If M= √4+3√4+4√4, Then the Value of M is GMAT Problem Solving

Question: If M= √4+3√4+4√4, then the value of M is:

1. Less than 3
2. Equal to 3
3. Between 3 and 4
4. Equal to 4
5. Greater than 4

“If M= √4+3√4+4√4, then the value of M is”- 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. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
Any positive integer root from a number more than 1 will be more than 1.

For instance: 1000√2>1.

Hence 3√4>1 and 4√4 -->

M √4+3√4+4√4= 2+(number more than 1)+(number more than 1)>4

Correct Answer: E

Approach Solution 2:
M=4^1/2+4^1/3+4^¼

Now we know that 4^1/2=2

We also know that 4^1/4= √2≈ 1.414>1

And finally 4^1/3>4^1/4⇒4^1/3>1

So combining all three together
M>2+1+1⇒ M>4

Correct Answer: E

Approach Solution 3:
We know that sqrt(4)= 2.

Since 1^3=1 < (cube root(4))^3=4 < 2^3=8, 1 < cube root(4) < 2.

Similarly 1^4=4 < (sqrt(sqrt(4)))^4=4 < 2^4=16 implies that 1 < sqrt(sqrt(4)) < 2.

So 2+1+1 < M < 2+2+2.

M is between 4 and 6.

Correct Answer: E

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