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M07-23

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M07-23 [#permalink]

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New post 16 Sep 2014, 00:35
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  45% (medium)

Question Stats:

65% (01:19) correct 35% (01:14) wrong based on 68 sessions

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Which of the following expressions has the greatest value?

A. \(0.456\)
B. \(\frac{1}{2}-(\frac{1}{2})^4\)
C. \(\frac{300}{650}\)
D. \(3(\frac{3}{19})\)
E. \(\sqrt{0.17}\)
[Reveal] Spoiler: OA

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Official Solution:

Which of the following expressions has the greatest value?

A. \(0.456\)
B. \(\frac{1}{2}-(\frac{1}{2})^4\)
C. \(\frac{300}{650}\)
D. \(3(\frac{3}{19})\)
E. \(\sqrt{0.17}\)


Find the best common base for these expressions.

B is \(\frac{1}{2} - \frac{1}{16}\), which gives us \(\frac{7}{16}\).

C is \(\frac{300}{650}\) or \(\frac{30}{65}\) or \(\frac{6}{13}\).

D is \(\frac{9}{19}\).

E is slightly greater than 0.4, not much more to surpass A, so we can eliminate it.

Now, let's see which of B, C, and D is the greatest. We can drop B as it does not add up to C or D - it is further away from \(\frac{1}{2}\) than C or D.

These two fractions are very close to \(\frac{1}{2}\). If we decrease the values of the denominators of each of the fraction by 1, we'll see that they equal \(\frac{1}{2}\). For these two fractions \(\frac{6}{13}\) and \(\frac{9}{19}\), the greater the value of denominator, the closer will the fraction be to \(\frac{1}{2}\). Therefore, \(\frac{9}{19}\) is greater. This fraction property can be vividly described by two fractions \(\frac{1}{2+1}=\frac{1}{3}\) and \(\frac{50}{100+1}=\frac{50}{101}\), clearly the second one is greater.

Now, we just need to compare it to A. \(\frac{9}{19} = 0.47...\).


Answer: D
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Re M07-23 [#permalink]

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New post 11 Jan 2015, 01:05
I think this question is poor and helpful.
The question involves good arithmetic knowledge. but option D is not written properly, it looks like 3 3/19 = 60/19, rather than 9/19

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Re: M07-23 [#permalink]

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New post 11 Jan 2015, 23:38
From option A-D , highest value came out to be D i.e. 9/19= 0.473.....To compare it to root 17....just square 0.473(17 is prime).....
comes out close to 0.22 so D is the highest value

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M07-23 [#permalink]

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Bunuel wrote:
Which of the following expressions has the greatest value?

A. \(0.456\)
B. \(\frac{1}{2}-(\frac{1}{2})^4\)
C. \(\frac{300}{650}\)
D. \(3(\frac{3}{19})\)
E. \(\sqrt{0.17}\)


IMO, answer choice E takes away from the problem. The purpose of the problem is to rationalize through the different fractions. The difference between A and E is slightly greater than three hundredths, and there isn't a good way to formulate that without a calculator or without prior experience with square roots of decimals, and therefore, I think this type of calculation isn't becoming of a 700-level test taker, even with estimation.

It might be improved if it plays off the divisor of 9 or 999, making answer choice E, \(\frac{2^{2}}{3^{3}}\) or \(\frac{450}{999}\). Hope it helps.

Thanks,

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Re: M07-23 [#permalink]

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New post 24 Feb 2016, 20:47
It took me 4 minutes to do this problem but at least I got it right. The way I figured sqrt.17 is that .4^2 = 16 and .5^2 = .25 so it's a whole lot closer to .4

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New post 30 Mar 2016, 22:41
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. why 9/19 ? and not 60/19 ?

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Re: M07-23 [#permalink]

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New post 21 Jul 2016, 13:41
How D is 9 / 19 [ 3(3/19) ] . I thought 3 + 3/ 19 . Although the question won't be so straight forward . But am I confusing something on the symbols.

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Re: M07-23 [#permalink]

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New post 10 Sep 2016, 07:12
I also interpreted it as 60/19 and got is right by mistake!
Not sure what logic this question is trying to test!

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Re: M07-23 [#permalink]

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New post 18 Jun 2017, 20:37
To compare 6/13 and 9/19 , take the common base.

Multiply 6*19 --- > 114

Multiply 9*13 -- > 117

Therefore 6/13 becomes 114/(19*13) ----> 114/247

9/19 becomes 117/(19*13) ----> 117/247

Hope this helps!

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Re: M07-23 [#permalink]

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New post 22 Aug 2017, 00:05
Bunuel wrote:
Which of the following expressions has the greatest value?

A. \(0.456\)
B. \(\frac{1}{2}-(\frac{1}{2})^4\)
C. \(\frac{300}{650}\)
D. \(3(\frac{3}{19})\)
E. \(\sqrt{0.17}\)


a) 0.456~9/20
b)take 1/2 common; 8.75/20
c)3/6.5~9/19.5
d)9/19
e)sqrt(17/100)~4.2/10~8.4/20

By looking at the approximations we can zero down to D
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Re: M07-23   [#permalink] 22 Aug 2017, 00:05
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