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# Which of the following, when multiplied by itself, will yield a fracti

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Math Expert
Joined: 02 Sep 2009
Posts: 50544
Which of the following, when multiplied by itself, will yield a fracti  [#permalink]

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22 Jul 2018, 21:59
00:00

Difficulty:

15% (low)

Question Stats:

87% (00:59) correct 13% (01:33) wrong based on 46 sessions

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Which of the following, when multiplied by itself, will yield a fraction greater than 2/3 ?

A. 5/7
B. 2/3
C. 0.7
D. 0.8
E. 0.027/0.03

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Joined: 31 Oct 2013
Posts: 773
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Which of the following, when multiplied by itself, will yield a fracti  [#permalink]

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22 Jul 2018, 22:07
Bunuel wrote:
Which of the following, when multiplied by itself, will yield a fraction greater than 2/3 ?

A. 5/7
B. 2/3
C. 0.7
D. 0.8
E. 0.027/0.03

we are asked to find out a fraction which will be greater that 2/3 = 66.66

Option E:

0.027 / 0.03

= 27/30..............multiply by 1000

= 9/10

= 0.9

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Joined: 22 May 2016
Posts: 2082
Which of the following, when multiplied by itself, will yield a fracti  [#permalink]

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23 Jul 2018, 16:34
Bunuel wrote:
Which of the following, when multiplied by itself, will yield a fraction greater than 2/3 ?

A. 5/7
B. 2/3
C. 0.7
D. 0.8
E. 0.027/0.03

I. Perfect square decimals
Answers C and D hint at a quick way to solve. Decimal equivalent of $$\frac{2}{3}\approx0.67\approx 0.7$$

C) $$(0.7)^2=0.49$$
D) $$(0.8)^2=0.64$$

Perfect square decimals in relation to 0.67 (NOT a perfect square decimal)

$$0.49<0.64<0.67<0.81$$

Eliminate B (~0.7), C, and D. To get closer to 0.81, we need an answer close to 0.9. Answer A or E?

A) $$\frac{5}{7}\approx{0.7}$$. Same as C. Eliminate.

Check. Move decimals three places to the right: $$\frac{27}{30}=\frac{9}{10}=0.9$$. And $$(0.9)^2=0.81$$. Perfect. 0.81 > 0.67

II. Multiply and estimate

A) $$(\frac{5}{7} *\frac{5}{7})=\frac{25}{49}$$ - about $$\frac{1}{2}$$. NO

B.$$(\frac{2}{3} *\frac{2}{3})=\frac{4}{9}$$. Less than half. NO

C. 0.7: $$(\frac{7}{10}*\frac{7}{10})=\frac{49}{100}$$. Less than half. NO

D. 0.8: $$(\frac{8}{10}*\frac{8}{10})=\frac{64}{100}$$
$$\frac{2}{3}\approx \frac{67}{100}$$
$$\frac{64}{100}<\frac{67}{100}$$ NO

By POE , the answer is E.

E. $$(\frac{0.027}{0.037}*\frac{1,000}{1,000})=\frac{27}{30} = \frac{9}{10}$$

$$(\frac{9}{10} * \frac{9}{10})=\frac{81}{100} > \frac{67}{100}$$. KEEP

Which of the following, when multiplied by itself, will yield a fracti &nbs [#permalink] 23 Jul 2018, 16:34
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