If v = 2(9.8)m/(0.5j), m=96 and j=4, which of the following most close

Question

If  v=\sqrt{\frac{2(9.8)m}{0.5j}} , m = 96 and j = 49, which of the following most closely approximates the value of v?

(A) 0
(B) 9
(C) 17
(D) 25
(E) 33

PS08397

I used the ball- parking strategy to easy calculate ugly number:

√(2(8) 100 / 1/2*50) = √(16*100/25) = 4*10/5 = 8

Number 8 is very close to 9 in answers.
 
Hence Answer B is correct.

mikemcgarry · Accepted Answer

Dear Rsohal , Your approximation approach is an excellent for this and many other official questions. Here, as I glance over the problem, I happen to notice that 49*2 = 98. This allows for a little simplification. v = \sqrt{\frac{2(9.8)m}{0.5j}} v = \sqrt{\frac{2(9.8)(96)}{(0.5)(49)}} v = \sqrt{\frac{4(9.8)(96)}{(0.5)(98)}} v = \sqrt{\frac{4(98)(96)}{(5)(98)}} v = \sqrt{\frac{4(96)}{5}} v = \sqrt{\frac{4(16*6)}{5}} v = 2\sqrt{\frac{(16*6)}{5}} v = 8\sqrt{\frac{6}{5}} v = 8\sqrt{1.2} We know that \sqrt{1}=1 and \sqrt{1.21}=1.1 , so 8\sqrt{1} < v < 8\sqrt{1.21} 8*1 < v < 8*1.1 8 < v < 8.8 This approximates the decimal to a relatively small band. From a calculator, I found the exact answer is 8.76356. Of the answer choices, 9 is clearly the closest. I hope this helps, my friend. Mike :-)

Kinshook · Answer

If  v=\sqrt{\frac{2(9.8)m}{(0.5)j}} , m = 96 and j = 49, which of the following most closely approximates the value of v?
m/j = 2 approx
9.8 = 10 approx

v=\sqrt{\frac{2*10*2}{(0.5)}} = \sqrt{80} = 9

IMO B

mikemcgarry · Answer

Dear Rsohal , I'm happy to respond. :-)

I gather that you are new to GMAT Club. A few points to observe. First of all, this particular subforum, "Ask GMAT Experts," is for general advice on test-taking strategies, questions about scheduling and retakes and logistics of the test, etc. This is not the correct forum at all for individual math questions, such as this. This should have been posted in the general math forum, in the problem solving section: gmat-problem-solving-ps-140/ I would be happy to respond, but unfortunately, I believe you have made mathematical mistakes in posting the question. It appears that you don't have a refined understanding of mathematical grouping symbols. For more on these, see: https://magoosh.com/gmat/2013/gmat-quant ... g-symbols/ I say this because you use the "√" character, but you give no indication of how much is included under the square root. Typically, in the rtf of GC, one would use parentheses for this. There is a world of difference between √(2)(9.8)m / 0.5j and √(2(9.8)m) / 0.5j and √(2(9.8)m / 0.5j) These ambiguities need to be clarified before the question is mathematical sensible. Does all this make sense? Mike :-)

RSOHAL · Answer

Thanks Mike for your reply. You are right. When i typed question, I could not draw square root bar, which was in text book. Anyhow, your suggestion was absolutely correct. I have edited question for better understanding.

thanks for help. much appreciated.

thanks for help. much appreciated.

RSOHAL · Answer

Mike,

There is one issue in following equation, when you input value of variables.
You made j = 49*2, where as J is 49.
If you multiply j with 2, you must multiply upper part of fraction to 2 as well.

v =  \sqrt{\frac{2(9.8)(96)}{(0.5)(98)}}

above equation should be

v =  \sqrt{\frac{2(9.8)(96)2}{(0.5)(98)}}

Thanks

mikemcgarry · Answer

Dear Rsohal , My friend, thanks for catching that! I simply plugged the wrong value of j into the equation. I edited my response above, so that it won't confuse others. Mike :-)

AkshdeepS · Answer

Replace m = 96 with 100 (as we are approximating)

Keep J = 49

Now, \sqrt{\frac{2 * 9.8 * 100}{0.5 * 49}}

Or  \sqrt{\frac{2 * 98* 10 * 100}{5 * 10 * 49}}

Cancel 10 from both numerator and denominator and replace "98" with "100"

\sqrt{\frac{2 * 100 * 100}{5 * 49}}

as  \sqrt{5}  is slightly greater than "2", replace  \sqrt{5}  with "2"

we can write it as,

\frac{\sqrt{2}*\sqrt{100}*\sqrt{100}}{\sqrt{5}*\sqrt{49}}

\frac{1.4*10*10}{2*7}

\frac{140}{14} = 10

Closest to "9"

Hence (B)

Probus · Answer

This could be alternate approach

Now, \sqrt{\frac{2 * 98 * 100}{5 * 49}}

Now, \sqrt{\frac{2 * 2 * 100}{5}}

\sqrt{80}

SO Closest to "9"

Fish181 · Answer

This problem is definitely one you want to solve via approximating and backsolving

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If v = 2(9.8)m/(0.5j), m=96 and j=4, which of the following most close

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If v = 2(9.8)m/(0.5j), m=96 and j=4, which of the following most close

Prep Toolkit

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My Rewards