# GMAT 700 Level Data Sufficieny Question 30

#### Number Properties | Divisibility & Perfect Squares

The given question is a GMAT 700 level data sufficiency question testing concepts in Number Properties. This question tests following concepts in number properties - divisibility, prime numbers, and perfect squares.

GMAT Data Sufficiency | Directions | Click Here ▼

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.

Question 30: Is the twelve-digit positive integer a perfect square?

Statement 1: The number comprises only the digits 0, 1, and 2, each written four times.
Statement 2: The sum of the digits of the twelve-digit number is 12.

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### Explanatory Answer | GMAT Number Properties DS

#### Step 1: Decode the Question Stem and Get Clarity

Q1. What kind of an answer will the question fetch?
An "Is" question will fetch a definite "Yes" or a "No" as an answer.
The data provided in the statements will be considered sufficient if the question is answered with a conclusive Yes or a conclusive No.

Q2. What is the concept?
If a perfect square 'n2' is divisible by a prime 'p', it will also be divisible by p2.

#### Step 2: Evaluate Statement 1 ALONE

Statement 1: The number comprises only the digits 0, 1, and 2, each written four times.
Therefore, sum of the digits of the number is 4(0) + 4(1) + 4(2) = 12

Sum of digits is divisible by 3. So, the number is divisible by 3.
If the number is a perfect square, if it is divisible by 3 it will also be divisible by 32 = 9.
However, the sum of the digits of the number is 12, which is not divisible by 9.
So, the number is divisible by a prime but not its square.
So, the given number is not a perfect square.

We are able to answer the question with a DEFNITE NO using Statement 1.
Hence, statement 1 alone is sufficient.
Eliminate answer option B, C, and E.

#### Step 3: Evaluate Statement 2 ALONE

Statement 2: The sum of the digits of the twelve digit number is 12.
The analysis is the same as that for statement 1.

The sum of the digits is given as 12. So, the number is divisible by 3.
If the number is a perfect square, if it is divisible by 3 it will also be divisible by 32 = 9.
However, the sum of the digits of the number is 12, which is not divisible by 9.
So, the number is divisible by a prime but not its square.
So, the given number is not a perfect square.

We are able to answer the question with a DEFNITE NO using Statement 2.
Hence, statement 2 alone is sufficient.
Eliminate answer option A.

Statements are independently sufficient.

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