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# ((-1.5)(1.2)-(4.5)(0.4))/30

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SOLUTION

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

(A) -1.2
(B) -0.12
(C) 0
(D) 0.12
(E) 1.2

$$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30}=\frac{-1.8-1.8}{30}=\frac{-3.6}{30}=-0.12$$.

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) -1.2
(B) -0.12
(C) 0
(D) 0.12
(E) 1.2

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.

Aside: Some students might look at the answer choices and conclude that they are NOT very spread apart. After all, 1.12 is only 1.08 greater than 0.12
Instead, we need to examine their relative values.
That is, 1.2 is TEN TIMES the value of 0.12
When we examine their relative values, we can conclude that they are very spread apart.

$$\frac{(-1.5)(1.2) - (4.5)(0.4)}{30} ≈\frac{ (-2)(1) - (4)(0.5)}{30}$$

$$≈ \frac{(-2) - 2}{30}$$

$$≈ \frac{-4}{30}$$

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Originally posted by BrentGMATPrepNow on 22 Jul 2016, 06:39.
Last edited by BrentGMATPrepNow on 08 Sep 2020, 09:35, edited 1 time in total.
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niks18 pushpitkc Abhishek009 pikolo2510 amanvermagmat

Can anyone explain below estimation step by GMATPrepNow :
Quote:
[(-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?
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niks18 pushpitkc Abhishek009 pikolo2510 amanvermagmat

Can anyone explain below estimation step by GMATPrepNow :
Quote:
[(-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?

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

Does that help?

Here's another question to practice with: https://gmatclub.com/forum/which-of-the ... 68916.html

Cheers,
Brent
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(A) -1.2
(B) -0.12
(C) 0
(D) 0.12
(E) 1.2

Simplifying we have:

(-1.8 - 1.8)/30 = -3.6/30 = -36/300 = -0.12

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GMATPrepNow ,

Could you elaborate on why these values are "very" spread apart? I can see from the equation the answer will be negative and with a little quick math you can see the number will be less than one, but my initial thought was not to estimate.

When you think about the "spread" of the answers are you thinking in just absolute magnitude or relative to each other. I.E. a question's "spread" with two answers: A:100 B=10 is equal to a questions with options A. .1 and B. .01?

Thanks
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5JUwiu4 wrote:
GMATPrepNow ,

Could you elaborate on why these values are "very" spread apart? I can see from the equation the answer will be negative and with a little quick math you can see the number will be less than one, but my initial thought was not to estimate.

When you think about the "spread" of the answers are you thinking in just absolute magnitude or relative to each other. I.E. a question's "spread" with two answers: A:100 B=10 is equal to a questions with options A. .1 and B. .01?

Thanks

For example, the answer choices 0.01, 0.02, 0.04, 0.08 and 0.16 have a big spread, since each answer choice is TWICE the value of the answer choice before it.
I consider this spread identical to the following answer choices: 3, 6, 12, 24 and 48

Cheers,
Brent
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