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# If (3 + a)(a/10 - 0.4) = -1, then a could be

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Math Expert
Joined: 02 Sep 2009
Posts: 47101
If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 06:14
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35% (medium)

Question Stats:

78% (01:15) correct 22% (01:35) wrong based on 155 sessions

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If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

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Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 06:26
given (3+a)(a/10−0.4)=−1

=>(3+a)(a−4)=−10 = (-10*1)=(-2*5)

if we try to get (-10*1) => a=7 => 10* 3 ... a=5 => 8*1

try to get (-2*5) => a=2 =>(5)*(-2) answer

Answer: D
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 07:54
Top Contributor
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Another approach is to eliminate the fractions/decimals first.

Given: (3 + a)(a/10 - 0.4) = -1
Multiply both sides by 10 to get: (3 + a)(a/10 - 0.4)(10) = (-1)(10)
Simplify: (3 + a)(a - 4) = -10
Expand and simplify: a² - a - 12 = -10
Add 10 to both sides: a² - a - 2 = 0
Factor: (a + 1)(a - 2) = 0

So, EITHER a = -1 OR a = 2

Answer:

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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 07:57
Top Contributor
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Alternatively, once you get to the point where you have the equation (3 + a)(a - 4) = -10 [see my post above for how I got there], you could easily plug in the answer choices until you found the one that satisfies the equation (3 + a)(a - 4) = -10

Cheers,
Brent
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 08:02
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

$$(3 + a)(\frac{a}{10} - 0.4) = -1$$

$$(3 + a)(\frac{a- 4}{10}) = -1$$

$$(3 + a)(a- 4) = -10$$

$$3a -12 + a^2 - 4a = -10$$

$$a^2 - 4a + 3a -12 +10 = 0$$

$$a^2 - a -2 = 0$$

$$(a -2)(a+1) = 0$$

$$a = 2$$ or $$-1$$

Therefore "$$a$$" could be $$2$$

Answer (D)...
Math Expert
Joined: 02 Aug 2009
Posts: 6243
Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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01 Oct 2017, 10:45
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Hi...

if I want to do it fast and use logic..
$$\frac{a}{10}-0.4=\frac{a-4}{10}$$
so looking at the choices, 3+a should be a factor of 10...
A) so a could be -4 as $$3-4=-1$$ but then the RHS will become positive so discard
B) a as -2 would make 3+a as 1 but $$\frac{a-4}{10}$$ can never be -1
C) a as 1 gives 3+a as $$3+1=4$$.. not a factor of 10.. Discard
D) a as 2 gives 3+a as $$3+2 = 5$$, a factor of 10.. try substituting .. FITs in
E) a as 4 gives $$3+4=7$$... Discard

substitution this way would be way faster than finding solution of a
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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02 Oct 2017, 12:56
Simplifying the equation we get:
(3+a)(a/10-0.4)=-1
(3+a)(a-4)(1/10)=-1
(3+a)(a-4)=-10

Replacing a accoding to the choices:
A. -4 => (3-4)(-4-4) = -1*-8 =8 (Discard)
(...)
D. 2 => (3+2)(2-4) = 5*-2 = -10 (correct)
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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04 Oct 2017, 16:46
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

We can simplify the given equation:

(3 + a)(a/10 - 4/10) = -1

(3 + a)[(a-4)/10] = -1

(3 + a)(a - 4) = -10

a^2 - a - 12 = -10

a^2 - a - 2 = 0

(a - 2)(a + 1) = 0

a = 2 or a = -1

Answer: D
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be   [#permalink] 04 Oct 2017, 16:46
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