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Andra, Elif, and Grady each invested in a certain stock. Andra investe

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Andra, Elif, and Grady each invested in a certain stock. Andra investe  [#permalink]

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New post 08 Mar 2020, 08:34
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E

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Question Stats:

72% (02:52) correct 28% (03:10) wrong based on 99 sessions

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Andra, Elif, and Grady each invested in a certain stock. Andra invested \(q\) dollars, which was \(40\)% more than Elif invested. If Elif invested \(25\)% less than Grady invested, what was the total amount invested by all three, in terms of \(q\)?
(A) \(2q \)
(B) \(\frac{41q}{20}\)
(C) \(\frac{12q}{5}\)
(D) \(\frac{18q}{7}\)
(E) \(\frac{8q}{3}\)
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Re: Andra, Elif, and Grady each invested in a certain stock. Andra investe  [#permalink]

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New post 09 Mar 2020, 00:07
Asad wrote:
Andra, Elif, and Grady each invested in a certain stock. Andra invested \(q\) dollars, which was \(40\)% more than Elif invested. If Elif invested \(25\)% less than Grady invested, what was the total amount invested by all three, in terms of \(q\)?
(A) \(2q \)
(B) \(\frac{41q}{20}\)
(C) \(\frac{12q}{5}\)
(D) \(\frac{18q}{7}\)
(E) \(\frac{8q}{3}\)



A = \(\frac{21*x}{20}\) = q
E = \(\frac{3*x}{4}\)
G = x

total amount = \(\frac{21*x}{20}+\frac{3*x}{4}+ x\) = \(\frac{14*x}{5}\) = \(\frac{8*q}{3}\)
Ans: E
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Re: Andra, Elif, and Grady each invested in a certain stock. Andra investe  [#permalink]

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New post 15 Mar 2020, 06:12
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I didnt understand the answer explanation
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Re: Andra, Elif, and Grady each invested in a certain stock. Andra investe  [#permalink]

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New post 17 Apr 2020, 08:57
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1
You should pick smart numbers.


Suppose:
Grady = 100
Elif = 75% of 100 = 75
Andra = Elif + 40 % = 75+30 = 105 (Q)

Total = 280

Plug in Q = 105 in the answer choices.
The objective is to find 280


(A) 2q=2(105) = 210 NO
(B) 41/20(105) = not an integer.
(C) 12/5(105) = 12(21) = 252 too little
(D) 18/7(105) = (18)(15)=270 too little
(E) 8/3(105) = (8)(35) = 280 CORRECT.

ANSWER E

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Re: Andra, Elif, and Grady each invested in a certain stock. Andra investe  [#permalink]

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New post 19 Apr 2020, 04:01
Asad wrote:
Andra, Elif, and Grady each invested in a certain stock. Andra invested \(q\) dollars, which was \(40\)% more than Elif invested. If Elif invested \(25\)% less than Grady invested, what was the total amount invested by all three, in terms of \(q\)?
(A) \(2q \)
(B) \(\frac{41q}{20}\)
(C) \(\frac{12q}{5}\)
(D) \(\frac{18q}{7}\)
(E) \(\frac{8q}{3}\)


We can let E = the amount Elif invested and G = the amount Grady invested. We can create the equations:

q = 1.4E

q/1.4 = E

10q/14 = E

5q/7 = E

and

5q/7 = 0.75G

5q/7 = 3G/4

20q/7 = 3G

20q/21 = G

So, the total invested is:

q + 5q/7 + 20q/21


21q/21 + 15q/21 + 20q/21 = 56q/21 = 8q/3

Answer: E


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Re: Andra, Elif, and Grady each invested in a certain stock. Andra investe   [#permalink] 19 Apr 2020, 04:01

Andra, Elif, and Grady each invested in a certain stock. Andra investe

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