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# M15-12

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Math Expert
Joined: 02 Sep 2009
Posts: 43896

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15 Sep 2014, 23:55
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Difficulty:

55% (hard)

Question Stats:

57% (01:08) correct 43% (00:50) wrong based on 87 sessions

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If 3 kilometers are equivalent to 1.8 miles, which of the following is closest to 4 miles?

A. $$5 \frac{8}{9} \text{ kilometers}$$
B. $$6 \frac{1}{3} \text{ kilometers}$$
C. $$6 \frac{3}{4} \text{ kilometers}$$
D. $$6 \frac{5}{6} \text{ kilometers}$$
E. $$7 \frac{2}{3} \text{ kilometers}$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:55
Expert's post
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Official Solution:

If 3 kilometers are equivalent to 1.8 miles, which of the following is closest to 4 miles?

A. $$5 \frac{8}{9} \text{ kilometers}$$
B. $$6 \frac{1}{3} \text{ kilometers}$$
C. $$6 \frac{3}{4} \text{ kilometers}$$
D. $$6 \frac{5}{6} \text{ kilometers}$$
E. $$7 \frac{2}{3} \text{ kilometers}$$

If 3 kilometers are equivalent to 1.8 miles then $$\frac{3}{1.8}$$ kilometers are equivalent to 1 mile. Therefore, the kilometer equivalent of 4 miles is $$\frac{3}{1.8}*4 = \frac{12}{1.8} = \frac{20}{3} = 6 \frac{2}{3}$$. This number is closer to $$6 \frac{3}{4}$$ than to $$6 \frac{1}{3}$$: $$\frac{3}{4} - \frac{2}{3} = \frac{1}{12}$$ which is smaller than $$\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$$.

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20 Dec 2015, 04:54
Bunuel wrote:
Official Solution:

If 3 kilometers are equivalent to 1.8 miles, which of the following is closest to 4 miles?

A. $$5 \frac{8}{9} \text{ kilometers}$$
B. $$6 \frac{1}{3} \text{ kilometers}$$
C. $$6 \frac{3}{4} \text{ kilometers}$$
D. $$6 \frac{5}{6} \text{ kilometers}$$
E. $$7 \frac{2}{3} \text{ kilometers}$$

If 3 kilometers are equivalent to 1.8 miles then $$\frac{3}{1.8}$$ kilometers are equivalent to 1 mile. Therefore, the kilometer equivalent of 4 miles is $$\frac{3}{1.8}*4 = \frac{12}{1.8} = \frac{20}{3} = 6 \frac{2}{3}$$. This number is closer to $$6 \frac{3}{4}$$ than to $$6 \frac{1}{3}$$: $$\frac{3}{4} - \frac{2}{3} = \frac{1}{12}$$ which is smaller than $$\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$$.

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10 Jan 2016, 16:21
I think this is a poor-quality question and I agree with explanation. Why is this problem listed as a 700 level question? It's closer to a 400 level.
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Joined: 14 Mar 2016
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17 Apr 2017, 22:35
Dear Bunuel

there is a mistake in calculation 3/ 1.8 is not equal to 1 but 1.6
Math Expert
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18 Apr 2017, 01:13
happyavi23 wrote:
Dear Bunuel

there is a mistake in calculation 3/ 1.8 is not equal to 1 but 1.6

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30 Sep 2017, 04:52
Dear Bunnel

Can you pls provide an alternate solution?
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30 Sep 2017, 05:13
yamini.mv wrote:
If 3 kilometers are equivalent to 1.8 miles, which of the following is closest to 4 miles?

Dear Bunnel

Can you pls provide an alternate solution?

1.8 miles = 9/5 miles.

Now, 4 miles is 4/(9/5) = 20/9 times as greater as 9/5 miles.

Since, 9/5 miles = 3 kilometers, then 4 miles is 3*20/9 = 20/3 kilometers = 6 2/3 kilometers.
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26 Oct 2017, 19:54
I think this is a poor-quality question and I agree with explanation.
Re M15-12   [#permalink] 26 Oct 2017, 19:54
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# M15-12

Moderators: chetan2u, Bunuel

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