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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Harold needs to buy a ticket to attend a conference for work  [#permalink]

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07 Aug 2014, 13:54
00:00

Difficulty:

15% (low)

Question Stats:

82% (02:14) correct 18% (02:47) wrong based on 250 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:
http://magoosh.com/gmat/2013/backsolving-on-gmat-math/
which also has the OE for this particular question.

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Joined: 14 May 2014
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Concentration: General Management, Operations
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Re: Harold needs to buy a ticket to attend a conference for work  [#permalink]

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07 Aug 2014, 17:50
1
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.

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Re: Harold needs to buy a ticket to attend a conference for work  [#permalink]

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07 Aug 2014, 23:27
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

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Re: Harold needs to buy a ticket to attend a conference for work  [#permalink]

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02 Apr 2020, 10:03
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

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Re: Harold needs to buy a ticket to attend a conference for work   [#permalink] 02 Apr 2020, 10:03