Question: A four digit number is formed by repeating a two digit number such as 2525, 3232, etc. Then any number of this form will always be divisible by:
(A) 7
(B) 11
(C) 13
(D) 101
(E) 235
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
In the above question it is mentioned that a four digit number is formed by repeating two digit numbers such as 2525, 3232, etc.
The opinion that is asked for in this question requires candidates any number of this form will always be divisible by:
Thus, in order to solve this question, let the number be represented by xyxy.
Therefore, in order to calculate this equation, we can solve the below-mentioned equation:
1000x + 100y + 10x + y = 1010x + 101y = 101 (10x+y)
The above-mentioned equation is a multiple of 101.
Therefore, any number of this form will always be divisible by 101.
Approach Solution 2:
Another way to solve the question is to consider repetition of the numbers. Thus, let us consider the below mentioned equations;
1st Equation: 2525= 25 * 101
2nd Equation: 3232= 32 * 101
3rd Equation: 7575= 74 * 101
It can be concluded from the above equations that all the given numbers are divisible by 101. Moreover, 101 is the smallest 3-digit prime number.
Therefore, any number of this form will always be divisible by 101
Approach Solution 3:
The easiest approach to solve this equation is to observe the basics.
First, we need to consider the smallest three-digit prime number i.e 101.
Now, it can be concluded that any given number in the combination of xyxy is always divisible by 101. Thus, the answer is 101 for the given question.
“A four digit number is formed by repeating a two digit number”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have basic knowledge of mathematics and calculations. The candidates can follow varieties of questions from the GMAT Quant practice papers that will help them to enhance their mathematical knowledge.
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