Which of the following is greatest? GMAT Problem Solving

Question: Which of the following is greatest?

1. 10√3
2. 9√4
3. 8√5
4. 7√6
5. 6√7

“Which of the following is greatest?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. 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:

Which of the five possible answers is the Greatest? is the question. In order to avoid having to perform the calculations, we can modify each of the five possible answers in the same manner.

The question's wording indicates that one of the five choices is unquestionably the largest,

To square everything is a preferred strategy.

1. 10√3
   100*3 = 300
2. 9√4
   81*4 = 324
3. 8√5
   64*5 = 320
4. 7√6
   49*6 = <300
5. 6√7
   36*7 = <300

The answer is 9√4

Correct Answer: B

Approach Solution 2:

There is another approach to answering this question which is Pretty simple

It is asked Which of the five possible answers is the Greatest? .In order to avoid having to perform the calculations, we can modify each of the five possible answers in the same manner.

The question's wording indicates that one of the five choices is unquestionably the largest,
Let us put every option under square root

1. 10√3
   \(\sqrt{100*3}\)
   \(\sqrt{300}\)
2. 9√4
   \(\sqrt{81*4}\)
   \(\sqrt324\)
3. 8√5
   \(\sqrt{64*5}\)
   \(\sqrt{320}\)
4. 7√6
   \(\sqrt{49*6}\)
   \(\sqrt{294}\)
5. 6√7
   \(\sqrt{36*7}\)
   \(\sqrt{252}\)

The answer is 9√4

Correct Answer: B

Approach Solution 3:

We can use a nice rule that says (√x)(√y) =√(xy)
Also, we'll rewrite each integer as a root.
For example 10 = √100

So, we get...
A) 10√3 = (√100)(√3) = √300
B) 9√4 = (√81)(√4) = √324
C) 8√5 = (√64)(√5) = √320
D) 7√6 = (√49)(√6) = √294
E) 6√7 = (√36)(√7) = √252

√324 is the greatest

Correct Answer: B

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