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Directions

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 -

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

Numbers
All numbers used are real numbers.

Figures
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.

Note
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.

Is the positive integer X divisible by 21?
(1)    When X is divided by 14, the remainder is 4
(2)    When X is divided by 15, the remainder is 5

The correct choice is (D). EACH statement ALONE is sufficient to answer the question asked.

The given question is an "Is" question. So, the answer has to be a definite YES or a definite NO. It cannot be a MAYBE.

We have to find out if X is divisible by 21.
Any positive integer is divisible by 21 if it is simultaneoulsy divisible by 3 and 7.

Statement (1):  When X is divided by 14, the remainder is 4
The number is therefore of the form 14k + 4. It will leave a remainder of 4 when divided by 7.

This number is definitely not divisible by 7.

Hence, X is not divisible by 21.

SUFFICIENT.

Statement (2):  When X is divided by 15, the remainder is 5
The number X is of the form 15m + 5
The number will therefore, leave a remainder of 2 when divided by 3.

Hence, it definitely not divisible by 3.

Hence, X is not divisible by 21.

SUFFICIENT.

As each statement is independently sufficient to answer the question, the correct answer is D.

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