M05-03

Question

What is the value of  \frac{0.2 * 14 - \frac{15}{3} + 15 * \frac{3}{90} }{8 * 0.0125} ?

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

Bunuel · Answer

Official Solution:

What is the value of  \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} , resulting in -1.7. The denominator is 0.1. Dividing the numerator by the denominator yields -17:
  
 \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

Answer: E

Alecita · Answer

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

AndrewN · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

kouassidrissa047 · Answer

I like the solution - it’s helpful.

M05-03

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