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A total of X bikes and cars were sold by a dealer. If the number of ca

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A total of X bikes and cars were sold by a dealer. If the number of ca  [#permalink]

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New post 25 Sep 2018, 05:12
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (02:29) correct 17% (02:12) wrong based on 48 sessions

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A total of X bikes and cars were sold by a dealer. If the number of ca  [#permalink]

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New post 25 Sep 2018, 18:58
Bunuel wrote:
A total of X bikes and cars were sold by a dealer. If the number of cars is (1/4)th the number of bikes, and 1/3 of the bikes are 200cc bikes, how many 200cc bikes, in terms of X, were sold by the dealer?


(A) 3X/20

(B) X/5

(C) 7X/11

(D) 8X/15

(E) 4X/15

In steps, algebraically, is probably easiest.
Find the # of ALL bikes sold in terms of X. \(\frac{1}{3}\) of that "general" number of bikes = the # of 200cc bikes sold in terms of X

\(B\) = # of bikes sold
\(C\) = # of cars sold
The number of cars is \(\frac{1}{4}\) the number of bikes:
\(C =\frac{1}{4}B\)

(1) B overall in terms of X
\((B + C)=X\)
\(B + \frac{1}{4}B=X\)
\(\frac{5}{4}B=X\)
\(B=\frac{4}{5}X\)

(2) 200cc bikes in terms of X?
200cc bikes = 1/3 of ALL bikes, so
200cc bikes = \(\frac{1}{3}B\)

Bikes generally in terms of \(X\):
\(B=\frac{4}{5}X\)

200cc bikes in terms of X:

\(\frac{1}{3}*B=(\frac{1}{3}*\frac{4}{5})*X\)

\(\frac{1}{3}B=\frac{4X}{15}\)

Answer E

*\(B=\frac{4}{5}X\)
is an equation. We need \(\frac{1}{3}\) of B on LHS. What we do to one side of the equation (multiply by \(\frac{1}{3}\)), we do to the other.

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Re: A total of X bikes and cars were sold by a dealer. If the number of ca  [#permalink]

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New post 20 Sep 2019, 02:36
let total cars+ bikes= 10
given
cars= 1/4 * bike
so 5bike= 40 ; bike = 8 and cars = 2
200 cc bikes ; 8/3
for given options put X=10
E ; 4X/15 ; 4*10/15 ; 8/3 sufficient


Bunuel wrote:
A total of X bikes and cars were sold by a dealer. If the number of cars is (1/4)th the number of bikes, and 1/3 of the bikes are 200cc bikes, how many 200cc bikes, in terms of X, were sold by the dealer?


(A) 3X/20

(B) X/5

(C) 7X/11

(D) 8X/15

(E) 4X/15

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Re: A total of X bikes and cars were sold by a dealer. If the number of ca   [#permalink] 20 Sep 2019, 02:36
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