Eliminate choice D.

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8. GMAT Number Theory | Prime factorization | Properties of squares & cubes

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11. 3 important properties of LCM & HCF | LCM & HCF of fractions

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

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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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