What Is The Remainder When 25^25 Is Divisible By 26 GMAT Problem Solving

Question: What is the remainder when 25^25 is divisible by 26?

(A) 1
(B) 2
(C) 3
(D) 24
(E) 25

“What is the remainder when 25^25 is divisible by 26”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT quant section enables the candidate to improve their mathematical and analytical abilities. This GMAT quantitive section tests the basic knowledge of candidates in arithmetic, algebra and geometry. The students must grasp a concrete understanding of mathematical calculations in order to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part comes up with calculative mathematical problems that would enhance the qualitative skills of the candidates. The candidates can boost their knowledge by practising more from the “GMAT Official Guide Quantitative Review”.

Solution and Explanation:

Approach Solution 1:

The problem statement suggests to find out the remainder when 25^25 is divided by 26.

We can write it as, 25^25/ 26
Therefore, it can be derived as (26 - 1)^25/26

Thus, the remainder is (26 -1) which is equal to 25.
Hence, E is the correct answer.

Correct Answer: E

Approach Solution 2:

The problem statement suggests that

Given:

• 25^25 is divided by 26

Find out:

• the remainder when 25^25 is divisible by 26

As per the question, we need to deduce 25^25/ 26

By applying the concept of negative remainders, we get,

25^25/ 26
= (-1)^25/ 26
= -1/26
= 25

Therefore the remainder is 25.

Hence, E is the correct option.

Correct Answer: E

Approach Solution 3:

The problem statement indicates that

Given:

• 25^25 is divided by 26

Find out:

• the remainder when 25^25 is divisible by 26

From the given argument of the question, we can say,

25^25 = (26 - 1)^25
Let’s assume P = (26 - 1)^25
By expanding the range of P, we can get,
26^25 + … + (-1)^25

Let assume T = (26 - 1)^25 - (-1)^25

Then T ≡ 0 mod 26
Therefore, (-1)^25 = -1 is the remainder but the value of the remainder cannot be less than 0.
Therefore, the remainder is 26 -1 = 25

Hence, E is the correct answer.

Correct Answer: E

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