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# M05-03

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Math Expert
Joined: 02 Sep 2009
Posts: 64102

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15 Sep 2014, 23:24
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Difficulty:

15% (low)

Question Stats:

80% (02:00) correct 20% (02:30) wrong based on 367 sessions

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$$\frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90}}{8 * 0.0125} = ?$$

A. 2
B. 1
C. 0
D. -1
E. -17

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Math Expert
Joined: 02 Sep 2009
Posts: 64102

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15 Sep 2014, 23:24
Official Solution:

$$\frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90}}{8 * 0.0125} = ?$$

A. 2
B. 1
C. 0
D. -1
E. -17

The numerator simplifies to $$2.8 - 5 + \frac{1}{2}$$, which equals -1.7. The denominator equals 0.1. Dividing the numerator by the denominator gives us -17.

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Intern
Joined: 02 Jun 2015
Posts: 19
Location: United States

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02 Apr 2018, 14:03
1
To make the calculation easier, I broke down the denominator into pieces ... 8 * 1/8 * 1/10 = 1 * 1/10 = 0.1

2.8 - 5 + 0.5 / 8 * 0.0125 = - 1.7 / 0.1 = - 17

Thanks! Ale
Intern
Joined: 09 Aug 2019
Posts: 1

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11 Aug 2019, 09:33
Is that wrong question because I see 15 divided by 3
Intern
Joined: 20 Aug 2019
Posts: 1

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20 Aug 2019, 07:03
Any suggestions on where to find more problems like this one?
Tutor
Joined: 16 May 2019
Posts: 709

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20 Aug 2019, 07:11
Bunuel wrote:
Official Solution:

$$\frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90}}{8 * 0.0125} = ?$$

A. 2
B. 1
C. 0
D. -1
E. -17

The numerator simplifies to $$2.8 - 5 + \frac{1}{2}$$, which equals -1.7. The denominator equals 0.1. Dividing the numerator by the denominator gives us -17.

An alternative approach - I will admit to solving this one the standard way, the same as Bunuel posted above. It took me about 1 1/2 minutes. However, I got to thinking about using the answers instead, since there are a few interesting splits that are easy enough to explore:

1) There are two positive answers, and 1 is about the easiest solution for a fraction. That is, do the top and bottom of the fraction match without being 0? This brings me to the second point.

2) 0 is an answer choice. For this to be true, the numerator would have to equal 0, and whatever is going on in the denominator is irrelevant (since "no solution" is not an option).

3) There are two negative answers. Also, one of those negative answers is -1, which, like its positive counterpart, is easy enough to test.

So, will the numerator be positive, negative, or 0? In any case, we will either get the answer directly (if it turns out to be (C)), or we will encounter a 50/50 split between the remaining two logical answer choices. With a single negative sign in the numerator, attached as it is to $$\frac{15}{3}$$, or 5, we can work out readily enough that (.2 * 14) - 5 will be negative. To be specific, we get 2.8 - 5 = -2.2. The second cluster in the numerator can be worked out either by reducing the 15 and 90 before multiplying or by reducing the fraction $$\frac{45}{90}$$ after multiplying. It makes no difference, as the answer will be positive 0.5 either way. Now we can see that the numerator is equivalent to -2.2 + 0.5, or -1.7. In one fell swoop, we can eliminate (A), (B), and (C), and unless the denominator works out to 1.7 exactly, it cannot be true that -1 will be the answer.

Here, you could work out the value of 8 * 0.0125, but you could just as easily reason that 0.0125 itself is slightly more than $$\frac{1}{100}$$, and multiplying it by 8 will not get the product anywhere near 1.7. Thus, we can rule out (D), and (E) must be the answer.
Senior Manager
Joined: 12 Dec 2015
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11 May 2020, 06:38
$$\frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90}}{8 * 0.0125} = ?$$

A. 2
B. 1
C. 0
D. -1
E. -17 --> correct: $$\frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90}}{8 * 0.0125} = \frac{2.8 - 5 + 0.5}{0.1} = \frac{-1.7}{0.1}$$ = -17
Re: M05-03   [#permalink] 11 May 2020, 06:38

# M05-03

Moderators: chetan2u, Bunuel