The given question is a GMAT Hard Math data sufficiency question testing concepts in Number Properties. Concepts covered: Prime Numbers and 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 -

- 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 31: If a and b are positive integers, is (a + b) prime?

**Statement 1**: 13a = 43b

**Statement 2**: 8a = 15b

INR

**Statement 1**: 13a = 43b

\\frac{a}{b}) = \\frac{43}{13})

a : b :: 43 : 13

So, a = 43x and b = 13x

a + b = 43x + 13x = 56x

56 is not prime. Therefore, 56x cannot be prime.

We are **able to answer the question with a DEFNITE NO.**

Hence, statement 1 alone is sufficient.

__Eliminate answer option B, C, and E__.

**Statement 2**: 8a = 15b

\\frac{a}{b}) = \\frac{15}{8})

a : b :: 15 : 8

So, a = 15x and b = 8x

a + b = 15x + 8x = 23x

23 is prime.

If x is 1, a + b will be prime. For other values of x, a + b will not be prime.

We are **not able to answer the question with a DEFNITE Yes or No.**

Hence, statement 2 alone is not sufficient.

__Eliminate answer option D__.

Statement 1 alone is sufficient. Statement 2 is NOT sufficient.

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