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# M07-23

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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15 Sep 2014, 23:35
Expert's post
8
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BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:25) correct 33% (01:14) wrong based on 73 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

_________________

Kudos [?]: 139549 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139549 [0], given: 12794

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15 Sep 2014, 23:35
Expert's post
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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. $$\frac{9}{19} = 0.47...$$.

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Kudos [?]: 139549 [0], given: 12794

Manager
Joined: 13 Sep 2014
Posts: 94

Kudos [?]: 37 [0], given: 51

WE: Engineering (Consulting)

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11 Jan 2015, 00:05
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

Kudos [?]: 37 [0], given: 51

Current Student
Joined: 03 Oct 2014
Posts: 139

Kudos [?]: 40 [0], given: 89

Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)

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11 Jan 2015, 22:38
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

Kudos [?]: 40 [0], given: 89

Senior Manager
Joined: 15 Sep 2011
Posts: 358

Kudos [?]: 443 [2], given: 46

Location: United States
WE: Corporate Finance (Manufacturing)

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05 Jul 2015, 12:15
2
KUDOS
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,

Kudos [?]: 443 [2], given: 46

Manager
Joined: 05 Jul 2015
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Kudos [?]: 28 [0], given: 3

GMAT 1: 600 Q33 V40
GPA: 3.3

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24 Feb 2016, 19:47
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

Kudos [?]: 28 [0], given: 3

Intern
Joined: 28 Oct 2015
Posts: 2

Kudos [?]: [0], given: 181

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30 Mar 2016, 21:41
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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Intern
Joined: 25 Mar 2013
Posts: 7

Kudos [?]: 2 [0], given: 1

Location: India
GMAT 1: 700 Q50 V39
WE: Information Technology (Consulting)

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21 Jul 2016, 12:41
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.

Kudos [?]: 2 [0], given: 1

Intern
Joined: 06 May 2016
Posts: 42

Kudos [?]: 2 [0], given: 110

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10 Sep 2016, 06:12
I also interpreted it as 60/19 and got is right by mistake!
Not sure what logic this question is trying to test!

Kudos [?]: 2 [0], given: 110

Intern
Joined: 23 Aug 2014
Posts: 3

Kudos [?]: [0], given: 50

GMAT 1: 670 Q49 V32
GPA: 3.6
WE: Analyst (Consulting)

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18 Jun 2017, 19:37
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!

Kudos please . Stuck on 0.

Kudos [?]: [0], given: 50

Manager
Status: GMAT...one last time for good!!
Joined: 10 Jul 2012
Posts: 71

Kudos [?]: 6 [0], given: 18

Location: India
Concentration: General Management
GMAT 1: 660 Q47 V34
GPA: 3.5

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21 Aug 2017, 23:05
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] 21 Aug 2017, 23:05
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# M07-23

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