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Harold needs to buy a ticket to attend a conference for work

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mikemcgarry
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Harold needs to buy a ticket to attend a conference for work [#permalink] New post   07 Aug 2014, 14:54
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15% (low)

Question Stats:

83% (02:13) correct 17% (02:49) wrong based on 306 sessions
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Harold needs to buy a ticket to attend a conference for work. His own department contributes $4 less than half the price of the ticket. The HR department will contributes $1 more than a third of the price of the ticket. With these two contributions, Harold has to pay only $10 out of his own pocket to cover the cost of the ticket. What was the price of the ticket?
(A) $36
(B) $42
(C) $48
(D) $54
(E) $60

This is a problem that is screaming for a solution by backsolving. If this is a technique with which you are unfamiliar, or if you have trouble deciding when to use this strategy, see:
https://magoosh.com/gmat/2013/backsolving-on-gmat-math/
which also has the OE for this particular question.

Mike :-)
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B
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wunsun
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Re: Harold needs to buy a ticket to attend a conference for work [#permalink] New post   07 Aug 2014, 18:50
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To me, this problem is still easier to solve with algebra. Probably since I'm an engineer and going with equations is our go to nature; brain seems to be hardwired for it. Only used backsolving when I couldn't readily create any equation.

\((\frac{1}{2}x-4)+(\frac{1}{3}x+1)+10=x\)
\(3x-24+2x+6+60=6x\)
\(x=42\)

Equation was relatively easy to set up and to solve.

Answer is B
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Re: Harold needs to buy a ticket to attend a conference for work [#permalink] New post   08 Aug 2014, 00:27
Say price of ticket = x

Own department contribution \(= \frac{x}{2} - 4\)

HR contribution \(= \frac{x}{3} + 1\)

Self contribution = 10

Setting up the equation

\(x = \frac{x}{2} - 4 + \frac{x}{3} + 1+10\)

x=42

Answer = B
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Re: Harold needs to buy a ticket to attend a conference for work [#permalink] New post   02 Apr 2020, 11:03
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mikemcgarry wrote:
Harold needs to buy a ticket to attend a conference for work. His own department contributes $4 less than half the price of the ticket. The HR department will contributes $1 more than a third of the price of the ticket. With these two contributions, Harold has to pay only $10 out of his own pocket to cover the cost of the ticket. What was the price of the ticket?
(A) $36
(B) $42
(C) $48
(D) $54
(E) $60



We can let p = the price of the ticket and create the equation:

p/2 - 4 + p/3 + 1 + 10 = p

p/2 + p/3 + 7 = p

Multiplying the equation by 6, we have:

3p + 2p + 42 = 6p

42 = p

Answer: B
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Re: Harold needs to buy a ticket to attend a conference for work [#permalink]
02 Apr 2020, 11:03
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