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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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This could be done by changing the decimals into fractions (-15/10)(12/10)=-18/10 (45/10)(4/10)=18/10 (-18/10)-(18/10)=-36/10 (-36/10)/30= -0.12 hence B

As always, scan the answers BEFORE solving the question. Here, the answer choices are VERY SPREAD APART, so we can be very aggressive with our estimation. [(-1.5)(1.2) - (4.5)(0.4)]/30 ≈ [(-2)(1) - (4)(0.5)]/30 ≈ [-2 - 2]/30 ≈ [-4]/30

The key to this problem is remembering Principles of Arithmetic and order of operations. Parenthesis are first. Resolve everything in the numerator before dividing by the denominator. Also, remember that subtracting a positive from a negative number is the same as subtracting in that (-) - (+) = (-) or moving left on the number line.

Answer is (B) -0.12

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Here is how I proceeded: I knew 15*12 = 180 and hence shifted decimals though this is prone to error, finally -1.8 approximated to -2 For 4.5* 0.4 I converted it in to fractions: (45/10) * (4/10) ie 18/10 finally 1.8 approximated to 2.0

Did Brent in highlighted text approximated 0.4 to 0.5 since 0.5 ie 1/2 is easier to multiply with fractions? But then can we simply deduct 0.1 from 4.5 ?? He deducted 0.1 from 4.5 and added 0.1 to 0.5, I suppose but is this a valid mathematical step?
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It's the journey that brings us happiness not the destination.

Here is how I proceeded: I knew 15*12 = 180 and hence shifted decimals though this is prone to error, finally -1.8 approximated to -2 For 4.5* 0.4 I converted it in to fractions: (45/10) * (4/10) ie 18/10 finally 1.8 approximated to 2.0

Did Brent in highlighted text approximated 0.4 to 0.5 since 0.5 ie 1/2 is easier to multiply with fractions? But then can we simply deduct 0.1 from 4.5 ?? He deducted 0.1 from 4.5 and added 0.1 to 0.5, I suppose but is this a valid mathematical step?

The key here is that the answer choices are quite spread apart, which means we can replace values with other values that are reasonably close. So, for example, we can replace -1.5 with -2 (close enough!) We can replace 1.2 with 1 We can replace 4.5 with 4 And we can replace 0.4 with 0.5

So, [(-1.5)(1.2) - (4.5)(0.4)]/30 ≈ [(-2)(1) - (4)(0.5)]30

Here is how I proceeded: I knew 15*12 = 180 and hence shifted decimals though this is prone to error, finally -1.8 approximated to -2 For 4.5* 0.4 I converted it in to fractions: (45/10) * (4/10) ie 18/10 finally 1.8 approximated to 2.0

Did Brent in highlighted text approximated 0.4 to 0.5 since 0.5 ie 1/2 is easier to multiply with fractions? But then can we simply deduct 0.1 from 4.5 ?? He deducted 0.1 from 4.5 and added 0.1 to 0.5, I suppose but is this a valid mathematical step?

Lets try again -

Bunuel wrote:

\(\frac{(-1.5)(1.2)-(4.5)(0.4)}{30}\)

\(\frac{-1.8-1.8}{30}\)

= \(\frac{-3.6}{30}\)

= \(−0.12\), Answer must be (B) _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

The key here is that the answer choices are quite spread apart, which means we can replace values with other values that are reasonably close. So, for example, we can replace -1.5 with -2 (close enough!) We can replace 1.2 with 1 We can replace 4.5 with 4 And we can replace 0.4 with 0.5

Is this different from rounding decimals in a whole number? See this post. If so 4.5 shall be approximated to 5.0 and only top two are correct since tenth place after decimal is less than 4. Let me know I understood your approach correctly.
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It's the journey that brings us happiness not the destination.