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If during a one-day period the Q train arrives at the station 30% less

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Bunuel
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If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   05 Jun 2018, 03:34
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If during a one-day period the Q train arrives at the station 30% less frequently than the B train, and the B train arrives 10% less frequently than the F train, then the Q train’s frequency is what percent of the F train’s frequency?

A. 27
B. 40
C. 60
D. 63
E. 90
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D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   05 Jun 2018, 03:42
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Solution



Given:
    • Train Q arrives 30% less frequently than train B
    • Train B arrives 10% less frequently than train F

To find:
    • Train Q’s frequency is what percent of train F’s frequency

Approach and Working:
If we assume the frequency of train F as 100, then we can write
    • The frequency of train B = 100 * 0.9 = 90
    • The frequency of train Q = 90 * 0.7 = 63

Hence, train Q’s frequency as a percentage of train F’s frequency = \(\frac{63}{100} * 100\) = 63%

Hence, the correct answer is option D.

Answer: D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   05 Jun 2018, 10:28
Let us assume that the frequency of train F is x. Then the frequency of train B is 9x/10.
Therefore, frequency of train Q is 70% of 9x/10 which is 63x/100.
Hence, the frequency of Q train is 63% of the frequency of train F.

The answer is D.
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Re: If during a one-day period the Q train [#permalink] New post   07 Jun 2018, 15:15
Bunuel wrote:
If during a one-day period the Q train arrives at the station 30% less frequently than the B train, and the B train arrives 10% less frequently than the F train, then the Q train’s frequency is what percent of the F train’s frequency?

A. 27
B. 40
C. 60
D. 63
E. 90


\(Q=.7B\)
\(B=.9F\)
\(Q=.7(.9F)\)
\(Q=.63F\)

Ans = D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   07 Jun 2018, 17:32
q = 0.7b
b = 0.9f

% = [0.7b/(b/0.9)]*100 = 0.43*100 = 63

Ans D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   30 Oct 2018, 12:33
Frequency of Q in terms of F = 1*(1-0.3)*(1-0.1) = 1*0.7*0.9 = 0.63 or 63%

Option D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   31 Oct 2018, 00:42
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Bunuel wrote:
If during a one-day period the Q train arrives at the station 30% less frequently than the B train, and the B train arrives 10% less frequently than the F train, then the Q train`s frequency is what percent of the F train`s frequency?

A. 27
B. 40
C. 60
D. 63
E. 90


Let, Frequency of Q = Q
Let, Frequency of B = B
Let, Frequency of F = F

Q = 0.7 B

and

B = 0.9 F

i.e. Q = 0.7*0.9F = 0.63F

i.e. Frequency of Q is 63% of frequency of train F

Answer: Option D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   31 Oct 2018, 02:15
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Bunuel wrote:
If during a one-day period the Q train arrives at the station 30% less frequently than the B train, and the B train arrives 10% less frequently than the F train, then the Q train`s frequency is what percent of the F train`s frequency?

A. 27
B. 40
C. 60
D. 63
E. 90


This question just uses the concept of successive percentage changes.

F reduces by 10% and then further reduces by 30% to give Q.

F * (70/100)* (90/100) = Q

F * (63/100) = Q

So Q is 63% of F.

Answer (D)
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink] New post   31 Oct 2018, 18:25
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Bunuel wrote:
If during a one-day period the Q train arrives at the station 30% less frequently than the B train, and the B train arrives 10% less frequently than the F train, then the Q train`s frequency is what percent of the F train`s frequency?

A. 27
B. 40
C. 60
D. 63
E. 90


We can create the equations:

Q = 0.7B

And

B = 0.9F

Substitute the second equation into the first, we have:

Q = 0.7(0.9F)

Q = 0.63F

Thus, the Q train’s frequency is 63 percent of the F train’s frequency.

Alternate Solution:

Let’s assume that the F train has 100 arrivals daily. The B train would then have (100)(0.9) = 90 arrivals, and the Q train would have (90)(0.7) = 63 arrivals. Thus, the Q train would have 63/100, or 63%, of the number of arrivals of the F train.

Answer: D
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Re: If during a one-day period the Q train arrives at the station 30% less [#permalink]
31 Oct 2018, 18:25
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