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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 66% (01:33) correct 34% (01:23) wrong based on 1077 sessions

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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

Problem Solving
Question: 93
Category: Arithmetic Operations on rational numbers
Page: 73
Difficulty: 550

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7
15*12 = 180 Shift two decimal left
45*4 = 180 Shift two decimal left
(- 1.8 - 1.8)/30 = -3.6/30 = -1.2/10 = -0.12

You only need to know that answer will be negative and eliminate C,D,E
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Math Expert V
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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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(-1,5*(1,2+3*0,4))/30 = (-1,5*(1,2+1,2))/30 = (-1,5*2*1,2)/30 = (-3/30)*1,2 = -1/10*1,2 = -0,12. Answer - B
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2
$$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30}$$

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

$$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30} =\frac{3((-0.5)(1.2)-(1.5)(0.4))}{30} =\frac{(-6-6)}{10} =\frac{-12}{10} =-0.12$$

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

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

$$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30} =\frac{3((-0.5)(1.2)-(1.5)(0.4))}{30} =\frac{(-6-6)}{10} =\frac{-12}{10} =-0.12$$[/b][/color]

= $$\frac{(-0.6-0.6)}{10}$$

= $$\frac{-1.2}{10}$$

= -0.12

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to speed up we can also convert decimals to fractions. my answer is B
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Re: 5)(1.2)-(4.5)(0.4) 30 equals? a)  [#permalink]

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Its an easy one ..

[(-1.5)(1.2)-(4.5)(0.4)]/30

= [-1.8-1.8]/30

= -3.6/30

=-0.12

Hence B
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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
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-1.8 - 1.8 /30 = -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.
[(-1.5)(1.2) - (4.5)(0.4)]/30 ≈ [(-2)(1) - (4)(0.5)]/30
≈ [-2 - 2]/30
≈ [-4]/30

The closest answer is

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[(-9/5)-(9/5)]/30 = -3/25 ~ -0.12
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My strategy is to convert fractions in decimal (1,5 =3/2; 1,2=6/5; 4,5=9/2; 0,4=2/5) thus:
[(-3/2 * 6/5) - (9/2 * 2/5)] /30
(-9/5 - 9/5) /30
(-18/5)/30
-6/50 =-0,12
hence B
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Looked Damn simple but had to do some work to get to the right answer! A lesson on not being overconfident Given = $$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30}$$

= $$\frac{-1.5*0.4*(3+3)}{30}$$ <----- Taking the common factors

= $$\frac{-1.5 * 0.4 * 6}{30}$$

= $$\frac{-1.5 * 0.4}{5}$$

= $$-3 * 0.4$$

= $$-0.12$$

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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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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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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?

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)
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GMATPrepNow

Thank you Brent for our prompt reply.
Quote:
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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Bunuel wrote:

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

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

Another way if you are familiar with fractions. It will take less time.

-1.5 = $$\frac{-3}{2}$$

1.2 = $$\frac{6}{5}$$

4.5 = $$\frac{9}{2}$$

0.4 = $$\frac{2}{5}$$

Nominator = $$\frac{-3}{2}$$ * $$\frac{6}{5}$$ - $$\frac{9}{2}$$ $$\frac{2}{5}$$ = $$\frac{-9}{5} - \frac{9}{5}$$ = $$\frac{-18}{5}$$

$$\frac{(-1.5)(1.2)-(4.5)(0.4)}{30}$$ = $$\frac{-18}{5}$$ * $$\frac{1}{30}$$ = $$\frac{-3}{25}$$... There are different way to deal with it.

$$\frac{-3}{25}$$...multiple by 4/4 ....$$\frac{-3}{25}$$ = $$\frac{-12}{100}$$ = -0.12

or

$$\frac{-3}{25}$$ = $$\frac{-3}{5}$$ * $$\frac{1}{5}$$ = -0.6 * 0.2 = -0.12 ((-1.5)(1.2)-(4.5)(0.4))/30   [#permalink] 06 Jul 2018, 08:46

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