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# M07-23

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Math Expert
Joined: 02 Sep 2009
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M07-23  [#permalink]

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16 Sep 2014, 00:35
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:01) correct 31% (01:57) wrong based on 61 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. $$\sqrt{0.17}$$

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Re: M07-23  [#permalink]

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16 Sep 2014, 00:35
2
1
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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11 Jan 2015, 01:05
1
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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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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Re: M07-23  [#permalink]

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05 Jul 2015, 13:15
2
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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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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Re: M07-23  [#permalink]

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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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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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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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18 Jun 2017, 20:37
3
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.
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Re: M07-23  [#permalink]

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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]

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31 Mar 2019, 00:43
Bunuel wrote:
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

Hi Xylan

These type of Qs take up a lot of time! Do you have a strategy to solve this?

Would appreciate your help!
THANKS
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Re: M07-23  [#permalink]

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31 Mar 2019, 06:31
1
JIAA wrote:
Bunuel wrote:
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

Hi Xylan

These type of Qs take up a lot of time! Do you have a strategy to solve this?

Would appreciate your help!
THANKS

JIAA For comparison Qs:
The rationale, we follow, in Comparison-Qs (Like, Unlike, As etc.) in SC is also applicable in Quants.
Quote:
We can ONLY compare entities, which are of comparable units.

For example, though pounds and kilograms are units of weight. We cannot directly compare and decide which is heavier or lighter.
We need a common conversion unit/comparable unit to decide which is what.

Similar ideology is applicable in this Q.
Though the values are given in numbers, either compare them in fractional-format or in decimal-system.

Convert the comparable entity in the same format such as either in fractions or in decimal and Be quick in discarding the smaller value.
PS: Do NOT force yourself to convert ALL the values in fractions or in decimals. Utilise it efficiently.

There is NO magic formula; To be quick with numbers and avoid strenuous calculations, I would suggest: Remember the following and actively Use it in Qs:
1) The inverse of 1-15.
2) Sq roots of 1-20.
3) Squares of 1-20 and cubes of 1-10.

Even if you do NOT remember the entire above set, You should know how to calculate and reach the approximate value faster.
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Re: M07-23  [#permalink]

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31 Mar 2019, 07:16
A. $$0.456$$

B. $$\frac{1}{2}(1-\frac{1}{8})$$

$$\frac{1}{2}(\frac{7}{8})$$

$$\frac{7}{16}$$

$$\approx{0.437}$$

C. $$\frac{30}{65}$$

$$\frac{6}{13}$$

$$\approx{0.46}$$

D. $$\frac{9}{19}$$

$$\approx{0.473}$$

E. $$\sqrt{0.17}$$

$$\approx{0.41}$$

OPTION: D
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if you like my explanation!!!
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Re M07-23  [#permalink]

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11 Jul 2019, 12:59
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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Re: M07-23  [#permalink]

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11 Jul 2019, 15:31
1
Another method for this one is to consider (approximately) how far each answer choice is away from an easy number. In this case, all of the answer choices are very close to 1/2:

A. $$0.456$$ --> $$0.044$$ below $$0.5$$ --> $$\frac{11}{250}$$ below $$\frac{1}{2}$$ --> >$$\frac{1}{25}$$ below $$\frac{1}{2}$$

B. $$\frac{1}{2}-(\frac{1}{2})^4$$ = $$\frac{1}{2}-\frac{1}{16}$$ --> $$\frac{1}{16}$$ below $$\frac{1}{2}$$

C. $$\frac{300}{650}$$ --> $$\frac{25}{650}$$ below $$\frac{325}{650}$$ --> $$\frac{1}{26}$$ below $$\frac{1}{2}$$

D. $$3(\frac{3}{19})$$ = $$\frac{9}{19}$$ --> $$\frac{0.5}{19}$$ below $$\frac{9.5}{19}$$ --> $$\frac{1}{38}$$ below $$\frac{1}{2}$$

E. $$\sqrt{0.17}$$ --> closer to $$\sqrt{0.16}$$ than to $$\sqrt{0.25}$$ --> closer to $$0.4$$ than $$0.5$$ --> >$$0.05$$ below $$0.5$$ --> >$$\frac{1}{20}$$ below $$\frac{1}{2}$$

Since all of these fractions have 1 in the numerator, we don't need a common denominator to compare them — the one with the largest denominator will be the smallest. 1/38 is the smallest fraction, so D is the closest to 1/2 of all of the answer choices.

A lot of folks in here aren't fans of answer choice E, but the way it's solved is a great example of the type of estimation this test will make you do — obviously calculating the square root of 0.17 would be bonkers, but calculating the square roots of close-by perfect squares (0.16 and 0.25) and then comparing which one its closer to is absolutely doable in the time frame. (Honestly, I did extra work here — once you know E is closer to 0.4 than 0.5, it should be out.)
Re: M07-23   [#permalink] 11 Jul 2019, 15:31
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