Which of the Following is Equal to the Value of 2^5+2^5+3^5+3^5+3^5 ? GMAT Problem Solving

Question: Which of the following is equal to the value of \(2^5+2^5+3^5+3^5+3^5 \)?

1. \(5^6\)
2. \(13^5\)
3. \(2^6+3^6\)
4. \(2^7+3^8\)
5. \(4^5+9^5\)

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
(2^5+2^5)+(3^5+3^5+3^5)
=2∗2^5+3∗3^5 (We have two 2^5 so you club them as 2*2^5. Similarly for 3)
=2^6+3^6

Approach Solution 2:
Given: 2^5 + 2^5 + 3^5 + 3^5 + 3^5

Notice that this expression has the same STRUCTURE as x + x + y + y + y
Simplifying, we get: x + x + y + y + y = 2x + 3y

LIKEWISE, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)
= (2^1)(2^5) + (3^1)(3^5)
= 2^6 + 3^6

Approach Solution 3:
Simplifying, we get:

2^5(1 + 1) + 3^5(1 + 1 + 1)
2^5 x 2^1 + 3^5 + 3^1
2^6 + 3^6

“Which of the following is equal to the value of 2^5+2^5+3^5+3^5+3^5?”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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